tse_notes

Transportation Systems Engineering 1. Fundamental Parameters of Traffic Flow

Chapter 1

Fundamental Parameters of Traffic

Flow

1.1 Overview

Traffic engineering pertains to the analysis of the behavior of traffic and to design the facilities

for a smooth, safe and economical operation of traffic. Traffic flow, like the flow of water,

has several parameters associated with it. The traffic stream parameters provide information

regarding the nature of traffic flow, which helps the analyst in detecting any variation in flow

characteristics. Understanding traffic behavior requires a thorough knowledge of traffic stream

parameters and their mutual relationships. In this chapter the basic concepts of traffic flow is

presented.

1.2 Traffic stream parameters

The traffic stream includes a combination of driver and vehicle behavior. The driver or human

behavior being non-uniform, traffic stream is also non-uniform in nature. It is influenced not

only by the individual characteristics of both vehicle and human but also by the way a group

of such units interacts with each other. Thus a flow of traffic through a street of defined

characteristics will vary both by location and time corresponding to the changes in the human

behavior.

The traffic engineer, but for the purpose of planning and design, assumes that these changes

are within certain ranges which can be predicted. For example, if the maximum permissible

speed of a highway is 60 kmph, the whole traffic stream can be assumed to move on an average

speed of 40 kmph rather than 100 or 20 kmph.

Thus the traffic stream itself is having some parameters on which the characteristics can

be predicted. The parameters can be mainly classified as : measurements of quantity, which

Dr. Tom V. Mathew, IIT Bombay 1.1 January 31, 2014


includes density and flow of traffic and measurements of quality which includes speed. The

traffic stream parameters can be macroscopic which characterizes the traffic as a whole or

microscopic which studies the behavior of individual vehicle in the stream with respect to each

other.

As far as the macroscopic characteristics are concerned, they can be grouped as measurement

of quantity or quality as described above, i.e. flow, density, and speed. While the microscopic

characteristics include the measures of separation, i.e. the headway or separation between

vehicles which can be either time or space headway. The fundamental stream characteristics

are speed, flow, and density and are discussed below.

1.3 Speed

Speed is considered as a quality measurement of travel as the drivers and passengers will be

concerned more about the speed of the journey than the design aspects of the traffic. It is

defined as the rate of motion in distance per unit of time. Mathematically speed or velocity v

is given by,

v =d

t(1.1)

where, v is the speed of the vehicle in m/s, d is distance traveled in m in time t seconds. Speed

of different vehicles will vary with respect to time and space. To represent these variation,

several types of speed can be defined. Important among them are spot speed, running speed,

journey speed, time mean speed and space mean speed. These are discussed below.

1.3.1 Spot Speed

Spot speed is the instantaneous speed of a vehicle at a specified location. Spot speed can be

used to design the geometry of road like horizontal and vertical curves, super elevation etc.

Location and size of signs, design of signals, safe speed, and speed zone determination, require

the spot speed data. Accident analysis, road maintenance, and congestion are the modern fields

of traffic engineer, which uses spot speed data as the basic input. Spot speed can be measured

using an enoscope, pressure contact tubes or direct timing procedure or radar speedometer or

by time-lapse photographic methods. It can be determined by speeds extracted from video

images by recording the distance travelling by all vehicles between a particular pair of frames.



1.3.2 Running speed

Running speed is the average speed maintained over a particular course while the vehicle is

moving and is found by dividing the length of the course by the time duration the vehicle was

in motion. i.e. this speed doesn’t consider the time during which the vehicle is brought to a

stop, or has to wait till it has a clear road ahead. The running speed will always be more than

or equal to the journey speed, as delays are not considered in calculating the running speed

1.3.3 Journey speed

Journey speed is the effective speed of the vehicle on a journey between two points and is the

distance between the two points divided by the total time taken for the vehicle to complete the

journey including any stopped time. If the journey speed is less than running speed, it indicates

that the journey follows a stop-go condition with enforced acceleration and deceleration. The

spot speed here may vary from zero to some maximum in excess of the running speed. A

uniformity between journey and running speeds denotes comfortable travel conditions.

1.3.4 Time mean speed and space mean speed

Time mean speed is defined as the average speed of all the vehicles passing a point on a highway

over some specified time period. Space mean speed is defined as the average speed of all the

vehicles occupying a given section of a highway over some specified time period. Both mean

speeds will always be different from each other except in the unlikely event that all vehicles

are traveling at the same speed. Time mean speed is a point measurement while space mean

speed is a measure relating to length of highway or lane, i.e. the mean speed of vehicles over

a period of time at a point in space is time mean speed and the mean speed over a space at a

given instant is the space mean speed.

1.4 Flow

There are practically two ways of counting the number of vehicles on a road. One is flow or

volume, which is defined as the number of vehicles that pass a point on a highway or a given

lane or direction of a highway during a specific time interval. The measurement is carried out

by counting the number of vehicles, nt, passing a particular point in one lane in a defined period

t. Then the flow q expressed in vehicles/hour is given by

q =nt

t(1.2)



Flow is expressed in planning and design field taking a day as the measurement of time.

1.4.1 Variations of Volume

The variation of volume with time, i.e. month to month, day to day, hour to hour and within a

hour is also as important as volume calculation. Volume variations can also be observed from

season to season. Volume will be above average in a pleasant motoring month of summer, but

will be more pronounced in rural than in urban area. But this is the most consistent of all the

variations and affects the traffic stream characteristics the least.

Weekdays, Saturdays and Sundays will also face difference in pattern. But comparing day

with day, patterns for routes of a similar nature often show a marked similarity, which is useful

in enabling predictions to be made.

The most significant variation is from hour to hour. The peak hour observed during morn-

ings and evenings of weekdays, which is usually 8 to 10 per cent of total daily flow or 2 to 3

times the average hourly volume. These trips are mainly the work trips, which are relatively

stable with time and more or less constant from day to day.

1.4.2 Types of volume measurements

Since there is considerable variation in the volume of traffic, several types of measurements of

volume are commonly adopted which will average these variations into a single volume count

to be used in many design purposes.

1. Average Annual Daily Traffic(AADT) : The average 24-hour traffic volume at a

given location over a full 365-day year, i.e. the total number of vehicles passing the site

in a year divided by 365.

2. Average Annual Weekday Traffic(AAWT) : The average 24-hour traffic volume

occurring on weekdays over a full year. It is computed by dividing the total weekday

traffic volume for the year by 260.

3. Average Daily Traffic(ADT) : An average 24-hour traffic volume at a given location

for some period of time less than a year. It may be measured for six months, a season, a

month, a week, or as little as two days. An ADT is a valid number only for the period

over which it was measured.

4. Average Weekday Traffic(AWT) : An average 24-hour traffic volume occurring on

weekdays for some period of time less than one year, such as for a month or a season.



B A

Figure 1:1: Illustration of density

The relationship between AAWT and AWT is analogous to that between AADT and ADT.

Volume in general is measured using different ways like manual counting, detector/sensor count-

ing, moving-car observer method, etc. Mainly the volume study establishes the importance of

a particular route with respect to the other routes, the distribution of traffic on road, and the

fluctuations in flow. All which eventually determines the design of a highway and the related

facilities. Thus, volume is treated as the most important of all the parameters of traffic stream.

1.5 Density

Density is defined as the number of vehicles occupying a given length of highway or lane and

is generally expressed as vehicles per km. One can photograph a length of road x, count the

number of vehicles, nx, in one lane of the road at that point of time and derive the density k

as,

k =nx

x(1.3)

This is illustrated in figure 1:1. From the figure, the density is the number of vehicles between

the point A and B divided by the distance between A and B. Density is also equally important

as flow but from a different angle as it is the measure most directly related to traffic demand.

Again it measures the proximity of vehicles in the stream which in turn affects the freedom to

maneuver and comfortable driving.

1.6 Derived characteristics

From the fundamental traffic flow characteristics like flow, density, and speed, a few other

parameters of traffic flow can be derived. Significant among them are the time headway,



distance headway and travel time. They are discussed one by one below.

1.6.1 Time headway

The microscopic character related to volume is the time headway or simply headway. Time

headway is defined as the time difference between any two successive vehicles when they cross

a given point. Practically, it involves the measurement of time between the passage of one rear

bumper and the next past a given point. If all headways h in time period, t, over which flow

has been measured are added then,nt∑

1

hi = t (1.4)

But the flow is defined as the number of vehicles nt measured in time interval t, that is,

q =nt

t=

nt∑nt

1hi

=1

hav

(1.5)

where, hav is the average headway. Thus average headway is the inverse of flow. Time headway

is often referred to as simply the headway.

1.6.2 Distance headway

Another related parameter is the distance headway. It is defined as the distance between

corresponding points of two successive vehicles at any given time. It involves the measurement

from a photograph, the distance from rear bumper of lead vehicle to rear bumper of following

vehicle at a point of time. If all the space headways in distance x over which the density has

been measured are added,nx∑

1

si = x (1.6)

But the density (k) is the number of vehicles nx at a distance of x, that is

k =nx

x=

nx∑nx

1si

=1

sav

(1.7)

Where, sav is average distance headway. The average distance headway is the inverse of density

and is sometimes called as spacing.

1.6.3 Travel time

Travel time is defined as the time taken to complete a journey. As the speed increases, travel

time required to reach the destination also decreases and vice-versa. Thus travel time is inversely



(a) (b)

(c)

time

dis

tan

ce

dis

tan

ce

time

dis

tan

ce

time

Figure 1:2: Time space diagram for a single vehicle

proportional to the speed. However, in practice, the speed of a vehicle fluctuates over time and

the travel time represents an average measure.

1.7 Time-space diagram

Time space diagram is a convenient tool in understanding the movement of vehicles. It shows

the trajectory of vehicles in the form of a two dimensional plot. Time space diagram can be

plotted for a single vehicle as well as multiple vehicles. They are discussed below.

1.7.1 Single vehicle

Taking one vehicle at a time, analysis can be carried out on the position of the vehicle with

respect to time. This analysis will generate a graph which gives the relation of its position on

a road stretch relative to time. This plot thus will be between distance x and time t and x

will be a functions the position of the vehicle for every t along the road stretch. This graphical

representation of x(t) in a (t, x) plane is a curve which is called as a trajectory. The trajectory

provide an intuitive, clear, and complete summary of vehicular motion in one dimension.

In figure 1:2(a), the the distance x goes on increasing with respect to the origin as time

progresses. The vehicle is moving at a smooth condition along the road way. In figure 1:2(b),

the vehicle at first moves with a smooth pace after reaching a position reverses its direction of

movement. In figure 1:2(c), the vehicle in between becomes stationary and maintains the same

position.



From the figure, steeply increasing section of x(t) denote a rapidly advancing vehicle and

horizontal portions of x(t) denote a stopped vehicle while shallow sections show a slow-moving

vehicle. A straight line denotes constant speed motion and curving sections denote accelerated

motion; and if the curve is concave downwards it denotes acceleration. But a curve which is

convex upwards denotes deceleration.

1.7.2 Multiple Vehicles

Time-space diagram can also be used to determine the fundamental parameters of traffic flow

like speed, density and volume. It can also be used to find the derived characteristics like space

headway and time headway. Figure 1:3 shows the time-space diagram for a set of vehicles

traveling at constant speed. Density, by definition is the number of vehicles per unit length.

From the figure, an observer looking into the stream can count 4 vehicles passing the stretch

of road between x1 and x2 at time t. Hence, the density is given as

k =4 vehicles

x2 − x1

(1.8)

We can also find volume from this time-space diagram. As per the definition, volume is the

number of vehicles counted for a particular interval of time. From the figure 1:3 we can see

that 6 vehicles are present between the time t1 and t2. Therefore, the volume q is given as

q =3 vehicles

t2 − t1(1.9)

Again the averages taken at a specific location (i.e., time ranging over an interval) are called

time means and those taken at an instant over a space interval are termed as space means.

Another related definition which can be given based on the time-space diagram is the head-

way. Space headway is defined as the distance between corresponding points of two successive

vehicles at any given time. Thus, the vertical gap between any two consecutive lines represents

space headway. The reciprocal of density otherwise gives the space headway between vehicles

at that time.

Similarly, time headway is defined as the time difference between any two successive vehicles

when they cross a given point. Thus, the horizontal gap between the vehicles represented by the

lines gives the time headway. The reciprocal of flow gives the average time headway between

vehicles at that point.



tTime

(h)headway

dis

tan

ce

(s)spacing

x2

x1

t1 t2

Figure 1:3: Time space diagram for many vehicles

1.8 Summary

Speed, flow and density are the basic parameters of traffic flow. Different measures of speed

are used in traffic flow analysis like spot speed, time mean speed, space mean speed etc. Time-

space diagram also can be used for determining these parameters. Speed and flow of the traffic

stream can be computed using moving observer method.

1.9 References

1. Highway Capacity Manual. Transportation Research Board. National Research Council,

Washington, D.C., 2000.

2. L. R Kadiyali. Traffic Engineering and Transportation Planning. Khanna Publishers,

New Delhi, 1987.

3. Adolf D. May. Fundamentals of Traffic Flow. Prentice - Hall, Inc. Englewood Cliff New

Jersey 07632, second edition, 1990.

4. William R McShane, Roger P Roesss, and Elena S Prassas. Traffic Engineering. Prentice-

Hall, Inc, Upper Saddle River, New Jesery, 1998.

5. C. S Papacostas. Fundamentals of Transportation Engineering. Prentice-Hall, New

Delhi, 1987.


Transportation Systems Engineering 2. Fundamental Relations of Traffic Flow

Chapter 2

Fundamental Relations of Traffic Flow

2.1 Overview

Speed is one of the basic parameters of traffic flow and time mean speed and space mean

speed are the two representations of speed. Time mean speed and space mean speed and the

relationship between them will be discussed in detail in this chapter. The relationship between

the fundamental parameters of traffic flow will also be derived. In addition, this relationship

can be represented in graphical form resulting in the fundamental diagrams of traffic flow.

2.2 Time mean speed (vt)

As noted earlier, time mean speed is the average of all vehicles passing a point over a duration

of time. It is the simple average of spot speed. Time mean speed vt is given by,

vt =1

n

n∑

i=1

vi, (2.1)

where vi is the spot speed of ith vehicle, and n is the number of observations. In many speed

studies, speeds are represented in the form of frequency table. Then the time mean speed is

given by,

vt =

∑n

i=1qivi∑n

i=1qi

, (2.2)

where qi is the number of vehicles having speed vi, and n is the number of such speed categories.

2.3 Space mean speed (vs)

The space mean speed also averages the spot speed, but spatial weightage is given instead of

temporal. This is derived as below. Consider unit length of a road, and let vi is the spot speed



of ith vehicle. Let ti is the time the vehicle takes to complete unit distance and is given by 1

vi.

If there are n such vehicles, then the average travel time ts is given by,

ts =Σtin

=1

nΣ

1

vi

. (2.3)

If tav is the average travel time, then average speed vs = 1

ts. Therefore, from the above equation,

vs =n∑n

i=1

1

vi

. (2.4)

This is simply the harmonic mean of the spot speed. If the spot speeds are expressed as a

frequency table, then,

vs =

∑n

i=1qi∑n

i=1

qi

vi

(2.5)

where qi vehicle will have vi speed and ni is the number of such observations.

Numerical Example

If the spot speeds are 50, 40, 60, 54 and 45, then find the time mean speed and space mean

speed.

Solution Time mean speed vt is the average of spot speed. Therefore, vt = Σvi

n= 50+40+60+54+45

5=

249

5= 49.8. Space mean speed is the harmonic mean of spot speed. Therefore, vs = n

Σ1

vi

=

51

50+

1

40+

1

60+

1

54+

1

45

= 5

0.12= 48.82.

Numerical Example

The results of a speed study is given in the form of a frequency distribution table. Find the

time mean speed and space mean speed.

speed range frequency

2-5 1

6-9 4

10-13 0

14-17 7

Solution The time mean speed and space mean speed can be found out from the frequency

table given below. First, the average speed is computed, which is the mean of the speed range.

For example, for the first speed range, average speed, vi = 2+5

2= 3.5 seconds. The volume of

flow qi for that speed range is same as the frequency. The terms vi.qi and qi

viare also tabulated,



No. speed range average speed (vi) volume of flow (qi) viqiqi

vi

1 2-5 3.5 1 3.5 2.29

2 6-9 7.5 4 30.0 0.54

3 10-13 11.5 0 0 0

4 14-17 15.5 7 108.5 0.45

total 12 142 3.28

10 m/s 10 m/s 10 m/s 10 m/s

20 m/s20 m/s20 m/s

100 100

5050 5050

10 m/s

ks = 1000/50 = 20

hf = 100/20 = 5sec nf = 60/5 = 12 kf = 1000/100 = 10

hs = 50/20 = 5sec ns = 60/5 = 12

Figure 2:1: Illustration of relation between time mean speed and space mean speed

and their summations given in the last row. Time mean speed can be computed as, vt = Σqivi

Σqi=

142

12= 11.83. Similarly, space mean speed can be computed as, vs = Σqi

Σqivi

= 12

3.28= 3.65.

2.4 Illustration of mean speeds

In order to understand the concept of time mean speed and space mean speed, following il-

lustration will help. Let there be a road stretch having two sets of vehicle as in figure 2:1.

The first vehicle is traveling at 10m/s with 50 m spacing, and the second set at 20m/s with

100 m spacing. Therefore, the headway of the slow vehicle hs will be 50 m divided by 10 m/s

which is 5 sec. Therefore, the number of slow moving vehicles observed at A in one hour ns

will be 60/5 = 12 vehicles. The density K is the number of vehicles in 1 km, and is the inverse

of spacing. Therefore, Ks = 1000/50 = 20 vehicles/km. Therefore, by definition, time mean

speed vt is given by vt = 12×10+12×20

24= 15 m/s. Similarly, by definition, space mean speed is

the mean of vehicle speeds over time. Therefore, vs = 20×10+10×20

30= 13.3 m/s. This is same as

the harmonic mean of spot speeds obtained at location A; ie vs = 24

12×1

10+12×

1

20

= 13.3 m/s. It

may be noted that since harmonic mean is always lower than the arithmetic mean, and also as

observed, space mean speed is always lower than the time mean speed. In other words, space

mean speed weights slower vehicles more heavily as they occupy the road stretch for longer



duration of time. For this reason, in many fundamental traffic equations, space mean speed is

preferred over time mean speed.

2.5 Relation between time mean speed and space mean

speed

The relation between time mean speed(vt) and space mean speed(vs) is given by the following

relation:

vt = vs +σ2

vs

(2.6)

where,σ2 is the standard deviation of the spot speed. The derivation of the formula is given in

the next subsection. The standard deviation(σ2) can be computed in the following equation:

σ2 =Σqiv

2i

Σqi

− (vt)2 (2.7)

where,qi is the frequency of the vehicle having vi speed.

2.5.1 Derivation of the relation

The relation between time mean speed and space mean speed can be derived as below. Consider

a stream of vehicles with a set of sub-stream flow q1, q2, . . . qi, . . . qn having speed v1,v2, . . . vi,

. . . vn. The fundamental relation between flow(q), density(k) and mean speed vs is,

q = k × vs (2.8)

Therefore for any sub-stream qi, the following relationship will be valid.

qi = ki × vi (2.9)

The summation of all sub-stream flows will give the total flow q:

Σqi = q. (2.10)

Similarly the summation of all sub-stream density will give the total density k.

Σki = k. (2.11)

Let fi denote the proportion of sub-stream density ki to the total density k,

fi =ki

k. (2.12)



Space mean speed averages the speed over space. Therefore, if ki vehicles has vi speed, then

space mean speed is given by,

vs =Σkivi

k. (2.13)

Time mean speed averages the speed over time. Therefore,

vt =Σqivi

q. (2.14)

Substituting 2.9, vt can be written as,

vt =Σkivi

2

q(2.15)

Rewriting the above equation and substituting 2.12, and then substituting 2.8, we get,

vt = kΣki

kv2

i

=kΣfivi

2

q

=Σfivi

2

vs

By adding and subtracting vs and doing algebraic manipulations, vt can be written as,

vt =Σfi(vs + (vi − vs))

2

vs

(2.16)

=Σfi(vs)

2 + (vi − vs)2 + 2.vs.(vi − vs)

vs

(2.17)

=Σfivs

2

vs

+Σfi(vi − vs)

2

vs

+2.vs.Σfi(vi − vs)

vs

(2.18)

The third term of the equation will be zero because Σfi(vi − vs) will be zero, since vs is the

mean speed of vi. The numerator of the second term gives the standard deviation of vi. Σfi

by definition is 1.Therefore,

vt = vsΣfi +σ2

vs

+ 0 (2.19)

= vs +σ2

vs

(2.20)

Hence, time mean speed is space mean speed plus standard deviation of the spot speed divided

by the space mean speed. Time mean speed will be always greater than space mean speed since

standard deviation cannot be negative. If all the speed of the vehicles are the same, then spot

speed, time mean speed and space mean speed will also be same.



speed mid interval flow

No. range vi = vl+vu

2qi qivi v2

i qiv2i qi/vi

vl < v < vu

1 0-10 5 6 30 25 150 6/5

2 10-20 15 16 240 225 3600 16/15

3 20-30 20 24 600 625 15000 24/25

4 30-40 25 25 875 1225 30625 25/35

5 40-50 30 17 765 2025 34425 17/45

total 88 2510 83800 4.3187

Numerical Example

For the data given below,compute the time mean speed and space mean speed. Also verify the

relationship between them. Finally compute the density of the stream.

speed range frequency

0-10 5

10-20 15

20-30 20

30-40 25

40-50 30

Solution The solution of this problem consist of computing the time mean speed vt =Σqivi

Σqi,space mean speed vs = Σqi

Σqivi

,verifying their relation by the equation vt = vs + σ2

vs,and

using this to compute the density. To verify their relation, the standard deviation also need to

be computed σ2 = Σqv2

Σq− v2

t . For convenience,the calculation can be done in a tabular form as

shown in table 2.5.1.

The time mean speed(vt) is computed as:

vt =Σqivi

Σqi

=2510

88= 28.52



The space mean speed can be computed as:

vs =Σqi

Σqi

vi

=88

4.3187= 20.38

The standard deviation can be computed as:

σ2 =Σqv2

Σq− v2

t

=83800

88− 28.522 = 138.727

The time mean speed can also vt can also be computed as:

vt = vs +σ2

vs

= 20.38 +138.727

20.38= 27.184

The density can be found as:

k =q

v=

88

20.38= 4.3 vehicle/km

2.6 Fundamental relations of traffic flow

The relationship between the fundamental variables of traffic flow, namely speed, volume, and

density is called the fundamental relations of traffic flow. This can be derived by a simple

concept. Let there be a road with length v km, and assume all the vehicles are moving with v

km/hr.(Fig 2:2). Let the number of vehicles counted by an observer at A for one hour be n1.

By definition, the number of vehicles counted in one hour is flow(q). Therefore,

n1 = q. (2.21)

Similarly, by definition, density is the number of vehicles in unit distance. Therefore number

of vehicles n2 in a road stretch of distance v1 will be density × distance.Therefore,

n2 = k × v. (2.22)



8

Bv km

67 5 4 3 2 1

A

Figure 2:2: Illustration of relation between fundamental parameters of traffic flow

Since all the vehicles have speed v, the number of vehicles counted in 1 hour and the number

of vehicles in the stretch of distance v will also be same.(ie n1 = n2). Therefore,

q = k × v. (2.23)

This is the fundamental equation of traffic flow. Please note that, v in the above equation refers

to the space mean speed will also be same.

2.7 Fundamental diagrams of traffic flow

The relation between flow and density, density and speed, speed and flow, can be represented

with the help of some curves. They are referred to as the fundamental diagrams of traffic flow.

They will be explained in detail one by one below.

2.7.1 Flow-density curve

The flow and density varies with time and location. The relation between the density and the

corresponding flow on a given stretch of road is referred to as one of the fundamental diagram

of traffic flow. Some characteristics of an ideal flow-density relationship is listed below:

1. When the density is zero, flow will also be zero,since there is no vehicles on the road.

2. When the number of vehicles gradually increases the density as well as flow increases.

3. When more and more vehicles are added, it reaches a situation where vehicles can’t move.

This is referred to as the jam density or the maximum density. At jam density, flow will

be zero because the vehicles are not moving.

4. There will be some density between zero density and jam density, when the flow is maxi-

mum. The relationship is normally represented by a parabolic curve as shown in figure 2:3



flo

w(q

)

C

B

A

q

O

density (k)

ED

qmax

k0k1 kmax k2

kjam

Figure 2:3: Flow density curve

The point O refers to the case with zero density and zero flow. The point B refers to the

maximum flow and the corresponding density is kmax. The point C refers to the maximum

density kjam and the corresponding flow is zero. OA is the tangent drawn to the parabola at O,

and the slope of the line OA gives the mean free flow speed, ie the speed with which a vehicle

can travel when there is no flow. It can also be noted that points D and E correspond to same

flow but has two different densities. Further, the slope of the line OD gives the mean speed at

density k1 and slope of the line OE will give mean speed at density k2. Clearly the speed at

density k1 will be higher since there are less number of vehicles on the road.

2.7.2 Speed-density diagram

Similar to the flow-density relationship, speed will be maximum, referred to as the free flow

speed, and when the density is maximum, the speed will be zero. The most simple assumption

is that this variation of speed with density is linear as shown by the solid line in figure 2:4.

Corresponding to the zero density, vehicles will be flowing with their desire speed, or free flow

speed. When the density is jam density, the speed of the vehicles becomes zero. It is also

possible to have non-linear relationships as shown by the dotted lines. These will be discussed

later.

2.7.3 Speed flow relation

The relationship between the speed and flow can be postulated as follows. The flow is zero

either because there is no vehicles or there are too many vehicles so that they cannot move.

At maximum flow, the speed will be in between zero and free flow speed. This relationship is

shown in figure 2:5. The maximum flow qmax occurs at speed u. It is possible to have two



spee

d u

density (k)k0

uf

kjam

Figure 2:4: Speed-density diagram

flow q

q

u

spee

d u

u0

u1

u2

uf

Qmax

Figure 2:5: Speed-flow diagram



spee

d u

flow q

flo

w q

density k

spee

d u

density k qmax

Figure 2:6: Fundamental diagram of traffic flow

different speeds for a given flow.

2.7.4 Combined diagrams

The diagrams shown in the relationship between speed-flow, speed-density, and flow-density

are called the fundamental diagrams of traffic flow. These are as shown in figure 2:6. One

could observe the inter-relationship of these diagrams.

2.8 Summary

Time mean speed and space mean speed are two important measures of speed. It is possible to

have a relation between them and was derived in this chapter. Also, time mean speed will be

always greater than or equal to space mean speed. The fundamental diagrams of traffic flow

are vital tools which enables analysis of fundamental relationships. There are three diagrams -

speed-density, speed-flow and flow-density. They can be together combined in a single diagram

as discussed in the last section of the chapter.

2.9 References


New Delhi, 1987.


Transportation Systems Engineering 3. Traffic Stream Models

Chapter 3

Traffic Stream Models

3.1 Overview

To figure out the exact relationship between the traffic parameters, a great deal of research

has been done over the past several decades. The results of these researches yielded many

mathematical models. Some important models among them will be discussed in this chapter.

3.2 Greenshield’s macroscopic stream model

Macroscopic stream models represent how the behaviour of one parameter of traffic flow changes

with respect to another. Most important among them is the relation between speed and density.

The first and most simple relation between them is proposed by Greenshield. Greenshield

assumed a linear speed-density relationship as illustrated in figure 3:1 to derive the model. The

equation for this relationship is shown below.

v = vf −

[

vf

kj

]

.k (3.1)

where v is the mean speed at density k, vf is the free speed and kj is the jam density. This

equation ( 3.1) is often referred to as the Greenshield’s model. It indicates that when density

becomes zero, speed approaches free flow speed (ie. v → vf when k → 0). Once the relation

between speed and flow is established, the relation with flow can be derived. This relation

between flow and density is parabolic in shape and is shown in figure 3:3. Also, we know that

q = k.v (3.2)

Now substituting equation 3.1 in equation 3.2, we get

q = vf .k −

[

vf

kj

]

k2 (3.3)



density (k)

spee

d u

kjam

uf

k0

Figure 3:1: Relation between speed and density

spee

d, u u

flow, qq qmax

uf

u0

Figure 3:2: Relation between speed and flow



flo

w(q

)

C

B

A

q

O

density (k)

ED

qmax

k0k1 kmax k2

kjam

Figure 3:3: Relation between flow and density 1

Similarly we can find the relation between speed and flow. For this, put k = q

vin equation 3.1

and solving, we get

q = kj.v −

[

kj

vf

]

v2 (3.4)

This relationship is again parabolic and is shown in figure 3:2. Once the relationship between

the fundamental variables of traffic flow is established, the boundary conditions can be derived.

The boundary conditions that are of interest are jam density, free-flow speed, and maximum

flow. To find density at maximum flow, differentiate equation 3.3 with respect to k and equate

it to zero. ie.,

dq

dk= 0

vf −

vf

kj

.2k = 0

k =kj

2

Denoting the density corresponding to maximum flow as k0,

k0 =kj

2(3.5)

Therefore, density corresponding to maximum flow is half the jam density. Once we get k0, we

can derive for maximum flow, qmax. Substituting equation 3.5 in equation 3.3

qmax = vf .kj

2−

vf

kj

.

[

kj

2

]2

= vf .kj

2− vf .

kj

4

=vf .kj

4



Thus the maximum flow is one fourth the product of free flow and jam density. Finally to get

the speed at maximum flow, v0, substitute equation 3.5 in equation 3.1 and solving we get,

v0 = vf −vf

kj

.kj

2

v0 =vf

2(3.6)

Therefore, speed at maximum flow is half of the free speed.

3.3 Calibration of Greenshield’s model

In order to use this model for any traffic stream, one should get the boundary values, especially

free flow speed (vf ) and jam density (kj). This has to be obtained by field survey and this is

called calibration process. Although it is difficult to determine exact free flow speed and jam

density directly from the field, approximate values can be obtained from a number of speed and

density observations and then fitting a linear equation between them. Let the linear equation

be y = a + bx such that y is density k and x denotes the speed v. Using linear regression

method, coefficients a and b can be solved as,

b =n

∑n

i=1xiyi −

∑n

i=1xi.

∑n

i=1yi

n.∑n

i=1xi

2− (

∑n

i=1xi)2

(3.7)

a = y − bx (3.8)

Alternate method of solving for b is,

b =

∑n

i=1(xi − x)(yi − y)

∑n

i=1(xi − x)2

(3.9)

where xi and yi are the samples, n is the number of samples, and x and y are the mean of xi

and yi respectively.

Numerical example

For the following data on speed and density, determine the parameters of the Greenshield’s

model. Also find the maximum flow and density corresponding to a speed of 30 km/hr.

k v

171 5

129 15

20 40

70 25



x(k) y(v) (xi − x) (yi − y) (xi − x)(yi − y) (xi − x2)

171 5 73.5 -16.3 -1198.1 5402.3

129 15 31.5 -6.3 -198.5 992.3

20 40 -77.5 18.7 -1449.3 6006.3

70 25 -27.5 3.7 -101.8 756.3

390 85 -2947.7 13157.2

Solution Denoting y = v and x = k, solve for a and b using equation 3.8 and equation 3.9.

The solution is tabulated as shown below. x = Σxn

= 390

4= 97.5, y = Σy

n= 85

4= 21.3. From

equation 3.9, b = −2947.713157.2

= -0.2 a = y − bx = 21.3 + 0.2×97.5 = 40.8 So the linear regression

equation will be,

v = 40.8 − 0.2k (3.10)

Here vf = 40.8 andvf

kj= 0.2. This implies, kj = 40.8

0.2= 204 veh/km. The basic parameters of

Greenshield’s model are free flow speed and jam density and they are obtained as 40.8 kmph

and 204 veh/km respectively. To find maximum flow, use equation 3.6, i.e., qmax = 40.8×204

4=

2080.8 veh/hr Density corresponding to the speed 30 km/hr can be found out by substituting

v = 30 in equation 3.10. i.e, 30 = 40.8 - 0.2 × k Therefore, k = 40.8−30

0.2= 54 veh/km.

3.4 Other macroscopic stream models

In Greenshield’s model, linear relationship between speed and density was assumed. But in

field we can hardly find such a relationship between speed and density. Therefore, the validity

of Greenshield’s model was questioned and many other models came up. Prominent among

them are Greenberg’s logarithmic model, Underwood’s exponential model, Pipe’s generalized

model, and multi-regime models. These are briefly discussed below.

3.4.1 Greenberg’s logarithmic model

Greenberg assumed a logarithmic relation between speed and density. He proposed,

v = v0 lnkj

k(3.11)

This model has gained very good popularity because this model can be derived analytically.

(This derivation is beyond the scope of this notes). However, main drawbacks of this model is

that as density tends to zero, speed tends to infinity. This shows the inability of the model to

predict the speeds at lower densities.



density, k

spee

d, v

Figure 3:4: Greenberg’s logarithmic model

spee

d, v

density, k

Figure 3:5: Underwood’s exponential model

3.4.2 Underwood’s exponential model

Trying to overcome the limitation of Greenberg’s model, Underwood put forward an exponential

model as shown below.

v = vf .e−kk0 (3.12)

where vfThe model can be graphically expressed as in figure 3:5. is the free flow speed and ko

is the optimum density, i.e. the density corresponding to the maximum flow. In this model,

speed becomes zero only when density reaches infinity which is the drawback of this model.

Hence this cannot be used for predicting speeds at high densities.



qA, vA, kA qB, vB, kB

Figure 3:6: Shock wave: Stream characteristics

3.4.3 Pipes’ generalized model

Further developments were made with the introduction of a new parameter (n) to provide for a

more generalized modeling approach. Pipes proposed a model shown by the following equation.

v = vf

[

1 −

(

k

kj

)n]

(3.13)

When n is set to one, Pipe’s model resembles Greenshield’s model. Thus by varying the values

of n, a family of models can be developed.

3.4.4 Multi-regime models

All the above models are based on the assumption that the same speed-density relation is

valid for the entire range of densities seen in traffic streams. Therefore, these models are

called single-regime models. However, human behaviour will be different at different densities.

This is corroborated with field observations which shows different relations at different range

of densities. Therefore, the speed-density relation will also be different in different zones of

densities. Based on this concept, many models were proposed generally called multi-regime

models. The most simple one is called a two-regime model, where separate equations are used

to represent the speed-density relation at congested and uncongested traffic.

3.5 Shock waves

The flow of traffic along a stream can be considered similar to a fluid flow. Consider a stream of

traffic flowing with steady state conditions, i.e., all the vehicles in the stream are moving with

a constant speed, density and flow. Let this be denoted as state A (refer figure 3:6. Suddenly

due to some obstructions in the stream (like an accident or traffic block) the steady state

characteristics changes and they acquire another state of flow, say state B. The speed, density

and flow of state A is denoted as vA, kA, and qA, and state B as vB, kB, and qB respectively.

The flow-density curve is shown in figure 3:7. The speed of the vehicles at state A is given

by the line joining the origin and point A in the graph. The time-space diagram of the traffic



density

A

B

flo

wqA

qB

vB

kA kB kj

vA

Figure 3:7: Shock wave: Flow-density curve

time

dis

tan

ce

AB

Figure 3:8: Shock wave : time-distance diagram



stream is also plotted in figure 3:8. All the lines are having the same slope which implies that

they are moving with constant speed. The sudden change in the characteristics of the stream

leads to the formation of a shock wave. There will be a cascading effect of the vehicles in the

upstream direction. Thus shock wave is basically the movement of the point that demarcates

the two stream conditions. This is clearly marked in the figure 3:7. Thus the shock waves

produced at state B are propagated in the backward direction. The speed of the vehicles at

state B is the line joining the origin and point B of the flow-density curve. Slope of the line AB

gives the speed of the shock wave (refer figure 3:7). If speed of the shock-wave is represented

as ωAB, then

ωAB =qA − qB

kA − kB

(3.14)

The above result can be analytically solved by equating the expressions for the number vehicles

leaving the upstream and joining the downstream of the shock wave boundary (this assumption

is true since the vehicles cannot be created or destroyed. Let NA be the number of vehicles

leaving the section A. Then, NA = qB t. The relative speed of these vehicles with respect to

the shock wave will be vA − ωAB. Hence,

NA = kA (vA − ωAB) t (3.15)

Similarly, the vehicles entering the state B is given as

NB = kA (vB − ωAB) t (3.16)

Equating equations 3.15 and 3.16, and solving for ωAB as follows will yield to:

NA = NB

kA (vA − ωAB) t = kB (vB − ωAB) t

kA vA t − kA ωAB t = kB vB t − kBωAB t

kAωAB t − kBωAB t = kA vA − kB vB

ωAB (kA − kB) = qA − qB

This will yield the following expression for the shock-wave speed.

ωAB =qA − qB

kA − kB

(3.17)

In this case, the shock wave move against the direction of traffic and is therefore called a

backward moving shock wave. There are other possibilities of shock waves such as forward

moving shock waves and stationary shock waves. The forward moving shock waves are formed

when a stream with higher density and higher flow meets a stream with relatively lesser density



and flow. For example, when the width of the road increases suddenly, there are chances for a

forward moving shock wave. Stationary shock waves will occur when two streams having the

same flow value but different densities meet.

3.6 Macroscopic flow models

If one looks into traffic flow from a very long distance, the flow of fairly heavy traffic appears

like a stream of a fluid. Therefore, a macroscopic theory of traffic can be developed with the

help of hydrodynamic theory of fluids by considering traffic as an effectively one-dimensional

compressible fluid. The behaviour of individual vehicle is ignored and one is concerned only

with the behaviour of sizable aggregate of vehicles. The earliest traffic flow models began by

writing the balance equation to address vehicle number conservation on a road. In fact, all

traffic flow models and theories must satisfy the law of conservation of the number of vehicles

on the road. Assuming that the vehicles are flowing from left to right, the continuity equation

can be written as∂k(x, t)

∂t+

∂q(x, t)

∂x= 0 (3.18)

where x denotes the spatial coordinate in the direction of traffic flow, t is the time, k is the

density and q denotes the flow. However, one cannot get two unknowns, namely k(x, t) by

and q(x, t) by solving one equation. One possible solution is to write two equations from two

regimes of the flow, say before and after a bottleneck. In this system the flow rate before and

after will be same, or

k1v1 = k2v2 (3.19)

From this the shock wave velocity can be derived as

v(to)p =q2 − q1

k2 − k1

(3.20)

This is normally referred to as Stock’s shock wave formula. An alternate possibility which

Lighthill and Whitham adopted in their landmark study is to assume that the flow rate q is

determined primarily by the local density k, so that flow q can be treated as a function of only

density k. Therefore the number of unknown variables will be reduced to one. Essentially this

assumption states that k(x,t) and q (x,t) are not independent of each other. Therefore the

continuity equation takes the form

∂k(x, t)

∂t+

∂q(k(x, t))

∂x= 0 (3.21)

However, the functional relationship between flow q and density k cannot be calculated from

fluid-dynamical theory. This has to be either taken as a phenomenological relation derived from



the empirical observation or from microscopic theories. Therefore, the flow rate q is a function

of the vehicular density k; q = q(k). Thus, the balance equation takes the form

∂k(x, t)

∂t+

∂q(k(x, t))

∂x= 0 (3.22)

Now there is only one independent variable in the balance equation, the vehicle density k. If

initial and boundary conditions are known, this can be solved. Solution to LWR models are

kinematic waves moving with velocitydq(k)

dk(3.23)

This velocity vk is positive when the flow rate increases with density, and it is negative when

the flow rate decreases with density. In some cases, this function may shift from one regime to

the other, and then a shock is said to be formed. This shock wave propagate at the velocity

vs =q(k2) − q(k1)

k2 − k1

(3.24)

where q(k2) and q(k1) are the flow rates corresponding to the upstream density k2 and down-

stream density k1 of the shock wave. Unlike Stock’s shock wave formula there is only one

variable here.

3.7 Summary

Traffic stream models attempt to establish a better relationship between the traffic parameters.

These models were based on many assumptions, for instance, Greenshield’s model assumed a

linear speed-density relationship. Other models were also discussed in this chapter. The models

are used for explaining several phenomena in connection with traffic flow like shock wave. The

topics of further interest are multi-regime model (formulation of both two and three regime

models) and three dimensional representation of these models.

3.8 References




Transportation Systems Engineering 4. Moving Observer Method

Chapter 4

Moving Observer Method

4.1 Overview

For a complete description of traffic stream modeling, one would require flow, speed, and density.

Obtaining these parameters simultaneously is a difficult task if we use separate techniques.

Since we have a fundamental equation of traffic flow, which gives the flow as the product of

density and space mean speed, if we knew any two parameters, the third can be computed.

Moving car or moving observer method of traffic stream measurement has been developed to

provide simultaneous measurement of traffic stream variables. It has the advantage of obtaining

the complete state with just three observers, and a vehicle. Determination of any of the two

parameters of the traffic flow will provide the third one by the equation q = u.k. Thus,

moving observer method is the most commonly used method to get the relationship between

the fundamental stream characteristics. In this method, the observer moves in the traffic stream

unlike all other previous methods.

4.2 Theory

Consider a stream of vehicles moving in the north bound direction. Two different cases of

motion can be considered. The first case considers the traffic stream to be moving and the

observer to be stationary. If no is the number of vehicles overtaking the observer during a

period, t, then flow q is n0

t, or

n0 = q × t (4.1)

The second case assumes that the stream is stationary and the observer moves with speed vo.

If np is the number of vehicles overtaken by observer over a length l, then by definition, density

k is np

l, or

np = k × l (4.2)



l

Figure 4:1: Illustration of moving observer method

or

np = k.vo.t (4.3)

where v0 is the speed of the observer and t is the time taken for the observer to cover the road

stretch. Now consider the case when the observer is moving within the stream. In that case

mo vehicles will overtake the observer and mp vehicles will be overtaken by the observer in the

test vehicle. Let the difference m is given by m0 - mp, then from equation 4.1 and equation

4.3,

m = m0 − mp = q t − k vo t (4.4)

This equation is the basic equation of moving observer method, which relates q, k to the counts

m, t and vo that can be obtained from the test. However, we have two unknowns, q and k, but

only one equation. For generating another equation, the test vehicle is run twice once with the

traffic stream and another one against traffic stream, i.e.

mw = q tw − k vw tw (4.5)

= q tw − k l

ma = q ta + k va ta (4.6)

= q ta + k l

where, a, w denotes against and with traffic flow. It may be noted that the sign of equation 4.6

is negative, because test vehicle moving in the opposite direction can be considered as a case

when the test vehicle is moving in the stream with negative velocity. Further, in this case, all

the vehicles will be overtaking, since it is moving with negative speed. In other words, when the

test vehicle moves in the opposite direction, the observer simply counts the number of vehicles

in the opposite direction. Adding equation 4.5 and 4.6, we will get the first parameter of the



stream, namely the flow(q) as:

q =mw + ma

tw + ta(4.7)

Now calculating space mean speed from equation 4.5,

mw

tw= q − kvw

= q −q

vvw

= q −q

v

[

l

tw

]

= q

(

1 −

l

v×

1

tw

)

= q

(

1 −

tavg

tw

)

If vs is the mean stream speed, then average travel time is given by tavg = lvs

. Therefore,

mw

q= tw(1 −

tavg

tw) = tw − tavg

tavg = tw −

mw

q=

l

v,

Rewriting the above equation, we get the second parameter of the traffic flow, namely the mean

speed vs and can be written as,

vs =l

tw −mw

q

(4.8)

Thus two parameters of the stream can be determined. Knowing the two parameters the third

parameter of traffic flow density (k) can be found out as

k =q

vs

(4.9)

For increase accuracy and reliability, the test is performed a number of times and the average

results are to be taken.



4.3 Proof

4.4 Assumptions

Numerical Example

The length of a road stretch used for conducting the moving observer test is 0.5 km and the speed

with which the test vehicle moved is 20 km/hr. Given that the number of vehicles encountered

in the stream while the test vehicle was moving against the traffic stream is 107, number of

vehicles that had overtaken the test vehicle is 10, and the number of vehicles overtaken by the

test vehicle is 74, find the flow, density and average speed of the stream.

Solution Time taken by the test vehicle to reach the other end of the stream while it is

moving along with the traffic is tw = 0.520

= 0.025 hr

Time taken by the observer to reach the other end of the stream while it is moving against the

traffic is ta = tw = 0.025 hr

Flow is given by equation, q = 107+(10−74)0.025+0.025

= 860 veh/hr

Stream speed vs can be found out from equationvs = 0.50.025− 10.74

860

= 5 km/hr

Density can be found out from equation as k = 8605

= 172veh/km

Numerical Example

The data from four moving observer test methods are shown in the table. Column 1 gives

the sample number, column 2 gives the number of vehicles moving against the stream, column

3 gives the number of vehicles that had overtaken the test vehicle, and last column gives the

number of vehicles overtaken by the test vehicle. Find the three fundamental stream parameters

for each set of data. Also plot the fundamental diagrams of traffic flow.

Sample no. 1 2 3

1 107 10 74

2 113 25 41

3 30 15 5

4 79 18 9

Solution From the calculated values of flow, density and speed, the three fundamental dia-

grams can be plotted as shown in figure 4:2.



Sample no. ma mo mp mw = (mo − mp) ta tw q = ma+mw

ta+twu = l

tw−

mw

q

k = q

v

1 107 10 74 -64 0.025 0.025 860 5.03 171

2 113 25 41 -16 0.025 0.025 1940 15.04 129

3 30 15 5 10 0.025 0.025 800 40 20

4 79 18 9 9 0.025 0.025 1760 25.14 70

density k

flo

w q

20 70 129171

800

1760

1940

flow q

spee

d u

860

40

density k5.03

15.0425.14

spee

d u

Figure 4:2: Fundamental diagrams of traffic flow



4.5 Summary

Traffic engineering studies differ from other studies in the fact that they require extensive data

from the field which cannot be exactly created in any laboratory. Speed data are collected

from measurements at a point or over a short section or over an area. Traffic flow data are

collected at a point. Moving observer method is one in which both speed and traffic flow data

are obtained by a single experiment.

4.6 References


New Delhi, 1987.


Transportation Systems Engineering 5. Measurement at a Point

Chapter 5

Measurement at a Point

5.1 Introduction

The data required by a traffic engineer can mainly be observed on field rather than at laboratory.

Now the field studies can be classified into three types depending upon the length of observation:

1. Measurement at a point

2. Measurement over a short section

3. Measurement over a long section

Out of these we will be discussing the first type here. Flow is the main traffic parameter

measured at a point. Flow can be defined as the no of vehicles passing a section per unit time.

Traffic volume studies are mainly carried out to obtain factual data concerning the movement

of vehicles at selected point on the street or highway system.

5.2 Basic concepts

5.2.1 Types of Volume Measurement

Volume count varies considerably with time. Hence, several types of measurement of volume

are commonly adopted to average these variations. These measurements are described below:

Average Annual Daily Traffic (AADT)

This is given by the total no. of vehicles passing through a section in a year divided by 365.

This can be used for following purposes:

1. Measuring the present demand for service by the street or highway



2. Developing the major or arterial street

3. Evaluating the present traffic flow with respect to the street system

4. Locating areas where new facilities or improvements to existing facilities are needed.

Average Annual Weekday Traffic (AAWT)

This is defined as the average 24-hour traffic volume occurring on weekdays over a full year.

Average Daily Traffic (ADT)

An average 24-hour traffic volume at a given location for some period of time less than a year.

It may be measured for six months, a season, a month, a week, or as little as two days. An

ADT is a valid number only for the period over which it was measured.

Average Weekday Traffic (AWT)

An average 24-hour traffic volume occurring on weekdays for some period of time less than one

year, such as for a month or a season.

5.2.2 Type of Counts

Various types of traffic counts are carried out, depending on the anticipated use of the data to

be collected. They include:

Cordon Count

These are made at the perimeter of an enclosed area (CBD, shopping centre etc.). Vehicles or

persons entering and leaving the area during a specified time period are counted.

Screen Line Count

These are classified counts taken at all streets intersecting an imaginary line (screen line)

bisecting the area. These counts are used to determine trends, expand urban travel data,

traffic assignment etc.

Pedestrian Count

These are used in evaluating sidewalk and crosswalk needs, justifying pedestrian signals, traffic

signal timings etc.



Intersection Count

These are measured at the intersections and are used in planning turn prohibitions, designing

channelization, computing capacity, analysing high accident intersections etc.

5.2.3 Counting Techniques

Number of vehicles can be counted either manually or by machine depending upon the duration

of study, accuracy required, location of study area etc.

Manual counting

In its simplest form an observer counts the numbers of vehicles along with its type, passing

through the section for a definite time interval. For light volumes, tally marks on a form are

adequate. Mechanical or electrical counters are used for heavy traffic. Although it is good to

take some manual observations for every counting for checking the instruments, some other

specific uses of manual counts are following:

1. Turning and through movement studies

2. Classification and occupancy studies

3. For analysis of crosswalks, sidewalks, street corner space and other pedestrian facilities

Automatic counting

These can be used to obtain vehicular counts at non-intersection points. Total volume, direc-

tional volume or lane volumes can be obtained depending upon the equipment available.

Permanent Counters

These are installed to obtain control counts on a continuous basis. A detector (sensor) which

responds on the passage of vehicle past a selected point is an essential part of this type of

counters. These can be mainly grouped into contact types, pulsed types, radar types. Among

the contact type counters, pneumatic tubes are mostly used. Air pulse actuated by vehicle

wheels, pass along the tube thereby increasing the count. Pulsed types mainly depend upon

the interruption of a beam generated from a station located near the site, which is detected

by the receiver. In radar types, a continuous beam of energy is directed towards the vehicle.

The frequency shift of energy reflected from approaching vehicle is conceived by sensors. Due

to tedious reduction of the voluminous amount of data obtained, use of such counters was

decreasing. But the use of computers and data readable counters has reversed the trend.



Portable Counters

These are used to obtain temporary or short term counts. Generally these make use of a

transducer unit actuated by energy pulses. Each axle or vehicle passage operates a switch

attached to a counter which is usually set to register one unit for every two axles. If significant

number of multi-axle vehicles is present, an error is introduced. A correction factor, obtained

from a sample classification count, is introduced to reduce this error. This can further be

sub-divided into two types:

1. Recording counters provides a permanent record of volumes by printing the total

volume. These may be set for various counting intervals.

2. Non-Recording Counters must be read by an observer at desired intervals.

5.2.4 Counting Periods

The time and length that a specific location should be counted depends upon the data desired

and the application in which the data are used. Counting periods vary from short counts at spot

points to continuous counts at permanent stations. Hourly counts are generally significant in all

engineering design, while daily and annual traffic is important in economic calculations, road

system classification and investment programmes. Continuous counts are made to establish

national and local highway use, trends of use and behaviour and for estimating purposes. Some

of the more commonly used intervals are:

1. 24-hour counts normally covering any 24-hour period between noon Monday and noon

Friday. If a specific day count is desired, the count should be from midnight to midnight.

2. 16 hour counts usually 5:30 am to 9:30 pm or 6 am to 9 pm.

3. 12 hour counts usually from 7 am to 7 pm

4. Peak Period counting times vary depending upon size of metropolitan area, proximity to

major generators and the type of facility. Commonly used periods are 7 to 9 am and 4

to 6 pm.

5.3 Variation of Volume Counts and Peak Hour Factors

Variation of volume counts can be further sub-divided into daily, weekly and seasonal variation.

For studying the daily variation, the flow in each hour has been expressed as percentage of daily



flow. Weekdays, Saturdays and Sundays usually show different patterns. That’s why comparing

day with day is much more useful. Peak Hour Volume is very important factor in the design of

roads and control of traffic, and is usually 2 - 2.5 times the average hourly volume. Apart from

this there is one additional feature of this variation: two dominant peaks (morning and evening

peak), especially in urban areas. These mainly include work trips and are not dependent on

weather and other travel conditions.

Similar to daily variation, weekly variation gives volumes expressed as a percentage of total

flow for the week. Weekdays flows are approximately constant but the weekend flows vary a

lot depending upon the season, weather and socio-economic factors. Seasonal variation is the

most consistent of all variation patterns and represents the economic and social condition of

the area served.

Peak hour factors should be applied in most capacity analyses in accordance with the

Highway Capacity Manual, which selected 15 minute flow rates as the basis for most of its

procedures. The peak-hour factor (PHF) is descriptive of trip generation patterns and may

apply to an area or portion of a street and highway system. The PHF is typically calculated

from traffic counts. It is the average volume during the peak 60 minute period V 60

av divided by

four times the average volume during the peak 15 minute’s period V 15

av .

PHF =V 60

av

4 × V 15av

(5.1)

One can also use 5, 10, or 20 minutes instead of 15 minutes interval for the calculation of

PHF. But in that case we have to change the multiplying factor in the denominator from 4.

Generalizing,

PHF =V 60

av60

n× V n

av

(5.2)

where V nav is the peak n minute flow. The Highway Capacity Manual advises that in absence

of field measurements reasonable approximations for peak hour factor can be made as follows:

• 0.95 for congested condition

• 0.92 for urban areas

• 0.88 for rural areas

General guidelines for finding future PHF can be found in the Development Review Guidelines,

which are as follows:

• 0.85 for minor street inflows and outflows

• 0.90 for minor arterials



Time interval Cars

4:00 - 4:15 30

4:15 - 4:30 26

4:30 - 4:45 35

4:45 - 5:00 40

5:00 - 5:15 49

5:15 - 5:30 55

5:30 - 5:45 65

5:45 - 6:00 50

6:00 - 6:15 39

6:15 - 6:30 30

Table 5:1: Volumetric data

• 0.95 for major streets

Numerical Example

The table below shows the volumetric data observed at an intersection. Calculate the peak

hour volume, peak hour factor (PHF), and the actual (design) flow rate for this approach.

Solution We can locate the hour with the highest volume and the 15 minute interval with

the highest volume. The peak hour is shown in blue below with the peak 15 minute period

shown in bold font. The peak hour volume is just the sum of the volumes of the four 15 minute

intervals within the peak hour (219). The peak 15 minute volume is 65 in this case. The peak

hour factor (PHF) is found by dividing the peak hour volume by four times the peak 15 minute

volume. PHF = 219

4×65= 0.84 The actual (design) flow rate can be calculated by dividing the

peak hour volume by the PHF, 219/0.84 = 260 vehicles/hr, or by multiplying the peak 15

minute volume by four, 4 × 65 = 260 vehicles per hour.

5.4 Passenger Car Unit (PCU)

Passenger Car Unit (PCU) is a metric used in Transportation Engineering, to assess traffic-flow

rate on a highway. A Passenger Car Unit is a measure of the impact that a mode of transport has

on traffic variables (such as headway, speed, density) compared to a single standard passenger



Time interval Cars

4:00 - 4:15 30

4:15 - 4:30 26

4:30 - 4:45 35

4:45 - 5:00 40

5:00 - 5:15 49

5:15 - 5:30 55

5:30 - 5:45 65

5:45 - 6:00 50

6:00 - 6:15 39

6:15 - 6:30 30

Table 5:2: Solution of the problem

Car 1.0

Motorcycle 0.5

Bicycle 0.2

LCV 2.2

Bus, Truck 3.5

3-wheeler 0.8

Table 5:3: Values of PCU

car. This is also known as passenger car equivalent. For example, typical values of PCU (or

PCE) are: Highway capacity is measured in PCU/hour daily.

Numerical Example

The table below shows the volumetric data collected at an intersection: Calculate the peak

hour volume, peak hour factor (PHF), and the actual (design) flow rate for this approach.

Solution The first step in this solution is to find the total traffic volume for each 15 minute

period in terms of passenger car units. For this purpose the PCU values given in the table are

used. Once we have this, we can locate the hour with the highest volume and the 15 minute

interval with the highest volume. The peak hour is shown in blue below with the peak 15

minute period shown in a darker shade of blue. The peak hour volume is just the sum of the



From To HCV LCV CAR 3W 2W

2.30 2.40 4 10 6 38 24

2.40 2.50 8 12 9 63 33

2.50 3.00 7 13 8 42 27

3.00 3.10 6 13 15 37 32

3.10 3.20 7 14 10 51 28

3.20 3.30 6 10 9 63 41

3.30 3.40 8 11 8 48 38

3.40 3.50 10 6 15 47 21

3.50 4.00 9 7 9 54 26

4.00 4.10 10 9 11 62 35

4.10 4.20 12 11 12 61 39

4.20 4.30 8 8 10 54 42

Table 5:4: Volumetric data collected

From To Flow in PCU

2.30 2.40 84.4

2.40 2.50 130.3

2.50 3.00 108.2

3.00 3.10 110.2

3.10 3.20 120.1

3.20 3.30 122.9

3.30 3.40 117.6

3.40 3.50 111.3

3.50 4.00 112.1

4.00 4.10 132.9

4.10 4.20 146.5

4.20 4.30 119.8

Table 5:5: Solution of the problem



volumes of the six 10 minute intervals within the peak hour (743.6 PCU). The peak 10 minute

volume is 146.5 PCU in this case. The peak hour factor (PHF) is found by dividing the peak

hour volume by four times the peak 10 minute volume.

PHF =743.6

6 × 146.5= 0.85

The actual (design) flow rate can be calculated by dividing the peak hour volume by the PHF,

743.6/0.85 = 879 PCU/hr, or by multiplying the peak 10 minute volume by six, 6 × 146.5 =

879 PCU/hr.

5.5 Determination of PCU

Traffic in many parts of the world is heterogeneous, where road space is shared among many

traffic modes with different physical dimensions. Loose lane discipline prevails; car following

is not the norm. This complicates computing of PCU. Some of the methods for determining

passenger car units (PCU) are following:

• Modified Density Method

• Chandra’s method

• Method Based on Relative Delay

• Headway method

• Multiple linear regression method

• Simulation method

It may be appropriate to use different values for the same vehicle type according to circum-

stances like volume of traffic, speed of vehicle, lane width and several external factors.

5.5.1 Method based on relative delay

The 1965 HCM used relative speed reduction to define PCUs for two lane highways and quan-

tified this by the relative number of passing known as the Walker method. For multilane

highways, PCUs were based on the relative delay due to trucks. PCUs for multilane highways

based on relative delay may be found as

Et =Dij − Db

Db

(5.3)



where Dij is the delay to passenger cars due to vehicle type i under condition j and Db is the

base delay to standard passenger cars due to slower passenger cars.

PCUs in the 1965 HCM were reported for grades of specific length and percent, proportion

of trucks, and LOS grouped as A through C or D and E. As expected, the highest PCU was

reported for the longest and steepest grade with the highest proportion of trucks and the lowest

LOS. However, in many cases the PCU for a given grade and LOS decreased with increasing

proportion of trucks. PCUs in the 1965 HCM were reported for grades of specific length and

percent, proportion of trucks, and LOS grouped as A through C or D and E. As expected,

the highest PCU was reported for the longest and steepest grade with the highest proportion

of trucks and the lowest LOS. However, in many cases the PCU for a given grade and LOS

decreased with increasing proportion of trucks.

5.5.2 Multiple linear regression model

Multiple linear regression method try to represen the speed of a traffic stream as function of

number of variables. For example, the percentile speed vp can represented as:

vp = vf + c1 × Vc + c2 × Vt + c3 × Vr + c4 × Vo + c5 × Va (5.4)

where vf is the free speed, Vc is the number of passenger cars, Vc is the number of trucks Vr

is the number of recreational vehicles, Vr is the number of other types of vehicles, Va is the

number of vehicles moving against the current stream, C1 to C5 are coefficient representing the

relative sizes of speed reductions for each vehicle type. Although this model was formulated

for two lane highways with opposing traffic flow, it could be applied to multilane highways by

setting the coefficient C5 to zero. Using the speed reduction coefficients, En, the PCU for a

vehicle type n is calculated as:

En =Cn

C1

where Cn is the speed reduction coefficient for vehicle type n and C1 is the speed reduction

coefficient for passenger cars.

5.5.3 Method based on headway

Realizing one of the primary effects of heavy vehicles in the traffic stream is that they take up

more space, headways have been used for some of the most popular methods to calculate PCUs.

In 1976, Werner and Morrall suggested that the headway method is best suited to determine

PCUs on level terrain at low levels of service. The PCU is calculated as

Et =(Hm

Hb

) − Pc

Pt

(5.5)



hm hc pc pt

2.70 2.5 0.90 0.10

2.80 2.5 0.85 0.15

2.94 2.5 0.80 0.20

3.10 2.5 0.75 0.25

3.25 2.5 0.70 0.30

3.35 2.5 0.65 0.35

3.70 2.5 0.50 0.50

3.80 2.5 0.45 0.55

3.95 2.5 0.40 0.60

4.20 2.5 0.30 0.70

Table 5:6: Headway data for a number of traffic conditions

where HM is the average headway for a sample including all vehicle types, HB is the average

headway for a sample of passenger cars only, PC is the proportion of cars, and PT is the

proportion of trucks.

Numerical Example

The table given below show headway data for a number of traffic conditions. It is assumed that

the traffic contains only car and truck. Compute the PCU value for each traffic condition Note

that hm, hc, pc, pt respectively denote the average headway for mixed traffic, average headway

for traffic consisting of cars only, the percentage of cars and percentage of trucks of the traffic

stream.

Solution Use the formula given above to find the value of PCU.

5.5.4 Chandra’s method

This method uses two factors: namely, velocity of vehicle type and its projected rectangular

area to calculate the PCU value.

(PCU)i =(Vc/Vi)

(Ac/Ai)(5.6)

where Vc and Vi are mean speeds of car and vehicle of type i respectively and Ac and Ai are

their respective projected rectangular area length * width on the road.



hm hc pc pt Et

2.70 2.5 0.90 0.10 1.80

2.80 2.5 0.85 0.15 1.80

2.94 2.5 0.80 0.20 1.88

3.10 2.5 0.75 0.25 1.96

3.25 2.5 0.70 0.30 2.00

3.35 2.5 0.65 0.35 1.97

3.70 2.5 0.50 0.50 1.96

3.80 2.5 0.45 0.55 1.95

3.95 2.5 0.40 0.60 1.97

4.20 2.5 0.30 0.70 1.97

Table 5:7: Table for the value of PCU

Category Vehicle Dimension Projected Area

Car Car, Jeep, Van 3.72 x 1.44 5.39

Bus Bus 10.10 x 2.43 24.74

Truck Truck 7.50 x 2.35 17.62

LCV Mini bus/trucks 6.10 x 2.10 12.81

M-Truck Multi-axle truck 2.35 x 12.0 28.60

Bikes Scooter, Motorbike 1.87 x 0.64 1.20

Cycle Pedal Cycle 1.90 x 0.45 0.85

Autos Auto, Tempo 3.20 x 1.40 4.48

Table 5:8: Table for calculation using Chandra’s method



PCU

Percentage of trucks

1.75

1.80

1.85

1.90

1.95

2.00

2.05

0 0.2 0.4 0.6 0.8

Figure 5:1: Graph showing the variation of PCU with percentage of truck using the data of the

problem given above

Numerical Example

The table given shows the data obtained in spot speed study for various vehicle types. Find

the PCU value for each vehicle type using the Chandra’s Method.

Solution Step 1 We have to find the space mean speed for each vehicle type using the

formula:

Vs =n

Σni=1

( 1

vi

)

Where n is the no. of observations and vi is the spot speeds.

Step 2 Find the PCU values using Chandra’s Method. Use the table having the areas of

various vehicle types given above. Then we can use the table given above to find the areas of

different vehicle types to find corresponding PCU values.

5.5.5 Density method

In the density method, the PCU of truck (Et) is computed as:

Et =(kc/Wl)

(kt)/Wl)(5.7)

where kc is the density of cars in pure homogenous conditions(car/km.), Wl is the width of the

lane in homogenous traffic, kt is the density of the truck in pure homogenous conditions and Et



No Car 3 wheeler 2 wheeler LCV HCV

1 11.32 8.67 6.67 6.0 7.4

2 6.74 7.25 8.27 6.88 6.09

3 11.11 9.68 7.75 7.5 5.88

4 6.67 6.98 6.12 8.57 6.38

5 8.11 8.77 9.52 9.67 5.66

6 7.41 8.77 11.9 8.57 5.66

7 8.11 9.52 6.97 5.7 5.55

8 9.93 9.40 6.97 4.68 6.12

Table 5:9: Table of spot speed study for various vehicle types

No Car 3 wheeler 2 wheeler LCV HCV

1 11.32 8.67 6.67 6.0 7.4

2 6.74 7.25 8.27 6.88 6.09

3 11.11 9.68 7.75 7.5 5.88

4 6.67 6.98 6.12 8.57 6.38

5 8.11 8.77 9.52 9.67 5.66

6 7.41 8.77 11.9 8.57 5.66

7 8.11 9.52 6.97 5.7 5.55

8 9.93 9.40 6.97 4.68 6.12

vs 8.34 8.52 7.70 6.83 6.05

Table 5:10: PCU values using Chandra’s Method

vs 8.34 8.52 7.70 6.83 6.05

PCU 1 0.81 0.24 2.90 6.33

Table 5:11: Table of PCU values



From To HCV Flow HCV Mean Speed CAR Flow CAR Mean Speed

2.30 2.40 4 10.4 16 14.32

2.40 2.50 6 9.09 19 12.74

2.50 3.00 5 8.88 18 13.11

3.00 3.10 6 9.38 20 10.67

3.10 3.20 6 10.66 17 12.11

3.20 3.30 6 9.66 21 13.41

3.30 3.40 5 9.55 18 13.11

3.40 3.50 8 10.12 17 10.93

3.50 4.00 7 9.2 22 13.33

4.00 4.10 6 9.54 19 13.58

4.10 4.20 10 10.67 25 12.34

4.20 4.30 8 9.61 20 10.58

Table 5:12: space mean speed of Car and HCV in a two lane road without shoulders

is the passenger car unit of the trucks given homogenous traffic behaviour. In density method

where car following and lane discipline behaviour prevails, all traffic entities use an equal Wl.

Numerical Example

The table given below shows the data of flow and space mean speed of Car and HCV in a two

lane road without shoulders. Assume the 85 percentile distribution width of HCV and Car to

be 9.50m. and 7.50m. Compute the PCU value of HCV for each time interval.

Solution We know that PCU value can be calculated using the formula:

(PCU)truck =(Kcar/Wl)

(Ktruck/Wl)(5.8)

Step 1 Find the density of car and truck using basic relationship between the traffic flow

parameters

Q = K × V (5.9)

Step 2 The using the method stated above we can find the PCU values. The table showing

the PCU values has been illustrated below.



From To HCV Flow HCV Speed Car Flow Car Speed Car density PCU

2.30 2.40 4 10.4 27 14.32 1.86 3.68

2.40 2.50 6 9.09 32 12.74 2.49 2.86

2.50 3.00 5 8.88 30 13.11 2.29 3.09

3.00 3.10 6 9.38 33 10.67 3.12 3.71

3.10 3.20 6 10.66 28 12.11 2.34 3.16

3.20 3.30 6 9.66 35 13.41 2.61 3.19

3.30 3.40 5 9.55 30 13.11 2.29 3.32

3.40 3.50 8 10.12 28 10.93 2.59 2.49

3.50 4.00 7 9.2 37 13.33 2.75 2.75

4.00 4.10 6 9.54 32 13.58 2.33 2.82

4.10 4.20 10 10.67 42 12.34 3.38 2.74

4.20 4.30 8 9.61 33 10.58 3.15 2.88

Table 5:13: PCU values for the above problem

5.6 Conclusion

Measurement over a section is probably one of the easiest field parameter that can be mea-

sured. Various types of volume counts and counting techniques have been discussed in brief.

Along with this a brief insight into various methods of calculating Passenger Car unit has been

provided. Out of the various methods discussed, Chandra’s Method is only method that can

be applied to the Indian condition of heterogeneous traffic that is characterized by loose lane

discipline. All the other methods are primarily based on homogeneous traffic conditions mainly

prevailing in developed countries.

5.7 References

1. S Chandra and U Kumar. Effect of lane width on capacity under mixed traffic conditions

in india. Journal of Transportation Engineering, ASCE, 129:155–160, 2003.

2. F D Hobbs. Traffic Planning and Engineering. Pergamon Press, 1979. 2nd Edition.

3. W S Homburger. Fundamentals of traffic engineering. 2019. 12th Edition, pp 5-1 to 5-5.

4. Anthony Ingle. Development of Passenger Car Equivalents for Basic Freeway Segments.

Blacksburg, Virginia, July 8, 2004.



5. Geetam Tiwari, Joseph Fazio, and Sri Pavitravas. Passenger Car Units for Heterogeneous

Traffic Using a Modified Density Method. 2019.


Transportation Systems Engineering 6. Measurement over a Short Section

Chapter 6

Measurement over a Short Section

6.1 Overview

The main purpose of this chapter is to determine traffic parameter, specially speed. Speed

measurements are most often taken at a point (or a short section) of road way under conditions

of free flow. The intent is to determine the speeds that drivers select, unaffected by the existence

of congestion. This information is used to determine general speed trends, to help determine

reasonable speed limits, and to assess safety.

6.2 Speed Studies

As speed defines the distance travelled by user in a given time, and this is a vibrant in every

traffic movement. In other words speed of movement is the ratio of distance travelled to time

of travel. The actual speed of traffic flow over a given route may fluctuated widely, as because

at each time the volume of traffic varies. Accordingly, speeds are generally classified into three

main categories

1. Spot speed This is the instantaneous speed of a vehicle at any specific location.

2. Running speed This is the average speed maintained over a particular course while the

vehicle is in the motion.

3. Journey speed This is the effective speed of the vehicle on a journey between two points

and the distance between two points and the distance between these points divided by

the total time taken for the vehicle to complete the journey, it includes all delay.



Stream Speed Length

below 15 30

15 -25 60

above 25 90

6.3 Spot Speed Studies

When we measure the traffic parameter over a short distance, we generally measure the spot

speed. A spot speed is made by measuring the individual speeds of a sample of the vehicle

passing a given spot on a street or highway. Spot speed studies are used to determine the speed

distribution of a traffic stream at a specific location. The data gathered in spot speed studies

are used to determine vehicle speed percentiles, which are useful in making many speed-related

decisions. Spot speed data have a number of safety applications, including the following

1. Speed trends,

2. Traffic control planning,

3. Accidental analysis,

4. Geometric design,

5. Research studies.

6.4 Methods of Measurement

Methods of conducting spot speed Studies are divided into two main categories: Manual and

Automatic. Spot speeds may be estimated by manually measuring the time it takes a vehicle

to travel between two defined points on the roadway a known distance apart (short distance),

usually less than 90m. Distance between two points is generally depending upon the average

speed of traffic stream. Following tables gives recommended study length (in meters) for various

average stream speed renages (in kmph) Following are the some methods to measure spot speed

of vehicles in a traffic stream, in which first two are manual methods and other are automatic:

6.4.1 Pavement markings

In this method, markings of pavement are placed across the road at each end of trap. Observer

start and stops the watch as vehicle passes lines. In this method, minimum two observers



required to collect the data, of which one is stand at the starting point to start and stop the

stop watch and other one is stand at end point to give indication to stop the watch when vehicle

passes the end line. Advantages of this method are that after the initial installation no set-up

time is required, markings are easily renewed, and disadvantage of this is that substantial error

can be introduced, and magnitude of error may change for substitute studies and this method

is only applicable for low traffic conditions.

Observer 1Observer 2X

Study length

Vertical Referencepoint

Vertical ReferencepointEnd Timing

Start timing

Approaching Vehicle

Figure 6:1: Pavement Marking

6.4.2 Enoscope or Mirror box

Enoscope consists of a simple open housing containing a mirror mounted on a tripod at the

side of the road in such a way that an observer’s line of sight turned through 90o. The observer

stands at one end of section and on the other end enoscope is placed and measure the time

taken by the vehicle to cross the section (fig 6.2). Advantages of this method are that it simple

and eliminate the errors due to parallax and considerable time is required to time each vehicle,

which lengthen the study period and under heavy traffic condition it may be difficult to relate

ostentatious to proper vehicle are the disadvantages of enoscope method.

6.4.3 Road Detector (Pressure contact strips)

Pressure contact strips, either pneumatic or electric, can be used to avoid error due to parallax

and due to manually starting and stopping the chronometer or stopwatch. This is the best

method over short distance it gives quite relevant data and if it is connected through graphical

recorder then it gives continuous data automatically.



observer enoscope

Base length

x

Figure 6:2: Enoscope Method

6.4.4 Doppler-Principle Meters (Radar)

This is recently developed method, it automatically records speed, employs a radar transmitter-

receiver unit. The apparatus transmits high frequency electromagnetic waves in a narrow beam

towards the moving vehicle, and reflected waves changed their length depending up on the

vehicles speed and returned to the receiving unit, through calibration gives directly spot speed

of the vehicle.

6.4.5 Electronic-Principle Detectors (Photography)

In this method a camera records the distance moved by a vehicle in a selected short time. In this

exposure of photograph should be in a constant time interval and the distance travelled by the

vehicle is measured by projecting the films during the exposure interval. The main advantage

of method that, it gives a permanent record with 100% sample obtained. This method is quite

expensive and generally used in developed cities. In this we can use video recorder which give

more accurate result.

6.5 Data Collection Sheets

The measured data by the above techniques should be collected into some formats, following

are the some types of data collection sheets which are used for manual and automatic methods,

1. For Enoscope and Pavement Marking Methods

2. For automatic methods



S NO.TIME TAKEN (in sec)

Car/jeep 2 Wheeler HCV3 Wheeler Cycle LCV

1

10

9

8

7

6

5

4

3

2

Date:

Base Length:

Measurement Technique:

Type of road:

Weather:

Location:

Time:

Surveyor:

Figure 6:3: Data collection sheet for Enoscope and Pavement Marking Methods

Surveyor:

SpeedVehicle No. Speed Vehicle No.

Type of road:

Weather:

Location:

Spot Speed Data Collection Form

Data:

Time:


0 5

5 10

10 15

15 20

20 25

25 30

30 35

35 40

40 45

45 5050 55

55 6060 65

Speed Rangein kmph

TotalTally Mark Number

Car/Jeep Bus/Truck Car/Jeep Bus/Truck

Surveyor:

Location:

Weather:

Type of road:


Base Length:

Date:

Time:

Spot Speed Data Collection Form

Figure 6:4: Data collection sheet for Automatic Methods

6.6 Data Presentation

From the above methods, the collected data have to present into the some representable form,

this makes its calculation and analysis simpler and easier. The following methods to present

the spot speed data:



6.6.1 Frequency Distribution Table

After the collection of data in the given conditions, arrange the spot speed values in order to

their magnitudes. Then select an interval speed (e.g. 5 kmph) and make grouping of data

which come under this range. Now, prepare the frequency distribution table.

6.6.2 Frequency Distribution Curve

For each speed group, the % frequency of observations within the group is plotted versus the

middle (midmark) speed of the group(s). As shown in Fig 6.5. From this curve the modal

speed and pace of traffic flow can be determine. Generally the shape of the curve follows the

normal distribution curve, this because the most of the vehicles move on road near by mean

speed and very few deviate from mean speed.

6.6.3 Cumulative Frequency Distribution Curve

For each speed group, the % cumulative frequency of observations is plotted versus the higher

limit of the speed group (Fig 6.5). The cumulative frequency distribution curve, however,

results in a very useful plot of speed versus the percent of vehicles traveling at or below the

designated speed. For this reason, the upper limit of the speed group is used as the plotting

point. In both the distribution curve, the plots are connected by a smooth curve that minimizes

the total distance of points falling above the line and those falling below the line. A smooth

curve is defined as one without.

6.7 Distribution Characteristics

Common descriptive statistics may be computed from the data in the frequency distribution ta-

ble or determined graphically from the frequency and cumulative frequency distribution curves.

These statistics are used to describe two important characteristics of the distribution:

6.7.1 Measure of Central Tendency

Measure which helps to describe the approximate middle or centre of the distribution. Measures

of central tendency include the average or mean speed, the median speed, the modal speed,

and the pace.



0

5

20

25

10

15

10

20

100

90

80

70

60

304050

0

32 36 40 44 48 52 56 60 64

32 64565248444036 60

Mode

Pace

Speed(kph)

Median

$14\%$

$86\%$

$\% Veh in pace =86−14= 72\%$

Speed(kph)

$Cum

.\%fr

eq$

$\%

Fre

quen

cy

Figure 6:5: Frequency and Cumulative Frequency Distribution curve

Mean Speed

The arithmetic (or harmonic) average speed is the most frequently used speed statistics. It is

the measure of central tendency of the data. Mean calculated gives two kinds of mean speeds.

vt =Σfivi

n(6.1)

where, vt is the mean or average speed, vi is the individual speed of the ith vehicle, fi is the

frequency of speed, and n is the total no of vehicle observed (sample size). Time mean Speed

If data collected at a point over a period of time, e.g. by radar meter or stopwatch, produce

speed distribution over time, so the mean of speed is time mean speed. Space mean Speed

If data obtained over a stretch (section) of road almost instantaneously, aerial photography or

enoscope, result in speed distribution in space and mean is space mean speed. Distribution

over space and time are not same. Time mean speed is higher than the space mean speed. The

spot speed sample at one end taken over a finite period of time will tend to include some fast

vehicles which had not yet entered the section at the start of the survey, but will exclude some

of the slower vehicles. The relationship between the two mean speeds is expressed by:

vt = vs +σ2

s

vs

(6.2)

where, vt and vs are the time mean speed and space mean speed respectively. And σs is the

standard deviation of distribution space.

Median Speed

The median speed is defined as the speed that divides the distribution in to equal parts (i.e.,

there are as many observations of speeds higher than the median as there are lower than



the median). It is a positional value and is not affected by the absolute value of extreme

observations. By definition, the median equally divides the distribution. Therefore, 50% of all

observed speeds should be less than the median. In the cumulative frequency curve, the 50th

percentile speed is the median of the speed distribution. Median Speed = v50

Pace

The pace is a traffic engineering measure not commonly used for other statistical analyses. It is

defined as the 10Km/h increment in speed in which the highest percentage of drivers is observed.

It is also found graphically using the frequency distribution curve. As shown in fig 6.5. The

pace is found as follows: A 10 Km/h template is scaled from the horizontal axis. Keeping this

template horizontal, place an end on the lower left side of the curve and move slowly along the

curve. When the right side of the template intersects the right side of the curve, the pace has

been located. This procedure identifies the 10 Km/h increments that intersect the peak of the

curve; this contains the most area and, therefore, the highest percentage of vehicles.

Modal Speed

The mode is defined as the single value of speed that is most likely to occur. As no discrete values

were recorded, the modal speed is also determined graphically from the frequency distribution

curve. A vertical line is dropped from the peak of the curve, with the result found on the

horizontal axis.

6.7.2 Measure of Dispersion

Measures describe the extent to which data spreads around the centre of the distribution.

Measures of dispersion include the different percentile speeds i.e. 15th, 85th,etc. and the

standard deviation.

Standard Deviation

The most common statistical measure of dispersion in a distribution is the standard deviation.

It is a measure of how far data spreads around the mean value. In simple terms, the standard

deviation is the average value of the difference between individual observations and the average

value of those observations. The Standard deviation, σs, of the sample can be calculated by

σs =

√

Σfi(vi − vv)2

n − 1(6.3)



Percentile Speeds

The 85th and 15th percentile speeds give a general description of the high and low speeds

observed by most reasonable drivers. It is generally thought that the upper and lower 15% of

the distribution represents speeds that are either too fast or too slow for existing conditions.

These values are found graphically from the cumulative frequency distribution curve of Figure

6.4. The curve is entered on the vertical axis at values of 85% and 15%. The respective speeds

are found on the horizontal axis. The 85th and 15th percentile speeds can be used to roughly

estimate the standard deviation of the distribution σest, although this is not recommended when

the data is available for a precise determination.

σest =v85 − v15

2(6.4)

The 85th and 15th percentile speeds give insight to both the central tendency and dispersion of

the distribution. As these values get closer to the mean, less dispersion exists and the stronger

the central tendency of the distribution becomes.

The 98th percentile speed is also determining from the cumulative frequency curve, this

speed is generally used for geometric design of the road.

6.8 Data Analysis

6.8.1 Standard Error of the mean

The means of different sample taken from the same population are distributed normally about

the true mean of population with a standard deviation, is known as standard error.

Se =σs√n

(6.5)

6.8.2 Sample Size

Generally, sample sizes of 50 to 200 vehicles are taken. In that case, standard error of mean is

usually under the acceptable limit. If precision is prior then minimum no. of sample should be

taken, that can be measured by using the following equation.

nr =Z2σ2

s

S2e

(6.6)

where, nr is the no. of sample required, σs is the Standard deviation, Z is value calculated from

Standard Normal distribution Table for a particular confidence level (i.e. for 95% confidence

Z=1.96 and for 99.7% confidence Z=3.0) and Se is the permissible (acceptable) error in mean

calculation.



6.8.3 Precision and Confidence Intervals

Confidence intervals express the range within which a result for the whole population would

occur for a particular proportion of times an experiment or test was repeated among a sample

of the population. Confidence interval is a standard way of articulate the statistical accuracy

of an experiment based assessment. If assess has a high error level, the equivalent confidence

interval will be ample, and the less confidence we can have that the experiment results depict

the situation among the whole population. When quoting confidence It is common to refer to

the some confidence interval around an experiment assessment or test result. So, the confidence

interval for estimated true mean speed can be calculated by

µ = vt ± Zσs (6.7)

where, µ is the confidence interval, vt is mean speed, σs is standard deviation and Z is constant

for specified confidence.

6.8.4 Numerical Example

Using the spot speed data given in the following table, collected from a freeway site operating

under free-flow conditions: (i) Plot the frequency and cumulative frequency curves for these

data; (ii) Obtain median speed, modal speed, pace, and percent vehicles in pace from these

plots; (iii) Compute the mean and standard deviation of the speed distribution; (iv) The

confidence bounds on the estimate of the true mean speed of the underlying distribution with

95% confidence? With 99.7% confidence; and (v) Based on these results, compute the sample

size needed to achieve a tolerance of ±1.5 kmph with 95% confidence.

Solution For the spot speed study, first draw a frequency distribution table show below.

1. From the table 6.3, we can draw frequency distribution and cumulative frequency distri-

bution curve.(shown in Fig 6.6 and 6.7)

2. From the curves, Median speed, v50 = 43 kmph; Modal speed, = 38 kmph; the Pace =

33 - 43 kmph; Percent vehicles in pace = 54-20= 34%; and the 85th Percentile speed =

58 kmph.

3. Mean is calculated by using

vt =Σfivi

n

=5950

130= 45.77 kmph



Speed Range Frequency fi

21-25 2

26-30 6

31-35 18

36-40 25

41-45 19

46-50 16

51-55 17

56-60 12

61-65 7

66-70 4

71-75 3

76-80 1

Speed Range Mid speed Vi Frequency fi % fi %∑

fi fi × Vi fi × (Vi − Vm)2

21-25 23 2 2% 2% 46 1036.876

26-30 28 6 5% 6% 168 1894.473

31-35 33 18 14% 20% 594 2934.959

36-40 38 25 19% 39% 950 1509.024

41-45 43 19 15% 54% 817 145.7041

46-50 48 16 12% 66% 768 79.6213

51-55 53 17 13% 79% 901 888.8284

56-60 58 12 9% 88% 696 1795.101

61-65 63 7 5% 94% 441 2078.296

66-70 68 4 3% 97% 272 1976.828

71-75 73 3 2% 99% 219 2224.544

76-80 78 1 1% 100% 78 1038.822

Total 130 100% 5950 17603.08

Table 6:1: Solution of the example problem



0 908070605040302010

0\%

5\%

10\%

15\%

20\%

25\%

33 38 43

pace

Mode

Fre

quen

cy(\

%)

Speed (kmph)

Figure 6:6: Frequency Distribution Curve

0 10 20 30 40 50 60 70 80 90

30\%

40\%

50\%

60\%

70\%

80\%

90\%

100\%

32 5843

$v_85$

$v_50$

$v_15$

Speed (kmph)

cum

ulat

ive

freq

uenc

y(\%

)

10\%

15\%

20\%

85\%

Figure 6:7: Cumulative Frequency Distribution Curve

Standard Deviation of the Speed

σs =

√

Σfi(vi − vt)2

n − 1

=

√

17603.08

130 − 1= 11.7 kmph

4. The confidence bounds on the estimate of the true mean speed of the underlying distri-

bution are:

µ = vt ± Zσs

(a) For 95% confidence, Z= 1.96, so

µ = 45.77 ± 1.96 × 11.7 = 45.77 ± 22.93 kmph

(b) For 99.7% confidence, Z= 3.0, so

µ = 45.77 ± 3.0 × 11.7 = 45.77 ± 35.1 kmph



Parameter Value

Median speed 43 kmph

Modal speed 38 kmph

Pace 33-43 kmph

Vehicles in pace 34%

Mean speed 45.77 kmph

Standard Deviation 11.7 kmph

85th percentile speed 58 kmph

15th percentile speed 32 kmph

98th percentile Speed 72 kmph

Confidence interval

For 95%. 45.7722.93 kmph

For 99.7% 45.7725.1 kmph

Required sample Size 234

Table 6:2: Result of the example problem

5. Sample size required for 95% confidence with acceptable error of 1.5 kmph

nr =Z2σ2

s

S2e

=1.962 × 11.72

1.52= 234.

So, given sample size is not sufficient and we require minimum 234 samples to achieve

that confidence with given acceptable error. The results are summaries in table 6.8.4

6.9 Location for Speed Studies

The speed studies are accompanied for eminently logical purposes that will influence what

traffic engineering measures are implemented in any given case. The location at which speed

measurements are taken must conform to the intentional purpose of the study. The guiding phi-

losophy behind spot speed studies is that measurements should include drivers freely selecting

their speeds, unaffected by traffic congestion. For example if driver approaches to a toll plaza,

then he has to slow his speed, so this is not suitable location to conduct the study, measure-

ments should be taken at a point before drivers start to decelerate. Similarly, if excessive speed

around a curve is thought to be contributing to off-the-road accidents, speed measurements



should be taken in advance of the curve, before deceleration begins. It may also be appro-

priate, however, to measure speeds at the point where accidents are occurring for evaluation

with approach speeds. This would allow the traffic engineer to assess whether the problem is

excessive approach speed or that drivers are not decelerating sufficiently through the subject

geometric element, or a combination of both. A study of intersection approach speeds must

also be taken at a point before drivers begin to decelerate. This may be a moving point, given

that queues get shorter and longer at different periods of the day.

6.10 Summary

This chapter has presented the basic concepts of speed studies. Spot speed studies are conducted

to estimate the distribution of speeds of vehicle in the traffic stream at a particular position

on highway. This is done by recording the speeds of vehicle at the specified location. These

data are used to obtain speed characteristics such as mean speed, modal speed, pace, standard

deviation and different percentile of speeds. The important factors which should consider during

plan of studies is the location of study, time and duration of study. The data sample collected

should contain samples size. These gives precision and accuracy of result.

6.11 References


2. Nicholas J Garber Lester A Hoe. Traffic and Highway Engineering. Cengage Learning

Product, Fourth Edition, 2009.

3. Theodore M Matson, Wilbure S smith, and Fredric W Hurd. Traffic engineering, 1955.

4. R P Roess, S E Prassas, and W R McShane. Traffic Engineering. Pearson Education

International, 2005.


Transportation Systems Engineering 7. Measurement along a Length of Road

Chapter 7

Measurement along a Length of Road

7.1 Overview

This is normally used to obtain variations in speed over a stretch of road. Usually the stretch

will be having a length more than 500 meters. We can also get speed ,travel time and delay.

Speed and travel time are the most commonly used indicators of performance for traffic facilities

and networks. Delays are often used to measure the performance of traffic flow at intersections.

7.2 Travel time study

Travel time is the elapsed time it takes for a vehicle to traverse a given segment of a street.

Travel time studies provide the necessary data to determine the average travel time. Combined

with the length of the corridor under study, this data can be used to produce average travel

speed. Travel time and delay are two of the principal measures of roadway system performance

used by traffic engineers, planners and analysts. Since vehicle speed is directly related to travel

time and delay, it is also an appropriate measure-of-performance to evaluate traffic systems.

A study conducted to determine the amount of time required to traverse a specific route

or section of a street or highway. The data obtained provide travel time and travel speed

information but not necessarily delay. This term is often used to include speed and delay

study. Travel time may be defined as the total elapsed time of travel, including stop and delay,

necessary for a vehicle to travel from one point to another point over a specified route under

existing traffic condition.

7.3 Delay studies

Delay is defined as an extra time spent by drivers against their expectation. Delay can have

many forms depending on different locations. A study made to provide information concerning



the amount, cause, location, duration and frequency of delay as well as travel time and similar

value. The time lost by traffic due to traffic friction and traffic control device is called delay.

7.4 Types of Delay

1. Congestion delay- Congestion delay is the delay caused by the constricting or slowing down

effect of overloaded intersections, inadequate carriageway widths, parked cars, crowded

pavement and similar factor.

2. Fixed Delay- The delay to which a vehicle is subjected regardless of the amount of traffic

volume and interference present.

3. Operational Delay-The delay caused by interference from other component of the traffic

stream. Examples include time lost while waiting for a gap in a conflicting traffic stream,

or resulting from congestion, parking maneuvers, pedestrians, and turning movement.

4. Stopped Delay- The time a vehicle is not moving.

5. Travel Time Delay- The difference between the actual time required to traverse a section

of street or highway and the time corresponding to the average speed of traffic under

uncongested condition. It includes acceleration and deceleration delay in addition to

stopped delay.

6. Approach Delay -Travel time delay encountered to an approach to an intersection.

7.5 Purpose of travel time and Delay Studies

1. The purpose of a Travel Time and Delay Study is to evaluate the quality of traffic move-

ment along a route and determine the locations, types, and extent of traffic delays by

using a moving test vehicle.

2. This study method can be used to compare operational conditions before and after road-

way or intersection improvements have been made. It can also be used as a tool to assist

in prioritizing projects by comparing the magnitude of the operational deficiencies (such

as delays and stops) for each project under consideration.

3. The Travel Time and Delay Study can also be used by planners to monitor level of service

for local government comprehensive plans.



4. The methodology presented herein provides the engineer with quantitative information

with which he can develop recommendations for improvements such as traffic signal re-

timing, safety improvements, turn lane additions, and channelization enhancements

7.6 Method for obtaining travel time and delay study

1. Floating Car Method: Floating car data are positions of vehicles traversing city streets

throughout the day. In this method the driver tries to float in the traffic stream passing

as many vehicles as pass the test car. If the test vehicle overtakes as many vehicles as

the test vehicle is passed by, the test vehicles should, with sufficient number of runs,

approach the median speed of the traffic movement on the route. In such a test vehicle,

one passenger acts as observer while another records duration of delays and the actual

elapsed time of passing control points along the route from start to finish of the run.

2. Average Speed Method: In this method the driver is instructed to travel at a speed

that is judge to the representative of the speed of all traffic at the time.

3. Moving-vehicle method: In this method, the observer moves in the traffic stream and

makes a round trip on a test section. The observer starts at section, drives the car in a

particular direction say eastward to another section, turns the vehicle around drives in

the opposite direction say westward toward the previous section again. Let, the time in

minutes it takes to travel east (from X-X to Y-Y) is ta, the time in minutes it takes to

travel west (from Y-Y to X-X) is tw, the number of vehicles traveling east in the opposite

lane while the test car is traveling west be ma, the number of vehicles that overtake the

test car while it is traveling west be mo, and the number of vehicles that the test car

passes while it is traveling west from be mp. The volume (qw) in the westbound direction

X Y

YX

West

East

Figure 7:1: Illustration of moving observer method



can then be obtained from the expression and

qw =ma + mo − mp

ta + tw

the average travel time in the westbound direction is obtained from

tw(avg) = tw −mo − mp

qw

4. Maximum-car method: In this procedure, the driver is asked to drive as fast as is safely

practical in the traffic stream without ever exceeding the design speed of the facility.

5. Elevated Observer method: In urban areas, it is sometime possible to station observers

in high buildings or other elevated points from which a considerable length of route may

be observed. These investigator select vehicle at random and record; time, location and

causes-of-delay. The drawback is that it is sometime difficult to secure suitable points for

observation throughout the length of the route to be studied.

6. License Plate Method: when the amount of turning off and on the route is not great

and only over all speed value are to be secured, the license-plate method of speed study

may be satisfactorily employed. Investigator stationed at control point along the route

enters, on a time control basis, the license-plate numbers of passing vehicles. These

are compared from point to point along the route, and the difference in time values,

through use of synchronized watches, is computed. This method requires careful and

time-consuming office work and does not show locations, causes, frequency, or duration of

delay. Four basic methods of collecting and processing license plates normally considered

are:

(a) Manual: collecting license plates via pen and paper or audio tape recorders and

manually entering license plates and arrival times into a computer.

(b) Portable Computer: collecting license plates in the field using portable computers

that automatically provide an arrival time stamp.

(c) Video with Manual Transcription: collecting license plates in the field using

video cameras or camcorders and manually transcribing license plates using human

observers.

(d) Video with Character Recognition: collecting license plates in the field using

video, and then automatically transcribing license plates and arrival times into a

computer using computerized license plate character recognition.



7. Photographic Method: This method is primarily a research tool, it is useful in studies of

interrelationship of several factors such as spacing, speeds, lane usage, acceleration rates,

merging and crossing maneuvers, and delays at intersections. This method is applicable

to a short test section only.

8. Interview Method: this method may be useful where a large amount of material is

needed in a minimum of time and at little expense for field observation. Usually the

employees of a farm or establishment are asked to record their travel time to and from

work on a particular day.

9. Highway Capacity Manual 2000 or (Cycle- based method): This method is appli-

cable to all under saturated signalized intersections. For oversaturated conditions, queue

buildup normally makes the method impractical. The method described here is applica-

ble to situations in which the average maximum queue per cycle is no more than about

20 to 25 veh/ln. When queues are long or the demand to capacity ratio is near 1.0,

care must be taken to continue the vehicle-in-queue count past the end of the arrival

count period, vehicles that arrived during the survey period until all of them have exited

the intersection.as detailed below. This requirement is for consistency with the analytic

delay equation used in the chapter text.method does not directly measure delay during

deceleration and during a portion of acceleration, which are very difficult to measure with-

out sophisticated tracking equipment. However, this method has been shown to yield a

reasonable estimate of control delay.

The method includes an adjustment for errors that may occurred when this type of

sampling technique is used, as well as an acceleration-deceleration delay correction factor

Table 7:1. The acceleration-deceleration factor is a function of the typical number of

vehicles in queue during each cycle and the normal free-flow speed when vehicles are

unimpeded by the signal. Before beginning the detailed survey, the observers need to

make an estimate of the average free-flow speed during the study period. Free-flow speed

is the speed at which vehicles would pass unimpeded through the intersection if the signal

were green for an extended period.be obtained by driving through the intersection a few

times when the signal is green and there is no queue and recording the speed at a location

least affected by signal control. Typically, the recording location should be upstream

about midblock. Table 7:2 is a worksheet that can be used for recording observations and

computation of average time-in-queue delay Steps for data reduction

(a) Sum each column of vehicle-in-queue counts, then sum the column totals for the

entire survey period.



Free-Flow Speed ≤ 7 Vehicles 8-19 Vehicles 20-30 Vehicles

≤ 60km/h 5 2 1

60-71 km/h 7 4 2

≥ 71 km/h 9 7 5

Table 7:1: Acceleration-Deceleration Delay Correction Factor, CF (seconds)

(b) A vehicle recorded as part of a vehicle-in-queue count is in queue, on average, for the

time interval between counts. The average time-in-queue per vehicle arriving during

the survey period is estimated.

dvq =

(

Is ×ΣViq

Vtot

)

0.9

where, Is = interval between vehicle-in-queue counts (s), ΣViq = sum of vehicle-in-

queue counts (veh), Vtot = total number of vehicles arriving during the survey period

(veh), and 0.9 = empirical adjustment factor. The 0.9 adjustment factor accounts

for the errors that may occur when this type of sampling technique is used to derive

actual delay values, normally resulting in an overestimate of delay.

(c) Compute the fraction of vehicles stopping and the average number of vehicles stop-

ping per lane in each signal cycle, as indicated on the worksheet.

(d) Using Table 7:1, look up a correction factor appropriate to the lane group free-flow

speed and the average number of vehicles stopping per lane in each cycle. This

factor adds an adjustment for deceleration and acceleration delay, which cannot be

measured directly with manual techniques.

(e) Multiply the correction factor by the fraction of vehicles stopping, and then add this

product to the time-in-queue value of Step 2 to obtain the final estimate of control

delay per vehicle.

Numerical Example

A test was conducted to determine the delay in an intersection. Table 7:3 presents a sample

computation on direct observation of vehicle-in-queue counts at the intersection. The traffic

signal at the intersection operates with a cycle time of 115 sec. The test was conducted on the

2 lane road over a 15-min period, which is almost thirteen cycles . Count interval was 15-s.

The total number of vehicle is 530 and the total number of stopped vehicle is 223. Assume the

free flow speed to be 65 km/h and the empirical adjustment factor 0.9



Site InformationGeneral Information

Analyst

Agency or Company

Date PerformedAnalysts Time Period

Input Initial Parameters

Number of lanes, NFree−flow speed,FFS (km/h)

Intersection

Area TypeJurisdiction

Analysis Year

OthersCAD

INTERSECTION CONTROL DELAY WORKSHEET

Cycle length,C (s)

Input Field Data

Total

Number of vehicles in queueCount interval

1 2 3 4 5 6 7 8 9 10

ClockTime

CycleNumber

Computations

Time−in−queue per vehicle,d_{vq}

No.of vehicles stopping per lane each cycle =

Number of cycles surveyed,N_{s}

Accel/Decel correction factor, CF(Ex.A1G−2)

Fraction of vehicles stopping, FVS =

Survey count interval,ls (s)

Total vehicle arriving,Varr

Stopped-vehicle count,Vstopped

Total vehicles in queue,ΣVtvq =

Accel/Decek correction delay,dacl = FV S × CF

Control delay/vehicles,d = dvq + dacl

Figure 7:2: Intersection delay worksheet

General Information Site Information

AnalystAgency or CompanyDate Performed

Analysis time period

Input initial Parameters

Intersection

Area Type

Jurisdiction

Analysis Year

Number of lanes, N

Free−flow speed,FFS (km/h)

Cycle length, C (s)

Input Field Data

Total 37 64 88 ’" 61 4 0 6

ClockTime

Cycle

Number

Number of vehicles in QueueCount Interval

1 2 4 5 6 7 8 9 10

2

2

1

1

0

0

0

0

0

0

0

0

2

0

0

2

0

0

0

0

12

6

2

13

3

4

12

9

15

16

14

13

13

16

12

12

15

14

10

10

9

8

"

"

3

8

12

7

6

7

6

7

"

3

6

7

5

4

5

3

4

1

2

3

4

5

6

7

8

4:34

4:42

4:47

Others

1999

530

223

265

15

CBD

Survey count interval,Is (s)

Stopped vehicle count,Vstop

Total vehicle arriving,Vtot

Cicera&Beimanc

Figure 7:3: Example of the intersection control delay worksheet

Solution:

1. Number of lane, N=2

2. Free-flow Speed, FFS =65 km/h

3. Survey count interval, Is =15 sec

4. Total vehicle in queue, ΣViq = 371

5. Total vehicles arriving, Vtot = 530

6. Stopped vehicles count, Vstop = 223

7. No of Cycle Surveyed, Nc=7.8

8. Accel/Decel correction factor, CF=4 (from Table 7.1)



9. No. Of Vehicles stopped per lane each cycle

VstopNc × N = 223

7.8×2= 14

10. Fraction of vehicles stopping,

FV S = Vstop

Vtot= 223

530= 0.42

11. Time-in-queue per vehicle ,

dvq = (Is ×ΣViq

Vtot)0.9 = 9.5sec

12. Accel/Decel correction delay,

dad = FV S × CF = 0.42 × 4 = 1.7sec

13. Control delay/vehicle,

d = dvq + dad = 11.2sec

7.7 Summary

The information assembled as part of this travel time and delay study forms a baseline for

future assessment. This study helps to determine the amount of time required to travel from

one point to another on a given route. Often, information may also be collected on the locations,

durations, and causes of delays. Good indication of the level of service and identifying problem

locations

7.8 References

1. Highway capacity manual, 2000. chapter-16.

2. Manual on uniform traffic studies, 2000. Topic No. 750-020-007 Travel Time and Delay

Study.

3. Travel Time Data Collection Handbook. 2019.


5. W S Hamburger J H Kell. Fundamentals of Traffic Engineering. 1989.



Transportation Systems Engineering 9. Intrusive Technologies

Chapter 9

Intrusive Technologies

9.1 Introduction

Typical examples of intrusive technologies, their sensor types and installation locations are

shown in Fig. 9:1. The first types of units (Fig. 9:1, Type 1) are passive magnetic or magne-

tometer sensors that are either permanently mounted within holes in the road, or affixed to the

road surface in some fashion. The unit communicates to a nearby base station processing unit

using either wires buried in the road, or wireless communications. The sensor has a circular or

elliptically offset zone of detection (i.e., the blue area).

The second types of units (Fig. 9:1, Type 2) use pneumatic tubes that are stretched across

the carriageway and affixed at the kerb side at both ends. Such systems are only be deployed

on a temporary basis, due to the fragile nature of tubes, which are easily damaged or torn up

by heavy or fast moving vehicles.

The third type (Fig. 9:1, Type 3) are inductive detector loops (IDL), consisting of coated

wire coils buried in grooves cut in the road surface, sealed over with bituminous filler. A ca-

ble buried with the loop sends data to a roadside processing unit. The zone of detection for

inductive loop sensors depends on the cut shape of the loop slots. The zones depending on

the overall sensitivity of system not correspond precisely to the slot dimensions. IDLs are a

cheap and mature technology. They are installed on both major roads and within urban areas,

forming the backbone detector network for most traffic control systems.

The fourth type of intrusive system is Weigh-In-Motion (WIM) shown in Fig. 9:2, detectors

that consist of a piezoelectric sensor (e.g. ‘bending-plate’ or fiber-optic) system laid in a chan-

nel across the road. These systems are relatively rare and are used in specific locations for

enforcement or access control. They are usually coupled with other systems, either intrusive or



Type:1. Embedded magnetometers2. Pneumatic tube detectors3. Inductive detector loops

23

1

1

Figure 9:1: Typical intrusive detector configurations, Source: IMAGINE- Collection Methods

for Additional Data

Signal sent

to processor

Figure 9:2: Weigh-In-Motion Detector system, Source

non-intrusive, to provide additional cross-checks on collected data.

9.2 Pneumatic Tube Detector

Pneumatic road tube sensors send a burst of air pressure along a rubber tube when a vehicles

tire passes over the tube. The pulse of air pressure closes an air switch, producing an electrical

signal that is transmitted to a counter or analysis software. The pneumatic road tube sensor

is portable, using lead-acid, gel, or other rechargeable batteries as a power source. The road

tube is installed perpendicular to the traffic flow direction and is commonly used for short-term

traffic counting, vehicle classification by axle count and spacing. Some data to calculate vehicle



gaps, intersection stop delay, stop sign delay, and saturation flow rate, spot speed as a func-

tion of vehicle class, and travel time when the counter is utilized in conjunction with a vehicle

transmission sensor.

Advantages

1. Cheap and self-contained, the easiest to deploy of all intrusive systems, recognized tech-

nology with acceptable accuracy for strategic traffic modeling purposes, hence very widely

used.

2. Axle-based classification appears attractive, given sub-vehicle categories are partially axle

based.

Disadvantages

1. Some units are not counted or classify vehicles.

2. Tube installations are not durable, the life of tubes are less than one month only.

3. The tube detectors are not suitable for high flow and high speed roads.

4. Units should not be positioned where there is the possibility of vehicles parking on the

tube.

5. It cant detect the two wheelers.

9.3 Inductive Detector Loop (IDL)

Oscillating electrical signal is applied to the loop. The metal content of a moving vehicle chassis

changes the electrical properties of circuit. Changes are detected at a roadside unit, triggering

a vehicle event. A single loop system collects flow and occupancy. The speed can be calculated

by the assumptions that are made for the mean length of vehicles. Two-loop systems collect

flow, occupancy, vehicle length, and speed.

Advantages

1. It is a very cheap technology. Almost every dynamic traffic control system in this world

uses IDL data.

Disadvantages



Electronics unitController cabinet

Roadway section

Lead−in conduit

Conduit−to−curb runPullbox

Shielded lead−in cable

Splice in pullbox

1 ft = 0.305 melectrical interference

Twisted wire to suppressLoop wire plan

Roa

dway

cen

terli

ne3 turns

Loop sawcut plan

Cur

b lin

e

3 ft 6 ft 3 ft12 ft

Figure 9:3: Schematic diagram of single loop detectors, source

1. Loops are damaged by utility and street maintenance activities or penetration of water.

2. IDLs with low sensitivity fail to detect vehicles with speed below a certain threshold,

and miscount vehicles with complex or unusual chassis configurations, or vehicles with

relatively low metal content (e.g. motorcycles).

3. IDL data supplied to traffic control systems have a very low sample rate.

4. Not suitable for mounting on metallic bridge decks.

5. Some radio interference occurs between loops in close proximity with each other.

9.3.1 Single Loop Detectors

A typical single loop system is shown in Fig. 9:3. The system consists of three components: a

detector oscillator, a lead-in cable and a loop embedded in the pavement. The size and shape

of loops largely depend on the specific application. The most common loop size is 1.83 m by

1.83 m and shape is hexagonal as single turn or two or three turns as shown in Fig. 9:3. When

a vehicle stops or passes over the loop, the inductance of the loop is decreased.The decreased

inductance then increases the oscillation frequency and causes the electronics unit to send a

pulse to controller, indicating the presence or passage of a vehicle. Single loop detectors output

predicts occupancy and traffic count data within specific time intervals like 20 sec, 30 sec.

9.3.2 Dual-loop Detectors

Dual-loop detectors are also called speed traps, T loops, or double loop detectors. In a dual-loop

system, two consecutive single inductance loops, called “M loop” and “S loop”, are embedded



lloop ldist

T = t2 T = t1

Figure 9:4: Schematic diagram of dual loop detectors

a few distance apart as shown in Fig. 9:4. With such a design, when one of them detects a

vehicle, timer is automatically started in the dual-loop system and runs until the same vehicle

is detected by other loop.Thus, in addition to outputs of vehicle count and occupancy data,

individual vehicle speeds can be trapped through the dividend of the distance between those

two single loops ldist by the elapsed time. Speed trap is defined as the measurement of the

time that a vehicle requires to travel between two detection points. Spot speed is measured by

following Eqn. 9.1.

Speed =ldist

t2t1(9.1)

where,

ldist = Distance between two loops in meters

t1 = Vehicle entry time at first loop in sec

t2 = Vehicle entry time at second loop in sec

Dual-loop detectors can also be used to measure vehicle lengths with extra data extracted from

controllers records. The length of vehicle is measured by following Eqn. 9.2:

Lvehicle =Speed|ot2 + 0t1|

2(9.2)

where,

Lvehicle = Length of vehicle in meters.

oti = on-time for loop detector i; Speed in m/sec

Example-1

If the vehicle entering the freeway in loop M at time 8:32:22:00 am and leaving loop N at

time 8:32:22:15 am, the distance between two loops will be 3.66 m. Find the spot speed of the

vehicle. Also find the length of the vehicle if time occupancy for M - loop is 0.25sec and 0.29

for N - loop.



Vehicle

VehicleSingle Loop

Single LoopDetector

Detector

lv ld

Figure 9:5: Layout of a roadway segment with single loop detectors

Solution:

Step 1 Spot Speed calculated from the equation 1, where given that the distance between

two loops are 3.66m and entry, exit times are 8:32:22:00 and 8:32:22:15 substitute in Eqn. 9.1.

SpotSpeed = (3.66)/(15 − 0)/100 = 24.4 m/sec.

Step 2 The vehicle length can obtained by the spot speed of the vehicle, so substitute the

occupancy times at exit and entry in the Eqn. 9.2.

Lvehicle =(52.7/3.6)|0.25 + 0.29|

2= 3.95 m. (9.3)

9.3.3 Speed Estimation by Single Loop

Fig. 9:5 shows a two-lane unidirectional roadway segment with single loop detectors installed.Assume

that the detection zone length is ld and is equal to the detector length, the length of the vehicle

is lv, the speed of the vehicle is S, then the actual time (the time period that the vehicle is over

the detector) can be calculated by:

S =EV L

to(9.4)

where,

S = Spot speed in m/sec

EV L =vehicle length lv + detector length ld

to = Occupancy time

There are many algorithms for estimating speed by single loop. The most common method is

based on the relationship between fundamental traffic variables. It uses a constant or a function

to convert loop occupancy into density. The variables include inductive loop length, average



vehicle length, occupancy, and traffic volume.For the given number of vehicle and duration of

the observed data the specimen speed can find by following Eqn. 9.5 is shown below.

s =N

T × O × g(9.5)

where,

S = Space mean speed in m/sec

N = Number of vehicles in the observed interval

T = Observation interval in sec

O = occupancy time

g = speed correction factor; (based upon assumed vehicle length, detector configuration, and

traffic conditions) Most of the algorithms followed as (40.9/6.55) for average vehicle length

6.55m.

Example-2

The length of vehicle is 4 m and the length of loop detector zone is 1.83 m. The time occupancy

in the loop is 0.3 sec, find the spot speed of the vehicle?

Solution:

From the given data the average vehicle length is 4 m and the length of loop detector zone is

1.833 m, the time occupancy in loop is 0.3 sec substitute in Eqn. 9.1.

spotspeed =EV L

to

s =4 + 1.83

0.3= 19.4 m/sec.

Example-3

In freeway 2500 vehicles are observed during 300 sec interval. The loop occupancy is 75 per-

centages and the average length of vehicle observed as 6.55 m, find the space mean speed on

the freeway section?

Solution

Given data is number of vehicle is 2500, duration is 300 sec, loop occupancy is 75 percent-

age, the average length of vehicle is 6.55 so speed correction factor is 40.99/6.55 substitute in

Eqn. 9.5.



specimenspeed =N

T × O × g

s =2500 × 6.55

300 × 0.75 × 40.9= 6.405 Kmph

9.3.4 Vehicle Signature

Loop detectors detect the frequency changes from zero to different level, the inductance changes

are computed by change in frequency. The change in inductance due to the presence of vehicle

is recorded at a small time interval. The waveform obtained by plotting the sampled inductance

changes is referred to as the vehicle inductive waveform or inductance signature.This waveform

depends on number of vehicle parameters such as vehicle length, speed, and metal surface of the

vehicle. Fig. 9:6 shows an inductive waveform of a typical passenger car.Horizontal axis records

data points at 10 milliseconds interval. This is the common shape of inductance waveform

that has one peak in the middle with monotonic decrease in both sides. Vehicle signatures are

functions of vehicle speed and vehicle type, so many features can be derived from the vehicle

signatures directly or indirectly. Volume and occupancy are directly derived from processing

raw vehicle signatures whereas speed is estimated based on the vehicle signature feature vectors.

Vehicle length is obtained based on vehicle speed. By combining vehicle length with existing

vehicle signature features, vehicle classification can be measured. It is easy to observe signature

differences arising from the vehicle speed. Duration or occupancy has an inverse proportional

relationship with speed while slew rate shows a proportional correspondence with speed.

A series of vehicle signature acquired by the Inductive Loop Detectors located at upstream

and downstream of a freeway and different distance measures to find the re identification accu-

racy level. Double-axle trucks produce a double picked vehicle signature when the resolution

of detector is adequate. Thus, it can be easily used for vehicle-type identification purposes.

9.4 Magnetometers/Passive magnetic systems

Magnetometers monitor for fluctuations in the relative strength of the Earths magnetic field,

which is changed by the presence of a moving metal object i.e., a vehicle. A single passive mag-

netic system collects flow and occupancy. Two magnetometer systems collect flow, occupancy,

vehicle length, and speed.



Vehicle Signature50

0

−50

−100

−150

−200

−250

−3000 10 20 30 40

Time (ms)50 60 70 80 90

Indu

ctan

ce C

hang

e (n

H)

Figure 9:6: Inductive waveform of a typical passenger car, source

Two types of magnetic field sensors are used for traffic flow parameter measurement. The

first type, the two-axis fluxgate magnetometer, detects changes in vertical and horizontal com-

ponents of the Earth s magnetic field produced by a ferrous metal vehicle. The two-axis fluxgate

magnetometer contains a primary winding and two secondary sense windings on a coil surround-

ing high permeability soft magnetic material core. The second type of magnetic field sensor is

the magnetic detector, more properly referred to as an induction or search coil magnetometer

shown in Fig. 9:7. It detects the vehicle signature by measuring the change in the magnetic

lines of flux caused by the change in field values produced by a moving ferrous metal vehicle.

These devices contain a single coil winding around a permeable magnetic material rod core.

However, most magnetic detectors cannot detect stopped vehicles, since they require a vehicle

to be moving or otherwise changing its signature characteristics with respect to time.

Advantages

1. More usually mounted in a small hole in road surface and hardwired to the processing

unit.

Suitable for deployment on bridges.

Disadvantages

1. Possibly damaged by utility maintenance activities, as with IDLs.



metal vehicleproduced by

magnetic field

+

W E

N

SW W W W W

N N N N N

E E E E E

S S S S S

VEHICLE MAGNETIC INFLUENCEVARIATIONSENSOR SIGNALVARIATION

COMPASS

TO THE EARTHS MAGNETIC FIELD

Magnetic dipoleEarth’s magnetic fieldin the absence of

ferrous materialsanomaly in Earth’sResultant magnetic

(a) Magnetic anomaly induced in the Earth’s magnetic field by a magnetic dipole

(b) Perturbation of Earth’s magnetic field by a ferrous metal vehicle

Figure 9:7: Weigh-In-Motion Detector system (Source: FHWA vehicle detection manual)

9.5 Weigh-In-Motion (WIM) systems

9.5.1 Bending Plate

Bending plate WIM systems utilize plates with strain gauges bonded to the underside. The

system records the strain measured by strain gauges and calculates the dynamic load. Static

load is estimated using the measured dynamic load and calibration parameters. Calibration

parameters account for factors, such as vehicle speed and pavement or suspension dynamics

that influence estimates of the static weight. The accuracy of bending plate WIM systems can

be expressed as a function of the vehicle speed traversed over the plates, assuming the system

is installed in a sound road structure and subject to normal traffic conditions.

Advantages

Bending plate WIM systems is used for traffic data collection as well as for weight enforcement

purposes. The accuracy of these systems is higher than piezoelectric systems and their cost is

lower than load cell systems. Bending plate WIM systems do not require complete replacement

of the sensor.

Disadvantages

Bending plate WIM systems are not as accurate as load cell systems and are considerably more

expensive than piezoelectric systems.



9.5.2 Piezoelectric

Piezoelectric WIM systems contain one or more piezoelectric sensors that detect a change in

voltage caused by pressure exerted on the sensor by an axle and thereby measure the axle s

weight. As a vehicle passes over the piezoelectric sensor, the system records the sensor output

voltage and calculates the dynamic load. With bending plate systems, the dynamic load pro-

vides an estimate of static load when the WIM system is properly calibrated.

The typical piezoelectric WIM system consists of at least one piezoelectric sensor and two

ILDs. The piezoelectric sensor is placed in the travel lane perpendicular to the travel direction.

The inductive loops are placed upstream and downstream of the piezoelectric sensor. The up-

stream loop detects vehicles and alerts the system to an approaching vehicle. The downstream

loop provides data to determine vehicle speed and axle spacing based on the time it takes the

vehicle to traverse the distance between the loops. Fig. 9:8 shows a full-lane width piezoelectric

WIM system installation. In this example, two piezoelectric sensors are utilized on either side

of the downstream loop.

Advantages

Typical piezoelectric WIM systems are among the least expensive systems in use today in terms

of initial capital costs and life cycle maintenance costs. Piezoelectric WIM systems can be used

at higher speed ranges (16 to 112 kmph) than other WIM systems. Piezoelectric WIM systems

can be used to monitor up to four lanes.

Disadvantages

Typical piezoelectric systems are less accurate than load cell and bending plate WIM systems.

Piezoelectric sensors for WIM systems must be replaced at least once every 3 years.

Problems:

1. If the vehicle 10% time occupied by loop M and 32% time occupied by loop N, the distance

between two loops are 4.22 m find the spot speed of the vehicle. Also find the length of

the vehicle if time occupancy for M - loop is 0.26sec and 0.32 for N-loop.



Cabinet

Traffic flowdirections

Road shoulder

Inductiveloops (2)

WIM strip,full−length, PVC conduit

below ground2 places

Figure 9:8: WIM installation with full-length piezoelectric sensors Source: FHWA vehicle de-

tection manual

Solution: Length is 4.22 m and occupancy times are 0.32 and 0.1.The speed is given by:

Speed =ldist

t2 − t1= (4.22)/(0.32− 0.1) = 19.18 m/sec.

For length calculation, the speed is 19.18 m/sec and occupancy times are 0.26 and 0.32.

Lvehicle =Speed(ot2 + ot1)

2

=19.18(0.26 + 0.32)

2= 5.56 m.

2. The average length of vehicle is 4.25 m and the length of loop detector zone is 1.85 m.

The time occupancy in the loop is 32 percentages, find the spot speed of the vehicle?

Solution: The average vehicle length is 4.25 and detector zone length is 1.85 m and

t0 is 0.32.the spot speed(s) is given by:

s =EV L

to

=4.25 + 1.85

0.32= 19.06m/sec

3. In freeway 1500 vehicles are observed during 120 sec interval. The lane occupancy is 65

percentage and the average length of vehicle observed as 6.55 m. Find the space mean

speed on the freeway section?

Solution: The number of vehicle N is 1500 vehicles; observation period is T= 120 sec.



The lane occupancy O is 0.65 and average length is 6.55, so g is (40.9/6.55) substitute

s =N

T × O × g

=1500 × 6.55

120 × 0.65 × (40.9)

= 3.08 m/sec

9.6 Summary

Each detector technology and particular device has its own limitations and individual capability.

The successful application of detector technologies largely depends on proper device selection.

Many factors impact detector selection, such as data type, data accuracy, ease of installation,

cost and reliability. ILDs are flexible to satisfy different variety of applications, but installation

requires pavement disturb.

9.7 References

1. Texas Transportation Institute, Texas A and M University System. Travel Time Data

Collection Handbook,Report FHWA-PL-98-035, 1998.

2. Traffic Detector Handbook. Third Edition Volume II, Publication No.FHWA-HRT-06-139

October 2006., 2006.

3. Final Report of Evaluation of Freeway Travel Time Estimates. Castle Rock Consultants

Inc, Portland State University, 2019.

4. Manual on Uniform Traffic Control Devices. Federal Highway Administration, U.S.

Department of Transportation, Washington, D.C., 2019.

5. B Coifman. Length based vehicle classification on freeways from single loop Detectors. al

University Transportation Center Final Report, 2009.

6. G C de Silva. Automation of Traffic Flow Measurement Using Video Images. Thesis

Report, University of Moratuwa, 2001.

7. S Ding. Freeway Travel Time Estimation using Limited Loop Data. Master Thesis, The

University of Akron, 2008.



8. M L Y Elena and L A Klein. Summary of vehicle detection and surveillance technologies

used in intelligent transportation systems. FHWA Report, New Mexico State University

and VDC Project Consultant, 2000.

9. A Faghri and K Hamad. Applications of GPS in Traffic Management. 2002.

10. L Guillaume. Road Traffic Data: Collection Methods and Applications. JRC Technical

note 47967, 2008.

11. U Leeds. Collection Methods for Additional Data, IMAGINE project no. 503549. Insti-

tute for Transport Studies, University of Leeds, United Kingdom, 2006.

12. P T Martin, Y Feng, and X Wang. Detector Technology Evaluation. Department of Civil

and Environmental Engineering, Utah Traffic Lab, 2003.

13. S T Mohammad. Vehicle re-identification Based on Inductance Signature Matching.

Master thesis, University of Toronto, 2011.

14. N Nihan, X Zhang, and Y Wang. Improved System for Collecting Real-Time Truck Data

from Dual Loop Detectors. Transportation Northwest, 2005.

15. S G Ritchie S Park and O Cheol. Field Investigation of Advanced Vehicle Re-identification

Techniques and Detector. California PATH Research Report, 2002.

16. A Parsekar. Blind Deconvolution of Vehicle Inductive Signatures for Travel Time Estima-

tion. Master thesis, Department of Computer Science, University of Minnesota Duluth,

Duluth, Minnesota -55812, 2004.

17. C Ulberg. Vehicle occupancy forecasting, Technical Report. Washington State De-

partment of Transportation Technical, Graduate School of Public Affairs University of

Washington Seattle, Washington 98105, 1994.

18. J Xia and M Chen. Freeway Travel Time Forecasting Under Incident. Final Report,

Southeastern Transportation Center, Department of Civil Engineering, University of Ken-

tucky, Lexington, KY 40506, 2007.

19. B Young and M Saito. Automated Delay Estimation at Signalized Intersections. Research

Division, 2011.

20. Y Zhirui. Speed estimation using single loop detector outputs. Some studies, Ph.D thesis,

Department of CIVIL Engineering, Texas A and M University, 2007.


Transportation Systems Engineering 10. Non-Intrusive Technologies

Chapter 10

Non-Intrusive Technologies

10.1 Introduction

Non-intrusive technologies include video data collection, passive or active infrared detectors,

microwave radar detectors, ultrasonic detectors, passive acoustic detectors, laser detectors and

aerial photography. All these technologies represent emergent fields that are expanding rapidly

with continuing advances in signal processing. At present time such technologies are used to

provide supplemental information for selected locations or for specific applications (e.g., queue

detection at traffic signals). Most non-intrusive systems are operationally and somewhat visu-

ally similar, consisting of small electronics unit mounted in a weatherproof housing placed in

various locations, as shown in Fig. 10:1.

The first type of non-invasive detectors are roadside mast-mounted. The detector possesses

a field-of-regard covering an oblique area upstream or downstream of the unit. There are also

multiple zones of detection defined within the overall field of regard, or the overall zone of

detection same as the field of regard, depending on the specific detector type and technology.

Obscuration problems occur when high-sided vehicles screens lower vehicles from the detector

or the field-of-view being too large, leading to detection of vehicles outside the desired lane.

The second type of non-invasive detectors are mounted on gantries or bridge undersides, with

field of regard directly below, or at a slight oblique to the unit. Finally, some units, such as

open-path pollutant monitors are mounted road side at ground level, firing a beam across the

road. Such units are subject to side-by-side masking and hence most suitable for only single

lane, unidirectional flows.



Type 1. Roadside, Mast−mounted type

13

2. Gantry or bridge underside3. Cross−fire

2 2

Figure 10:1: Typical non-intrusive technology configurations

10.2 Video image detection (VID)

The traffic parameters are collected by frame-by-frame analysis of video images captured

by roadside cameras. The following parameters are collected: Depending on the processing

methodology almost all traffic parameters are captured from video analysis. Simple video sys-

tems often collect flow volume and occupancy. More complex systems allow the extraction of

further parameters.

Advantages

Possibility to capture all desired traffic information, including some parameters that are not

readily obtainable using other types of detectors Possibility of a permanent visual record of the

traffic flow that reviewed and analyzed by a human operator.

Disadvantages

VID systems are susceptible to obscure issues, as with other non-intrusive detectors. Perfor-

mance of VID systems might be degraded in bad weather or low light conditions.

1. Video Image Processor

A video image processor (VIP) system typically consists of one or more cameras, a

microprocessor-based computer for digitizing and processing the imagery, and software

for interpreting the images and converting them into traffic flow data.

2. Principles of Operation

Video image processor systems detect vehicles by analyzing the imagery from a traffic

scene to determine changes between successive frames. VIP system typically consists of



one or more cameras, a microprocessor-based computer for digitizing and processing the

imagery, and software for interpreting the images and converting them into traffic flow

data.

The algorithms are designed to remove gray level variations in the image background

caused by weather conditions, shadows, and daytime or night time artifacts and retain

objects identified as automobiles, trucks, motorcycles, and bicycles. Traffic flow param-

eters are calculated by analyzing successive video frames. Color imagery can also be

exploited to obtain traffic flow data. However, somewhat reduced dynamic range and

sensitivity have so far inhibited this approach. Traffic flow parameters are calculated by

analyzing successive video frames. Color imagery can also be exploited to obtain traffic

flow data.

Three different types of VIP systems are available; they are tripline, closed-loop tracking,

and data association tracking. Fig. 10:2 shows tripline systems which operate by allowing

the user to define a limited number of detection zones in the field of view of the video

camera. When a vehicle crosses one of these zones, it is identified by noting changes in the

pixels caused by the vehicle relative to roadway in the absence of a vehicle. Surface-based

and grid-based analyses are utilized to detect vehicles in tripline VIPs. Tripline systems

estimate vehicle speed by measuring the time it takes for an identified vehicle to travel a

detection zone of known length. The speed is found as the length divided by the travel

time.

Closed-loop tracking systems are an extension of the tripline approach that permits ve-

hicle detection along larger roadway sections. The closed-loop systems track vehicles

continuously through the field of view of camera. Multiple detections of the vehicle along

a track are used to validate the detection. These tracking systems provide additional

traffic flow data such as lane-to-lane vehicle movements. These have the potential to

transmit information to roadside displays and radios to alert drivers to erratic behavior

that can lead to an incident. Data association tracking systems identify and track a

particular vehicle or groups of vehicles as they pass through the field of view of camera.

The computer identifies vehicles by searching for unique connected areas of pixels. These

areas are then tracked frame-to-frame to produce tracking data for the selected vehicle

or vehicle groups.

3. System Design



06

05

02

02

02

0204

DETECTIONZONE

Figure 10:2: Video Image processing by tripline detector system, source

System design consist of following four stages, construction of background image, detec-

tion of frame features, matching of detected frame features and refining matched vehicle

features. Creating a background image (an image representing the scene without mov-

ing vehicles) using a computer is a difficult task. The reason is that a computer, unlike

humans, is unable to distinguish background and vehicles by considering a single image.

The number of frames improves the quality of background images, it increases the time

consumed in creating them. This is caused by the large number of mathematical instruc-

tions required to construct a background image.

In the second stage it analyzes each frame in the sequence and detects features that

correspond to moving vehicles in the scene. Depending on the method used, several types

of features can be highlighted to represent moving vehicles. In the second stage apply

background subtraction on each frame to remove the static background of the scene. The

resulting image consists of blobs (collections of pixels with non-zero values) corresponding

to moving vehicles. These blobs are enhanced by processing further and detected as the

main feature. Several attributes about the blobs are recorded in memory for processing

in the coming stages.

Also, there are false blobs, not corresponding to any moving object. Such blobs are

present because of excessive noise in the image or poor quality of the background image.

Such features need not be processed further for estimating traffic flow. Therefore, these

features are identified from the input features and discarded. Now, the remaining features

can be considered as vehicle features. In third stage by matching the features detected in



(Reflective term)

Passive sensor

Receiving aperture

(Emissive term)

Road surface with emissivity andsurface temperature

Vehicle with emissivity andsurface temperature

ER and TR EV and TV

ET

θ

Tsky

(1 − E)Tsky

Figure 10:3: Emission and reflection of energy by vehicle and road surface. (Source: FHWA

vehicle detection manual)

previous frames with those from the current frame, vehicles can be tracked. In the final

stage matched vehicle features can be refined to correct features in the frames. However,

this is a complex task, as most of the information in the image has been lost after labeling.

Therefore, it is necessary to extract information from original frames to perform this task.

All these system design process are done by different algorithms.

10.3 Infrared Sensors

The sensors are mounted overhead to view approaching or departing traffic or traffic from a

side-looking configuration. Infrared sensors are used for signal control; volume, speed, and

class measurement, as well as detecting pedestrians in crosswalks. With infrared sensors, the

word detector takes on another meaning, namely the light-sensitive element that converts the

reflected or emitted energy into electrical signals. Real-time signal processing is used to analyze

the received signals for the presence of a vehicle.

1. Passive Infrared (PIR)

Detection of vehicle based on emission or reflection of infrared (electromagnetic radia-

tion of frequency 1011− 1014

Hz) radiation from vehicle surface, as compared to ambient

levels emitted or reflected from the road surface shown in Fig. 10:3. The PIR system

collected following parameters: Flow volume, Vehicle presence, and detection zone occu-

pancy. Speed with unit with multiple detection zones.

Advantages

(a) Relatively long wavelength of light used in PIR systems makes them less susceptible

to weather effects.



Disadvantages

(a) Accuracy of speed information is poor with low resolution sensors. Vehicle length

determination is highly problematic for the same reason.

2. Active Infrared (AIR)/Laser

Low power LED or laser diode fires a pulsed or continuous beam down to road surface as

shown in Fig. 10:4. Time for reflection to return is measured. Presence of a vehicle lowers

the time of reflection. High scanning rates provides a detailed profile for classification

determination. Use of Doppler frequency shift from moving object allows for very accu-

rate speed determination. The AIR system collected following parameters flow volume,

speed, classification, vehicle presence, traffic density.

Advantages

(a) Very accurate flow, speed and classifications possible.

(b) Laser systems work in day and night conditions.

Disadvantages

(a) Active near-IR sensors adversely affected by weather conditions.

(b) Laser systems impeded by haze or smoke.

(c) Some problems with tracking small vehicles reported.

(d) Relatively high costs compared to other units. Precise, but limited zone of detection

require additional units over other systems.

10.4 Microwave - Doppler and Radar

Low energy microwave radiation (2.5 to 24 GHz) is transmitted into the detection zone. Ob-

jects within the zone reflect a portion of the radiation back to a receiver. Doppler units use

the frequency shift of the return to calculate speed as shown in Fig. 10:5. It cant detect the

stationary objects. The microwave system collected following parameters.

Doppler - Flow volume and speed;

Frequency-Modulated, Continuous Wave (FMCW) - Flow volume, speed and presence;

Microwave - Flow volume, speed, presence, possibly classification;



Scanning beams

Figure 10:4: Laser radar beam geometry. (Source: FHWA vehicle detection manual)

MicrowaveRadar

Antenna

Power and data cables

Path of transmitted and received

ControllerCabinet

Sign bridge,

or mast arm mountingoverpass, pole,

Reflected signal from vehiclecan be used to determine presence

that is transmitted by the radar sensorand speed, depending on the waveform

Vehicle

(occupancy), passage (count), and

Figure 10:5: Microwave radar operation. Source

Advantages

1. Very accurate. Easy to install, long ranged.

2. Multiple detection zones possible.

3. Day or night operation.

Disadvantages

1. Possible sensitivity to spurious returns from adjacent objects

2. Restrictions on use due to electromagnetic interference with other electronics.



��

��

��

��

HORIZONTAL

MOUNTOVERHEAD

MOUNT

Figure 10:6: Ultrasonic range-measuring sensors, source

10.5 Pulsed and Active Ultrasonic

Ultrasonic sensors transmit pressure waves of sound energy at a frequency between 25 and 50

KHz. Pulse waveforms measure distances to the road surface and vehicle surface by detecting

the portion of the transmitted energy that is reflected towards the sensor from an area defined

by the transmitters beam width. When a distance other than that to the background road

surface is measured, the sensor interprets that measurement as the presence of a vehicle as

shown in Fig. 10:6. The received ultrasonic energy is converted into electrical energy that is

analyzed by signal processing electronics that is either collocated with the transducer or placed

in a roadside controller. Vehicles flow and vehicular speed can be calculated by recording the

time at which the vehicle crosses each beam.

Advantages

1. Highly accurate.

Disadvantages

1. Environmental effects affecting sound propagation degrade performance.

2. Pulsed units with low sampling rate miscount or misclassify fast moving vehicles.

10.6 Passive Acoustic Array Sensors

An array of microphones is used to detect the sound of an approaching vehicle above an am-

bient threshold level. Time lags and signal variations between microphone positions are used

to determine vehicle location relative to the array as shown in Fig. 10:7. Further processing



Figure 10:7: Acoustic array sensors, source

of signal yield to speed information and possibly engine type classification. It collected flow,

speed, occupancy, possibly classification.

Advantages

1. Completely passive system

2. Direct speed measurement.

Disadvantages

1. Environmental effects affecting sound propagation degrade performance

2. Low accuracy in busy locations due to interference from adjacent sources.

10.7 Summary

A non- Intrusive technology is very effective compared to the Intrusive technologies.

10.8 References




October 2006., 2006.


















note 47967, 2008.























Division, 2011.




Transportation Systems Engineering 11. Travel Time Data Collection

Chapter 11

Travel Time Data Collection

11.1 Introduction

Travel time can be defined as the period of time to transverse a route between any two points

of interest. It is a fundamental measure in transportation. Travel time is also one of the most

readily understood and communicated measure indices used by a wide variety of users, includ-

ing transportation engineers, planners, and consumers. Travel time data is useful for a wide

range of transportation analyses including congestion management, transportation planning,

and traveler information. Congestion management systems commonly use travel time-based

performance measures to evaluate and monitor traffic congestion. In addition, some metropoli-

tan areas provide real-time travel time prediction as part of their advanced traveler information

systems (ATIS). Travel time data can be obtained through a number of methods. Some of the

methods involve direct measures of travel times along with test vehicles, license plate match-

ing technique, and ITS probe vehicles. Additionally, various sensors (e.g. inductance loop

detectors, acoustic sensors) in ITS deployment collect a large amount of traffic data every day,

especially in metropolitan areas. Such data can be used for travel time estimation for extensive

applications when direct measurements of travel times are not available [19].

Travel time, or the time required to traverse a route between any two points of interest,

is a fundamental measure in transportation. Travel time is a simple concept understood and

communicated by a wide variety of applications for transportation engineers and planners.

Several data collection techniques can be used to collect travel times. These techniques are

designed to collect travel times and average speeds on designated roadway segments or links.

Following are the different techniques available for the travel time data collection.

• Test Vehicle Techniques

• License Plate Matching Techniques

• ITS Probe Vehicle Techniques



• Emerging and Non-Traditional Techniques

11.2 Test Vehicle Techniques

Travel time data using active test vehicles in combination with varying levels of instrumenta-

tion: manual (clipboard and stopwatch), an electronic distance measuring instrument (DMI), or

a global positioning system (GPS) receiver. It involves the use of data collection vehicle within

which an observer records cumulative travel time at predefined checkpoints along a travel route.

Then this information converted to travel time, speed, and delay for each segment along the

survey route. There are several different methods for performing this type of data collection,

depending upon the instrumentation used in the vehicle. These vehicles are instrumented and

then sent into the field for travel time data collection, they are sometimes referred to as “active”

test vehicles [16].

Advantages

• Advanced test vehicle techniques (e.g., DMI or GPS use) result in detailed data.

• Low initial cost.

Disadvantages

• Sources of possible error from either human or electric sources that require adequate

quality control,

• Data storage difficulties.

11.3 License Plate Matching Techniques

Travel times by matching vehicle license plates between consecutive checkpoints with varying

levels of instrumentation: tape recorders, video cameras, portable computers, or automatic

license plate character recognition [16].

Advantages

• Travel times from a large sample of motorists, very simple technique.

• Provides a continuum of travel times during the data collection period.



Disadvantages

• Travel time data limited to locations where observers or video cameras can be positioned;

• Limited geographic coverage on a single day

• Accuracy of license plate reading is an issue for manual and portable computer

11.4 ITS Probe Vehicle Techniques

Travel times using ITS components and passive probe vehicles in the traffic stream equipped

with signpost-based transponders, automatic vehicle identification (AVI) transponders, ground-

based radio navigation, cellular phones, or GPS receivers [16].

Some vehicles are equipped with dynamic route guidance (DRG) device which act as roving

traffic detectors, a non-infrastructure based traffic monitoring system. Such vehicles, which are

participating in the traffic flow and capable of determining experienced traffic conditions and

transmitting these to a traffic center, are called probe vehicles. To determine its position and

to register experienced traffic conditions, a probe vehicle is equipped with on-board electronics,

such as a location and a communication device. By means of the location device, the probe

vehicle keeps track of its own geographic position [16].

Through the communication device, the probe vehicle transmits its traffic experiences via a

mobile communication link to a traffic center. For instance, each probe can transmit traffic

messages once every time interval containing its location and its speed at the instant of trans-

mission. In this traffic center the traffic data received from probe vehicles is gathered, and

combined with data from the other monitoring sources, and processed into relevant traffic in-

formation. It is very useful for Advanced Traveler Information system (ATIS).

Advantages

• Low cost per unit of data

• Continuous data collection

• Automated data collection

• Data are in electronic format

• No disruption of traffic



TransmitterSignalpost

Location Antenna

SignalpostI.D

Signpost−Bus Communication Link

RadioAntenna

Central Computer

Bus−Computer Center Communication Link

RadioTransmitter

Time/Date StampOdometer ReadingSignal I.D, Bus I.D,

Vehicle LocationUnit

Figure 11:1: Signpost-Based AVL Communication Processes, Source: Travel Time Detection

Hand Book, [16]

Disadvantages

• High implementation cost

• Fixed infrastructure constraints - Coverage area, including locations of antenna

• Requires skilled software

• Not recommended for small scale data collection efforts

ITS probe vehicle data collection systems

1. Signpost-Based Automatic Vehicle Location (AVL) - This technique has mostly

been used by transit agencies. Probe vehicles communicate with transmitters mounted

on existing signpost structures shown in Fig. 11:1 [16].

2. Automatic Vehicle Identification (AVI) - Probe vehicles are equipped with electronic

tags. These tags communicate with roadside transceivers to identify unique vehicles shown

in Fig. 11:2 and collect travel times between transceivers [16].

3. Ground-Based Radio Navigation - It is used for transit or commercial fleet manage-

ment, this system is similar to the global positioning system (GPS). Data are collected

by communication between probe vehicles and a radio tower infrastructure as shown in

Fig. 11:3 [16].



Leased Phone Lines

ReaderUnit

Antenna I.D.Date Stamp,Time Stamp

Tag I.D. #,

ReaderUnit

MicrowaveRadio Wave, orCoaxial Cable, Tag I.D. #

Antenna SpacingVaries, Typically

2−5 km

AVI tag

Central ComputerToll Plaza, Sign Bridge, Overpass, or Gantry

AntennaTransceiver

Tag I.D. #

Figure 11:2: AVI Vehicle-to-Roadside Communication Process, Source: Travel Time Detection

Hand Book, [16]

Vehicle Location Unit

Ground−BasedRadio Tower

Time Stamp

Time Stamp

Time Stamp

Time Stamp

RequestVehicle Location

Central ComputerVehicle I.D.

Vehicle I.D.

Vehicle I.D.

Vehicle I.D.

Figure 11:3: Ground-Based Radio Navigation Communication Process, Source: Travel Time

Detection Hand Book, [16]



11.5 Cellular Geo-location

This experimental technology can collect travel time data by discretely tracking cellular tele-

phone call transmissions. Cellular telephones are also useful to collect travel time data. Two

techniques have been applied using cellular technology: cellular telephone reporting and cellular

geolocating [16].

11.5.1 Cellular Telephone Reporting

An operator at the central control facility records each driver’s identification, location, and time,

by monitoring the time between successive telephone calls, travel time or travel speed between

reporting locations are determined. It is useful for assessment of current traffic conditions and

for collecting travel time data during delays or accidents. The cellular telephone reporting

method is recommended for short-term studies with low accuracy requirements.

11.5.2 Cellular Geolocation

The cellular geolocating methodology discreetly tracks cellular telephone calls to collect travel

time data and monitor freeway conditions. This technique utilizes an existing cellular telephone

network, vehicle locating devices, and a central control facility to collect travel time data. All

vehicles equipped with cellular telephones are potential probe vehicles. The system automati-

cally detects cellular telephone call initiations and locates the respective probe vehicle within

a few seconds.

Advantages

• Driver recruitment not necessary

• No in-vehicle equipment to install

• Large potential sample

Disadvantages

• Low accuracy

• Privacy issues

• Infrastructure dependent



11.6 Emerging and Non-Traditional Techniques

Emerging or non-traditional techniques are based on using “point” vehicle detection equipment,

such as inductance loop detectors or video cameras. Travel time estimation algorithms have

been developed based upon measurable point parameters such as volume, lane occupancy, or

vehicle headways. Image matching algorithms are used to match vehicle images or signatures

captured at two consecutive observation points. Following are some of the methods used in

emerging techniques [16].

11.6.1 Extrapolation Method

Estimates average travel time by spot speeds, applied for short roadway segments between de-

tection devices. It is more suitable for low accuracy application. The most accurate method to

measure vehicle speed with loop detectors is to place two detectors in series, which is referred to

as “speed trap” or “loop trap”. The accuracy of inductance loop speed traps is dependent upon

the trap length, inductance loop wire type, and consistency in design. Many inductance loop

detectors are single loops; primary application is to collect vehicle counts and lane occupancy.

Many research attempts have been made to utilize speed-flow relationships to estimate vehicle

speeds from single loop detectors. The following 11.1 and 11.2 equations have been used to

estimate spot speeds from single loop detectors [16].

Spotspeed =volume

laneoccupancy × g(11.1)

where,

g = speed correction factor (based upon assumed vehicle length, detector configuration, and

traffic conditions).

Traveltime =LinkLengthinkm

Spotspeedinkm

hr

× 3600sec

hr(11.2)

11.6.2 Vehicle Signature Matching

Calculates travel time by matching unique vehicle signatures between sequential observation

points. These methods can utilize a number of point detectors such as inductance loop detec-

tors, weigh-in motion sensors, video cameras, and laser scanning detectors. Vehicle signatures

between two consecutive locations to provide a link based travel time and speed. It provides

alternative to ITS probe vehicle based on travel time measurement, in which a probe vehicle is

identified and matched between two locations using a unique identification number.



Vehicle signature matching had been investigated using a number of different point detection

devices, mostly with inductance loop detectors. Several algorithms are available to capture

vehicle signatures from a loop detector frequency detuning curve. Different types and classes of

vehicles provide different types of signatures. The unique features of a vehicle signature are then

compared to signatures within a given time frame at a downstream location. The signature is

matched when a large number of feature correlations have been found within vehicle signatures

at the downstream location. The vehicle signature matching technique does not match every

vehicle signature captured, but potentially match a large enough percentage as to be significant

[16].

11.7 Summary

Detailed travel time estimation by different techniques has been discussed in this chapter. Also

travel time estimation by vehicle technology and emerging techniques such as vehicle signature

have also been discussed in this chapter.

11.8 References




October 2006., 2006.


















note 47967, 2008.





















Division, 2011.




Transportation Systems Engineering 12. Vehicle Arrival Models : Headway

Chapter 12

Vehicle Arrival Models : Headway

12.1 Introduction

Modelling arrival of vehicle at section of road is an important step in traffic flow modelling.

It has important application in traffic flow simulation where vehicles are to be generated how

vehicles arrive at a section. The vehicle arrival is obviously a random process. This is evident

if one observe how vehicles are arriving at a cross section. Some times several vehicles come

together, while at other times, they come sparsely. Hence, vehicle arrival at a section need to be

characterized statistically. Vehicle arrivals can be modelled in two inter-related ways; namely

modelling what is the time interval between the successive arrival of vehicles or modelling how

many vehicle arrive in a given interval of time. In the former approach, the random variables

the time denoting interval between successive arrival of vehicle can be any positive real values

and hence some suitable continuous distribution can be used to model the vehicle arrival. In the

later approach, the random variables represent the number of vehicles arrived in a given interval

of time and hence takes some integer values. Here in this approach, a discrete distribution can

be used to model the process. This chapter presents how some continuous distributions can be

used to model the vehicle arrival process.

12.2 Headway modelling

An important parameter to characterize the traffic is to model the inter-arrival time of vehicle

at a section on the road. The inter-arrival time or the time headway is not constant due to

the stochastic nature of vehicle arrival. A common way of modeling to treat the inter-arrival

time or the time headway as a random variable and use some mathematical distributions to

model them. The behavior of vehicle arrival is different at different flow condition. It may be

possible that different distributions may work better at different flow conditions. Suppose the

vehicle arrive at a point at time t1, t2, . . . . Then the time difference between two consecutive



Time gap

Time

Dis

tan

ce

Observation

point

Occupancy Time

��

��

��

��

��

��

t1 t2 t3 t4

Figure 12:1: Illustration of headways

arrivals is defined as headway. This is shown as a time-distance diagram in figure 12:1. In fact

the headway consist of two components, the occupancy time which is the duration required for

the vehicle to pass the observation point and the time gap between the rear of the lead vehicle

and front of the following vehicle. Hence, the headways h1 = t2 − t1, h2 = t3 − t2, . . . It

may be noted that the headways h1, h2, . . . will not be constant, but follows some random

distribution. Further, under various traffic states, different distribution may best explain the

arrival pattern. A brief discussion of the various traffic states and suitable distributions are

discussed next.

12.2.1 Classification of traffic state

Generally, traffic state can be divided into three; namely low, medium and high flow conditions.

Salient features of each of the flow state is presented below after a brief discussion of the

probability distribution.

1. Low volume flow

(a) Headway follow a random process as there is no interaction between the arrival of

two vehicles.

(b) The arrival of one vehicle is independent of the arrival of other vehicle.

(c) The minimum headway is governed by the safety criteria.



(d) A negative exponential distribution can be used to model such flow.

2. High volume flow

(a) The flow is very high and is near to the capacity.

(b) There is very high interaction between the vehicle.

(c) This is characterized by near constant headway.

(d) The mean and variance of the headway is very low.

(e) A normal distribution can used to model such flow.

3. Intermediate flow

(a) Some vehicle travel independently and some vehicle has interaction with other vehi-

cles.

(b) More difficult to analyze, however, has more application in the field.

(c) Pearson Type III Distribution can be used which is a very general case of negative

exponential distribution.

12.3 Negative exponential distribution

The low flow traffic can be modeled using the negative exponential distribution. First, some

basics of negative exponential distribution is presented. The probability density function f(t)

of any distribution has the following two important properties: First,

p[−∞ < t < +∞] =

∫ +∞

−∞

f(t) dt = 1 (12.1)

where t is the random variable. This means that the total probability defined by the probability

density function is one. Second:

p[a ≤ t ≤ b] =

∫ b

a

f(t) dt (12.2)

This gives an expression for the probability that the random variable t takes a value with in

an interval, which is essentially the area under the probability density function curve. The

probability density function of negative exponential distribution is given as:

f(t) = λe−λt, t ≥ 0 (12.3)



f(t)

λ = 1.5

λ = 1

λ = 0.5

t

Figure 12:2: Shape of the Negative exponential distribution for various values of λ

where λ is a parameter that determines the shape of the distribution often called as the shape

parameter. The shape of the negative exponential distribution for various values of λ (0.5, 1,

1.5) is shown in figure 12:2. The probability that the random variable t is greater than or equal

to zero can be derived as follow,

p(t ≥ 0) =

∫

∞

0

λ e−λt dt (12.4)

= λ

∫

∞

0

e−λt dt

= λ

∣

∣

∣

∣

e−λt

−λ

∣

∣

∣

∣

∞

0

=∣

∣−e−λt∣

∣

∞

0

= −e−λ∞ + e−λ0

= 0 + 1 = 1

The probability that the random variable t is greater than a specific value h is given as

p(t ≥ h) = 1 − p(t < h) (12.5)

= 1 −∫ h

0

λ.e−λt dt

= 1 − λ

[

e−λt

−λ

]h

0

= 1 +∣

∣e−λt∣

∣

h

0

= 1 +[

e−λh − e−λ0]

= 1 + e−λh − 1

= e−λh



t

f(t)

h h + δ h

p(h ≤ t ≤ h + δh)

t

f(t)

h + δ h

p(t ≥ h + δh)

t

f(t)

h

p(t ≥ h)

Figure 12:3: Evaluation of negative exponential distribution for an interval

Unlike many other distributions, one of the key advantages of the negative exponential dis-

tribution is the existence of a closed form solution to the probability density function as seen

above. The probability that the random variable t lies between an interval is given as:

p[h ≤ t ≤ (h + δh)] = p[t ≥ h] − p[t ≥ (h + δh)] (12.6)

= e−λ h − eλ (h+δh)

This is illustrated in figure 12:3. The negative exponential distribution is closely related to

the Poisson distribution which is a discrete distribution. The probability density function of

Poisson distribution is given as:

p(x) =λx e−λ

x!(12.7)

where, p(x) is the probability of x events (vehicle arrivals) in some time interval (t), and λ is

the expected (mean) arrival rate in that interval. If the mean flow rate is q vehicles per hour,

then λ = q

3600vehicles per second. Now, the probability that zero vehicle arrive in an interval

t, denoted as p(0), will be same as the probability that the headway (inter arrival time) greater

than or equal to t. Therefore,

p(x = 0) =λ0 e−λ

0!= e−λ

= p(h ≥ t)

= e−λ t



Here, λ is defined as average number of vehicles arriving in time t. If the flow rate is q vehicles

per hour, then,

λ =q × t

3600=

t

µ(12.8)

Since mean flow rate is inverse of mean headway, an alternate way of representing the probability

density function of negative exponential distribution is given as

f(t) =1

µe

−t

µ (12.9)

where µ = 1λ

or λ = 1µ. Here, µ is the mean headway in seconds which is again the inverse

of flow rate. Using equation 12.6 and equation 12.5 the probability that headway between

any interval and flow rate can be computed. The next example illustrates how a negative

exponential distribution can be fitted to an observed headway frequency distribution.

Numerical Example

An observation from 2434 samples is given table below. Mean headway and the standard

deviation observed is 3.5 and 2.6 seconds respectively. Fit a negative exponential distribution.

Table 12:1: Observed headway distribution

h h + dh poi

0.0 1.0 0.012

1.0 2.0 0.178

2.0 3.0 0.316

3.0 4.0 0.218

4.0 5.0 0.108

5.0 6.0 0.055

6.0 7.0 0.033

7.0 8.0 0.022

8.0 9.0 0.013

9.0 > 0.045

Total 1.00

Solution: The solution is shown in Table 12:2. The headway range and the observed proba-

bility (or proportion) is given in column (2), (3) and (4). The observed frequency for the first



interval (0 to 1) can be computed as the product of observed frequency pi and the number of

observation (N). That is, f oi = pi × N = 0.012 × 2434 = 29.21 and is shown in column (5).

The probability that the headway greater than t = 0 is computed as p(t ≥ 0) = e−0 = 1 (refer

equation 12.5) and is given in column (6). These steps are repeated for the second interval,

that is f oi = 0.178 × 2434 = 433.25, and p(t ≥ 1) = e−1 = 0.751. Now, the probability of

headway lies between 0 and 1 for the first interval is given by the probability that headway

greater than zero from the first interval minus probability that headway greater than one from

second interval. That is pi(0 ≤ t ≤ 1) = pi(t > 0) − pi(t > 1) = 1.00 − 0.751 = 0.249 and

is given in column (7). Now the computed frequency f ci is pi × N = 0.249 × 2434 = 604.904

and is given in column (8). This procedure is repeated for all the subsequent items. It may be

noted that probability of headway > 9.0 is computed by 1-probability of headway less than 9.0

= 1 − (0.249 + 0.187 + . . . ) = 0.076.

Table 12:2: Illustration of fitting a negative exponential distribution

No h h + dh poi f o

i p(t >= h) pci f c

i

(1) (2) (3) (4) (5) (6) (7) (8)

1 0.0 1.0 0.012 29.21 1.000 0.249 604.904

2 1.0 2.0 0.178 433.25 0.751 0.187 454.572

3 2.0 3.0 0.316 769.14 0.565 0.140 341.600

4 3.0 4.0 0.218 530.61 0.424 0.105 256.705

5 4.0 5.0 0.108 262.87 0.319 0.079 192.908

6 5.0 6.0 0.055 133.87 0.240 0.060 144.966

7 6.0 7.0 0.033 80.32 0.180 0.045 108.939

8 7.0 8.0 0.022 53.55 0.135 0.034 81.865

9 8.0 9.0 0.013 31.64 0.102 0.025 61.520

10 9.0 > 0.045 109.53 0.076 0.076 186.022

Total 2434 1.000 2434

12.4 Normal distribution

The probability density function of the normal distribution is given by:

f(t) =1

σ√

2πe

−(t−µ)2

2σ2 ;−∞ < t < ∞,−∞ < µ < ∞, σ > 0 (12.10)



0

f(t)

−α−α

Figure 12:4: Shape of normal distribution curve

where µ is the mean of the headway and σ is the standard deviation of the headways. The

shape of the probability density function is shown in figure 12:4. The probability that the time

headway (t) less than a given time headway (h) is given by

p(t ≤ h) =

∫ h

−∞

f(t) dt (12.11)

and the value of this is shown as the area under the curve in figure 12:5 (a) and the probability

of time headway (t) less than a given time headway (h + δh) is given by

p(t ≤ h + δh) =

∫ h+δh

−∞

f(t) dt (12.12)

This is shown as the area under the curve in figure 12:5 (b). Hence, the probability that the

time headway lies in an interval, say h and h + δh is given by

p(h ≤ t ≤ h + δh) = p(t ≤ h + δh) − p(t ≤ h) (12.13)

=

∫ h+δh

−∞

f(t) dt −∫ h

−∞

f(t) dt

This is illustrated as the area under the curve in figure 12:5 (c). Although the probability

for headway for an interval can be computed easily using equation 12.13, there is no closed

form solution to the equation 12.11. Eventhough it is possible to solve the above equation

by numerical integration, the computations are time consuming for regular applications. One

way to overcome this difficulty is to use the standard normal distribution table which gives

the solution to the equation 12.11 for a standard normal distribution. A standard normal

distribution is normal distribution of a random variable whose mean is zero and standard

deviation is one. The probability for any random variable, having a mean (µ) and standard

deviation (σ) can be computed by normalizing that random variable with respect to its mean



t

f(t)

h h + δ h

p(h ≤ t ≤ h + δh)

t

f(t)

h + δ h

p(t ≤ h + δh)

t

f(t)

h

p(t ≤ h)

Figure 12:5: Illustration of the expression for probability that the random variable lies in an

interval for normal distribution

and standard deviation and then use the standard normal distribution table. This is based on

the concept of normalizing any normal distribution based on the assumption that if t follows

normal distribution with mean µ and standard deviation σ, then (t − µ)/σ follows a standard

normal distribution having zero mean and unit standard deviation. The normalization steps

shown below.

p[h ≤ t ≤ (h + δh)] = p

[

h − µ

σ≤

t − µ

σ≤

(h + δh) − µ

σ

]

(12.14)

= p

[

t ≤(h + δh) − µ

σ

]

− p

[

t ≤h − µ

σ

]

The first and second term in this equation be obtained from standard normal distribution table.

The following example illustrates this procedure.

Numerical Example

If the mean and standard deviation of certain observed set of headways is 2.25 and 0.875

respectively, then compute the probability that the headway lies in an interval of 1.5 to 2.0

seconds.



f(t)

3σ t2σ σ µ σ 2σ

Figure 12:6: Normal Distribution

Solution: The probability that headway lies between 1.5 and 2.0 can be obtained using

equation 12.14, given that µ = 2.25 and σ = 0.85 as:

p[1.5 ≤ t ≤ 2.0] = p[t ≤ 2.0] − p[t ≤ 1.5]

= p

[

t ≤2.0 − 2.25

0.875

]

− p

[

t ≤1.5 − 2.25

0.875

]

= p [t ≤ −0.29] − p [t ≤ −0.86]

= 0.3859 − 0.1949 (from tables)

= 0.191.

Note that the p(t ≤ −0.29) and p(t ≤ −0.80) are obtained from the standard normal distri-

bution tables. Since the normal distribution is defined from −α to +α unlike an exponential

distribution which is defined only for positive number, it is possible that normal distribution

may generate negative headways. A practical way of avoiding this is to shift the distribution

by some value so that it will mostly generate realistic headways. The concept is illustrated in

figure 12:6. Suppose α is the minimum possible headway and if we set α = µ − σ than about

60% of headway will be greater than α. Alternatively, if we set α = µ − 2σ, than about 90%

of the headway will be greater than α. Further, if we set α = µ − 3σ, than about 99% of the

headway will be greater than α. To generalize,

α = µ − nσ

where n is 1, 2, 3, etc and higher the value of n, then is better the precision. From this equation,

we can compute the value of σ to be used in normal distribution calculation when the random

variable cannot be negative as:

σ =µ − α

n(12.15)



Numerical Example

Given that observed mean headway is 3.5 seconds and standard distribution is 2.6 seconds, then

compute the probability that the headway lies between 0 and 0.5. Assume that the minimum

expected headway is 0.5 seconds.

Solution: First, compute the standard deviation to be used in calculation using equation 12.15,

given that µ = 3.5, σ = 2.6, and α = 0.5. Then:

σ =µ − α

2=

3.5 − 0.5

2= 1.5 (12.16)

Second, compute the probability that headway less than zero.

p(t < 0) ≈ p

(

t ≤0 − 3.5

1.5

)

= p(t ≤ −2.33) = 0.01

The value 0.01 is obtained from standard normal distribution table. Similarly, compute the

probability that headway less than 0.5 as

p(t ≤ 0.5) ≈ p

(

t ≤0.5 − 3.5

1.5

)

= p(t < −2)

= 0.023

The value 0.23 is obtained from the standard normal distribution table. Hence, the probability

that headway lies between 0 and 0.5 is obtained using equation 12.14 as p(0 ≤ t ≤ 0.5)=0.023−0.010 = 0.023.

Numerical Example

An observation from 2434 samples is given table below. Mean headway observed was 3.5 seconds

and the standard deviation observed was 2.6 seconds. Fit a normal distribution, if we assume

minimum expected headway is 0.5.

Solutions The given headway range and the observed probability is given in column (2), (3)

and (4). The observed frequency for the first interval (0 to 1) can be computed as the product of

observed frequency pi and the number of observation (N) i.e. poi = pi×N = 0.012×2434 = 29.21

as shown in column (5). Compute the standard deviation to be used in calculation, given that

µ = 3.5, σ = 2.6, and α = 0.5 as:

σ =µ − α

2=

3.5 − 0.5

2= 1.5




h h + dh poi

0.0 1.0 0.012

1.0 2.0 0.178

2.0 3.0 0.316

3.0 4.0 0.218

4.0 5.0 0.108

5.0 6.0 0.055

6.0 7.0 0.033

7.0 8.0 0.022

8.0 9.0 0.013

9.0 > 0.045

Total 1.00

Second, compute the probability that headway less than zero.

p(t < 0) ≈ p

(

t ≤0 − 3.5

1.5

)

= p(t ≤ −2.33) = 0.010

The value 0.01 is obtained for standard normal distribution table is shown in column (6).

Similarly, compute the probability that headway less than 1.0 as:

p(t ≤ 1) ≈ p

(

t ≤1.0 − 3.5

1.5

)

= p(t < −2)

= 0.048

The value 0.048 is obtained from the standard normal distribution table is shown in column (6).

Hence, the probability that headway between 0 and 1 is obtained using equation 12.14 as

p(0 ≤ t ≤ 1)=0.048− 0.010 = 0.038 and is shown in column (7). Now the computed frequency

F ci is p(t < h < t+1)×N = 0.038× 2434 = 92.431 and is given in column (8). This procedure

is repeated for all the subsequent items. It may be noted that probability of headway > 9.0 is

computed by one minus probability of headway less than 9.0 = 1−(0.038+0.111+. . . ) = 0.010.



Table 12:4: Solution using normal distribution

No h h + δ h poi f o

i = poi × N p(t ≤ h) p(t < h < t + δ h) f c

i = pci × N

(1) (2) (3) (4) (5) (6) (7) (8)

1 0.0 1.0 0.012 29.21 0.010 0.038 92.431

2 1.0 2.0 0.178 433.25 0.048 0.111 269.845

3 2.0 3.0 0.316 769.14 0.159 0.211 513.053

4 3.0 4.0 0.218 530.61 0.369 0.261 635.560

5 4.0 5.0 0.108 262.87 0.631 0.211 513.053

6 5.0 6.0 0.055 133.87 0.841 0.111 269.845

7 6.0 7.0 0.033 80.32 0.952 0.038 92.431

8 7.0 8.0 0.022 53.55 0.990 0.008 20.605

9 8.0 9.0 0.013 31.64 0.999 0.001 2.987

10 9.0 > 0.045 109.53 1.000 0.010 24.190

Total 2434

12.5 Pearson Type III distribution

As noted earlier, the intermediate flow is more complex since certain vehicles will have interac-

tion with the other vehicles and certain may not. Here, Pearson Type III distribution can be

used for modelling intermediate flow. The probability density function for the Pearson Type

III distribution is given as

f(t) = λΓ(K)

[λ(t − α)]K−1 e−λ(t−α), K, α ∈ R (12.17)

where λ is a parameter which is a function of µ, K and α, and determine the shape of the

distribution. The term µ is the mean of the observed headways, K is a user specified parameter

greater than 0 and is called as a shift parameter. The Γ() is the gamma function and given as

Γ(K) = (K − 1)! (12.18)

It may also be noted that Pearson Type III is a general case of Gamma, Erlang and Negative

Exponential distribution as shown in below:

f(t) = λΓ(K)

[λ(t − α)]K−1 e−λ(t−α) K, α ∈ R Pearson

= λΓ(K)

[λt]K−1 e−λt if α = 0 Gamma

= λ(K−1)!

[λt]K−1 e−λt if K ∈ I Erlang

= λe−λt if K = 1 Neg. Exp.



The expression for the probability that the random headway (t) is greater than a given headway

(h), p(t ≥ h), is given as:

p(t ≥ h) =

∫

∞

h

f(t) dt (12.19)

and similarly p(t > h + δh) is given as:

p(t > h + δh) =

∫

∞

(h+δh)

f(t) dt (12.20)

and hence, the probability that the headway between h and h + δh is given as

p(h ≤ t ≤ (h + δh)) =

∫

∞

h

f(t)dt −∫

∞

(h+δh)

f(t) dt (12.21)

It may be noted that closed form solution to equation 12.19 and equation 12.20 is not available.

Numerical integration is also difficult due to computational requirement. Using table as in the

case of Normal Distribution is difficult, since the table will be different for each K. A common

way of solving this is by using the numerical approximation to equation 12.21. The solution

to equation 12.21 is essentially the area under the curve defined by the probability density

function between h and h + δh. If we assume that line joining f(h) and f(h + δh) is linear,

which is a reasonable assumption if δh is small, than the are under the curve can be found out

by the following approximate expression:

p(h ≤ t ≤ (h + δh)) ≈[

f(h) + f(h + δh)

2

]

× δh (12.22)

This concept is illustrated in figure 12:7

Stepwise procedure to fit a Pearson Type III distribution

1. Input required: the mean (µ) and the standard deviation (σ) of the headways.

2. Set the minimum expected headway (α). Say, for example, 0.5. It means that the

p(t < 0.5) ≈ 0.

3. Compute the shape factor using the mean (µ) the standard deviation (σ) and the mini-

mum expected headway (α)

K =µ − α

σ



t

f(t)

h h + δ h

p(h ≤ t ≤ h + δh) ≈[

f(h)+f(h+δh)2

]

× δh

b

b

t

f(t)

h + δ h

p(t ≤ h + δh)

b

f(h + δh)

t

f(t)

h

p(t ≤ h)b

f(h)

Figure 12:7: Illustration of the expression for probability that the random variable lies in an

interval for Person Type III distribution

4. Compute the term flow rate (λ) as

λ =K

µ − α

Note that if K = 1 and α = 0, then λ = 1µ

which is the flow rate.

5. Compute gamma function value for K as:

Γ(K) = (K − 1)! if K ∈ I (Integer)

= (K − 1) Γ(K − 1) if K ∈ R (Real)(12.23)

Although the closed form solution of Γ(K) is available, it is difficult to compute. Hence,

it can be obtained from gamma table. For, example:

Γ(4.785) = 3.785 × Γ(3.785)

= 3.785 × 2.785 × Γ(2.785)

= 3.785 × 2.785 × 1.785 × Γ(1.785)

= 3.785 × 2.785 × 1.785 × 0.92750

= 17.45

Note that the value of Γ(1.785) is obtained from gamma table for Γ(x) which is given for

1 ≤ x ≤ 2.

6. Using equation 12.17 solve for f(h) by setting t = h where h is the lower value of the

range and f(h+δh) by setting t = h+δh where (h+δh) is the upper value of the headway



range. Compute the probability that headway lies between the interval of h and h + δh

using equation 12.22.

The Gamma function can be evaluated by the following approximate expression also:

Gamma(x) = xx e−x

√

2 π

x

(

1 +1

12 x+

1

288x2+ . . .

)

(12.24)

Numerical Example

An observation from 2434 samples is given table below. Mean headway observed was 3.5 seconds

and the standard deviation 2.6 seconds. Fit a Person Type III Distribution.


h h + dh poi

0.0 1.0 0.012

1.0 2.0 0.178

2.0 3.0 0.316

3.0 4.0 0.218

4.0 5.0 0.108

5.0 6.0 0.055

6.0 7.0 0.033

7.0 8.0 0.022

8.0 9.0 0.013

9.0 > 0.045

Total 1.00

Solutions Given that mean headway (µ) is 3.5 and the standard deviation (σ) is 2.6. As-

suming the expected minimum headway (α) is 0.5, K can be computed as

K =µ − α

σ=

3.5 − 0.5

2.6= 1.15

and flow rate term λ as

λ =K

µ − α=

1.15

3.5 − 0.5= 0.3896



Now, since K = 1.15 which is between 1 and 2, Γ(K) can be obtained directly from the

gamma table as Γ(K) = 0.93304. Here, the probability density function for this example can

be expressed as

f(t) =0.3846

0.93304× [ 0.3846 × (t − 0.5) ]1.15−1 × e−0.3846 (t−0.5)

The given headway range and the observed probability is given in column (2), (3) and (4). The

observed frequency (f oi ) for the first interval (0 to 1) can be computed as the product of observed

proportion poi and the number of observations (N). That is, f o

i = poi ×N = 0.012×2434 = 29.21

as shown in column (5). The probability density function value for the lower limit of the first

interval (h=0) is shown in column (6) and computed as:

f(0) =0.3846

0.93304[ 0.3846 × (0 − 0.5)]1.15−1 × e−0.3846 (0−0.5) ≈ 0.

Note that since t−α (0−0.5) is negative and K−1 (1.15−1) is a fraction, the above expression

cannot be evaluated and hence approximated to zero (corresponding to t=0.5). Similarly, the

probability density function value for the lower limit of the second interval (h=1) is shown in

column 6 and computed as:

f(1) =0.3846

0.93304[0.3846(1 − 0.5)]1.15−1 × e−0.3846(1−0.5) = 0.264

Now, for the first interval, the probability for headway between 0 and 1 is computed by equa-

tion ?? as pci(0 ≤ t ≤ 1) =

(

f(0)+(f(1)2

)

× (1 − 0) = (0 + 0.0264)/2 × 1 = 0.132 and is

given in column (7). Now the computed frequency f ci is pc

i × N = 0.132 × 2434 = 321.1 and

is given in column (8). This procedure is repeated for all the subsequent items. It may be

noted that probability of headway > 9 is computed by 1-probability of headway less than 9

= 1− (0.132+0.238+ . . . ) = 0.044. The comparison of the three disribution for the above data

is plotted in Figure 12:8.

ut

ut

ut

ut

ut

utut ut ut

ut

ut utObserved

ld

ld

ldld

ldld ld ld ld

ld

ld ld Exponential

rs

rs

rs

rs

rs

rs

rsrs rs rs

rs rs Normal

b

b

b

bb

bb b b

b

b b Pearson Type III

1 2 3 4 5 6 7 8 9

0.1

0.2

0.3

Figure 12:8: Comparison of distributions

12.6 Conclusion

This chapter covers how the vehicle arrival can be modelled using various distributions. The

negative exponential distribution is used when the traffic is low and is most simplest of the



Table 12:6: Solution using Pearson Type III distribution

No h h + δ h poi f o

i f(t) pci f c

i

(1) (2) (3) (4) (5) (6) (7) (8)

1 0 1 0.012 29.2 0.000 0.132 321.2

2 1 2 0.178 433.3 0.264 0.238 580.1

3 2 3 0.316 769.1 0.213 0.185 449.5

4 3 4 0.218 530.6 0.157 0.134 327.3

5 4 5 0.108 262.9 0.112 0.096 233.4

6 5 6 0.055 133.9 0.079 0.068 164.6

7 6 7 0.033 80.3 0.056 0.047 115.3

8 7 8 0.022 53.6 0.039 0.033 80.4

9 8 9 0.013 31.6 0.027 0.023 55.9

10 >9 0.045 109.5 0.019 0.044 106.4

Total 1.0 2434 1.0 2434

distributions in terms of computation effort. The normal distribution on the other hand is

used for highly congested traffic and its evaluation require standard normal distribution tables.

The Pearson Type III distribution is a most general kind of distribution and can be used

intermediate or normal traffic conditions.

12.7 References


New Delhi, 1987.




Transportation Systems Engineering 13. Vehicle Arrival Models : Count

Chapter 13

Vehicle Arrival Models : Count

13.1 Introduction

As already noted in the previous chapter that vehicle arrivals can be modelled in two inter-

related ways; namely modelling how many vehicle arrive in a given interval of time, or modelling

what is the time interval between the successive arrival of vehicles. Having discussed in detail

the former approach in the previous chapter, the first part of this chapter discuss how a discrete

distribution can be used to model the vehicle arrival. Traditionally, Poisson distribution is used

to model the random process, the number of vehicles arriving a given time period. The second

part will discuss methodologies to generate random vehicle arrivals, be it the generation of

random headways or random number of vehicles in a given duration. The third part will

elaborate various ways of evaluating the performance of a distribution.

13.2 Poisson Distribution

Suppose, if we plot the arrival of vehicles at a section as dot in a time axis, it may look like

Figure 13:1. Let h1, h2, ... etc indicate the headways, then as mentioned earlier, they take some

real values. Hence, these headways or inter arrival time can be modelled using some continuous

distribution. Also, let t1, t2, t3 and t4 are four equal time intervals, then the number of vehicles

arrived in each of these interval is an integer value. For example, in Fig. 13:1, 3, 2, 3 and 1

vehicles arrived in time interval t1, t2, t3 and t4 respectively. Any discrete distribution that best

fit the observed number of vehicle arrival in a given time interval can be used. Similarly, any

Time

t1 t2 t3 t4

h1 h2 h3 h4 h5 h6 h7 h8 h9 h10

Figure 13:1: Illustration of vehicle arrival modeling



continuous distribution that best fit the observed headways (or inter-arrival time) can be used in

modelling. However, since these process are inter-related, the distributions that describe these

relations should also be inter-related for better explanation of the phenomenon. Interestingly,

there exist distributions that meet the above requirements. First, we will see the distribution

to model the number of vehicles arrived in a given duration of time. Poisson distribution is

commonly used to describe such a random process. The probability density function of the

Poisson distribution is given as:

p(x) =µxe−µ

x!(13.1)

where p(x) is the probability for x events will occur in the time interval, and µ is the expected

rate of occurrence of that event in that interval. Some special cases of this distribution is given

below.

p(0) = e−µ

p(1) =µe−µ

1= µ p(0)

p(2) =µ2e−µ

2!=

µ

2p(1)

∴ p(n) =µ

np(n − 1).

Since the events are discrete, the probability that certain number of vehicles (n) arriving in an

interval can be computed as:

p(x ≤ n) =

n∑

i=0

p(i), i ∈ I.

Similarly, the probability that the number of vehicles arriving in the interval is exactly in a

range (between a and b, both inclusive and a < b) is given as:

p(a ≤ x ≤ b) =b∑

i=a

p(i), i ∈ I.

Numerical Example

The hourly flow rate in a road section is 120 vph. Use Poisson distribution to model this vehicle

arrival.

Solution: The flow rate is given as (µ) = 120 vph = 12060

= 2 vehicle per minute. Hence, the

probability of zero vehicles arriving in one minute p(0) can be computed as follows:

p(0) =µxe−µ

x!=

20.e−2

0!= 0.135.



Table 13:1: Probability values of vehicle arrivals computed using Poisson distribution

n p(n) p(x ≤ n) F (n)

0 0.135 0.135 8.120

1 0.271 0.406 16.240

2 0.271 0.677 16.240

3 0.180 0.857 10.827

4 0.090 0.947 5.413

5 0.036 0.983 2.165

6 0.012 0.995 0.722

7 0.003 0.999 0.206

8 0.001 1.000 0.052

9 0.000 1.000 0.011

10 0.000 1.000 0.011

Similarly, the probability of one vehicles arriving in one minute p(1) is given by,

p(1) =µxe−µ

x!=

2.e−2

1!= 0.271.

Now, the probability that number of vehicles arriving is less than or equal to zero is given as

p(x ≤ 0) = p(0) = 0.135.

Similarly, probability that the number of vehicles arriving is less than or equal to 1 is given as:

p(x ≤ 1) = p(0) + p(1) = 0.135 + 0.275 = 0.406.

Again, the probability that the number of vehicles arriving is between 2 to 4 is given as:

p(2 ≤ x ≤ 4) = p(2) + p(3) + p(4),

= .271 + .18 + .09 = 0.54.

Now, if the p(0) = 0.135, then the number of intervals in an hour where there is no vehicle

arriving is

F (x) = p(0) × 60 = 0.135 × 60 = 8.12.

The above calculations can be repeated for all the cases as tabulated in Table 13:1. The shape

of this distribution can be seen from Figure 13:2 and the corresponding cumulative distribution

is shown in Figure 13:3.



ut

ut ut

ut

ut

ut

utut ut ut ut

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

n

p(n)

Figure 13:2: Probability values of vehicle arrivals computed using Poisson distribution

ut

ut

ut

ut

ut

ut ut ut ut ut ut

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

n

∑p(n)

Figure 13:3: Cumulative probability values of vehicle arrivals computed using Poisson distri-

bution



13.3 Random variates following Poisson distribution

For simulation purposes, it may be required to generate number of vehicles arrived in a given in-

terval so that it follows typical vehicle arrival. This is the reverse of computing the probabilities

as seen above. The following steps give the procedure:

1. Input: mean arrival rate µ in an interval t

2. Compute p(x = n) and p(x ≤ n)

3. Generate a random number X such that 0 ≤ X ≤ 1

4. Find n such that p(x ≤ n − 1) ≤ X and p(x ≤ n) ≥ X

5. Set ni = n, where ni is the number of vehicles arrived in ith interval.

The steps 3 to 5 can be repeated for required number of intervals.

Numerical Example

Generate vehicles for ten minutes if the flow rate is 120 vph.

Solution The first two steps of this problem is same as the example problem solved earlier and

the resulted from the table is used. For the first interval, the random number (X) generated is

0.201 which is greater than p(0) but less than p(1). Hence, the number of vehicles generated in

this interval is one (ni = 1). Similarly, for the subsequent intervals. It can also be computed that

at the end of 10th interval (one minute), total 23 vehicle are generated. Note: This amounts

to 2.3 vehicles per minute which is higher than given flow rate. However, this discrepancy is

because of the small number of intervals conducted. If this is continued for one hour, then this

average will be about 1.78 and if continued for then this average will be close to 2.02.

13.4 Random variates following Exponential distribution

One can generate random variate following negative exponential distribution rather simply due

to availability of closed form solutions. The method for generating exponential variates is based

on inverse transform sampling:

t = f−1(X)



Table 13:2: Vehicles generated using Poisson distribution

No X n

1 0.201 1

2 0.714 3

3 0.565 2

4 0.257 1

5 0.228 1

6 0.926 4

7 0.634 2

8 0.959 5

9 0.188 1

10 0.832 3

Total 23

has an exponential distribution, where f−1, called as quantile function, is defined as

f−1(X) =log(1 − X)

λ.

Note that if X is uniform, then 1 − X is also uniform and λ = 1/µ. Hence, one can generate

exponential variates as follows:

t = −µ × log(X)

where, X is a random number between 0 and 1, µ is the mean headway, and the resultant

headways generated (t) will follow exponential distribution.

Numerical Example

Simulate the headways for 10 vehicles if the flow rate is 120 vph.

Solution Since the given flow rate is 120 vph, then the mean headway (µ) is 30 seconds.

Generate a random number between 0 and 1 and let this be 0.62. Hence, by the above equation,

t = 30 × (− log(0.62)) = 14.57. Similarly, headways can be generated. The table below given

the generation of 15 vehicles and it takes little over 10 minutes. In other words, the table below

gives the vehicles generated for 10 minutes. Note: The mean headway obtained from this 15

headways is about 43 seconds; much higher than the given value of 30 seconds. Of, course this

is due to the lower sample size. For example, if the generation is continued to 100 vehicles,



Table 13:3: Headways generated using Exponential distribution

No X t∑

t

1 0.62 14.57 14.57

2 0.17 53.70 68.27

3 0.27 39.14 107.41

4 0.01 157.36 264.77

5 0.26 40.01 304.78

6 0.47 22.72 327.5

7 0.96 1.38 328.88

8 0.24 42.76 371.64

9 0.59 15.94 387.58

10 0.45 24.05 411.63

11 0.26 40.82 452.45

12 0.11 67.39 519.84

13 0.10 69.33 589.17

14 0.73 9.63 598.8

15 0.31 34.74 633.54

then the mean would be about 35 seconds, and if continued till 1000 vehicles, then the mean

would be about 30.8 seconds.

13.5 Evaluation of the mathematical distribution

The mathematical distribution such as negative exponential distribution, normal distribution,

etc needs to be evaluated to see how best these distributions fits the observed data. It can be

evaluated by comparing some aggregate statistics as discussed below.

13.5.1 Mean and Standard deviation

One of the easiest ways to compute the mean and standard deviation of the observed data

and compare with mean and standard deviation obtained from the computed frequencies. If

pci is the computed probability of the headway is the ith interval, and N is the total number of

observations, then the computed frequency of the ith interval is given as:

f ci = pc

i × N.



Then the mean of the computed frequencies (µc) is obtained as

µc =Σf c

i × (2hi+δh2

)

N,

where hi is the lower limit of the ith interval, and δh is the interval range. The standard

deviation σc can be obtained by

σc =Σ(hm

i − µc)2f ci

N.

If the distribution fit closely, then the mean and the standard deviation of the observed and

fitted data will match. However, it is possible, that two sample can have similar mean and

standard deviation, but, may differ widely in the individual interval. Hence, this can be con-

sidered as a quick test for the comparison purposes. For better comparison, Chi-square test

which gives a better description of the suitability of the distribution may be used.

13.5.2 Chi-square test

The Chi-square value (X2) can be computed using the following formula:

X2C =

n∑

i=1

(f oi − f c

i )2

f ci

where f oi is the observed frequency, f c

i is the computed (theoretical) frequency of the ith interval,

and n is the number of intervals. Obviously, a X2 value close to zero implies a good fit of the

data, while, high X2 value indicate poor fit. For an objective comparison Chi-square tables are

used. A chi-square table gives X2 values for various degree of freedom. The degree of freedom

(DOF) is given as

DOF = n − 1 − p

where n is the number of intervals, and p is the number of parameter defining the distribution.

Since negative exponential distribution is defined by mean headway alone, the value of p is one,

where as Pearson and Normal distribution has the value of p as two, since they are defined by µ

and σ. Chi-square value is obtained from various significant levels. For example, a significance

level of 0.05 implies that the likelihood that the observed frequencies following the theoretical

distribution is is 5%. In other words, one could say with 95% confidence that the observed data

follows the theoretical distribution under testing.

Numerical Example

Compute the X2 statistic of the following distribution, where N = 2434.



Table 13:4: χ2distribution

h h + dh poi pc

i

0.0 1 0.012 0.249

1.0 2 0.178 0.187

2.0 3 0.316 0.140

3.0 4 0.218 0.105

4.0 5 0.108 0.079

5.0 6 0.055 0.060

6.0 7 0.033 0.045

7.0 8 0.022 0.034

8.0 9 0.013 0.025

9.0 > 0.045 0.076

Total 1 1

Solution: The given headway range and the observed probability is given in column (2),

(3) and (4). The observed frequency for the first interval (0 to 1) can be computed as the

product of observed probability pi and the number of observation (N) i.e. f oi = po

i × N =

0.012 × 2434 = 29.21 as shown in column (5). Now the computed frequency for the first

interval (0 to 1) is the product of computed probability and the number of observation (N) i.e.

f ci = pc

i ×N = 0.249×2434 = 441.21 as shown in column (7). The χ2 value can be computed as(29.21−441.21)2

441.21= 384.73. Similarly, all the rows are computed and the total χ2 value is obtained

as 1825.52. A chi-square table gives X2 values for various degree of freedom. The degree of

freedom (DOF) is given as: DOF = n − 1 − p = 10 − 1 − 1 = 8, where n is the number of

intervals (10), and p is the number of parameter (1 because it is exponential distribution). Now

at a significance level of 0.05 and DOF 8, from the table, X2T = 15.5. Since χ2

T < χ2C hence

reject that the observed frequency follows exponential distribution.

13.6 Conclusion

The chapter covers three aspects: modeling vehicle arrival using Poisson distribution, generation

of random variates following certain distribution, and evaluation of distributions. Specific

evaluation include comapring the mean and standard deviation at macro level and using chi-

square test which is essentially a micro-level comparison.



Table 13:5: Solution using comparison with X2

No h h + dh poi f o

i pci f c

i χ2

(1) (2) (3) (4) (5) (6) (7) (8)

1 0.0 1 0.012 29.21 0.249 441.21 384.73

2 1.0 2 0.178 433.25 0.187 361.23 14.36

3 2.0 3 0.316 769.14 0.140 295.75 757.73

4 3.0 4 0.218 530.61 0.105 242.14 343.67

5 4.0 5 0.108 262.87 0.079 198.25 21.07

6 5.0 6 0.055 133.87 0.060 162.31 4.98

7 6.0 7 0.033 80.32 0.045 132.89 20.79

8 7.0 8 0.022 53.55 0.034 108.80 28.06

9 8.0 9 0.013 31.64 0.025 89.08 37.03

10 9.0 > 0.045 109.53 0.076 402.34 213.10

Total 1 1 1825.52

13.7 References


New Delhi, 1987.




Transportation Systems Engineering 14. Car Following Models

Chapter 14

Car Following Models

14.1 Overview

Longitudinal spacing of vehicles are of particular importance from the points of view of safety,

capacity and level of service. The longitudinal space occupied by a vehicle depend on the

physical dimensions of the vehicles as well as the gaps between vehicles. For measuring this

longitudinal space, two microscopic measures are used- distance headway and distance gap.

Distance headway is defined as the distance from a selected point (usually front bumper) on

the lead vehicle to the corresponding point on the following vehicles. Hence, it includes the

length of the lead vehicle and the gap length between the lead and the following vehicles.

14.2 Car following models

Car following theories describe how one vehicle follows another vehicle in an uninterrupted flow.

Various models were formulated to represent how a driver reacts to the changes in the relative

positions of the vehicle ahead. Models like Pipes, Forbes, General Motors and Optimal velocity

model are worth discussing.

14.2.1 Notation

Before going in to the details, various notations used in car-following models are discussed here

with the help of figure 14:1. The leader vehicle is denoted as n and the following vehicle as

(n+1). Two characteristics at an instant t are of importance; location and speed. Location and

speed of the lead vehicle at time instant t are represented by xtn and vt

n respectively. Similarly,

the location and speed of the follower are denoted by xtn+1 and vt

n+1 respectively. The following

vehicle is assumed to accelerate at time t + ∆T and not at t, where ∆T is the interval of time

required for a driver to react to a changing situation. The gap between the leader and the

follower vehicle is therefore xtn − xt

n+1.



Follower Leader

n

Direction of traffic

n + 1

vn

xn

yn+1

vn+1

xn − xn+1

Figure 14:1: Notation for car following model

14.2.2 Pipe’s model

The basic assumption of this model is “A good rule for following another vehicle at a safe

distance is to allow yourself at least the length of a car between your vehicle and the vehicle

ahead for every ten miles per hour of speed at which you are traveling” According to Pipe’s

car-following model, the minimum safe distance headway increases linearly with speed. A

disadvantage of this model is that at low speeds, the minimum headways proposed by the

theory are considerably less than the corresponding field measurements.

14.2.3 Forbes’ model

In this model, the reaction time needed for the following vehicle to perceive the need to deceler-

ate and apply the brakes is considered. That is, the time gap between the rear of the leader and

the front of the follower should always be equal to or greater than the reaction time. Therefore,

the minimum time headway is equal to the reaction time (minimum time gap) and the time

required for the lead vehicle to traverse a distance equivalent to its length. A disadvantage of

this model is that, similar to Pipe’s model, there is a wide difference in the minimum distance

headway at low and high speeds.

14.2.4 General Motors’ model

The General Motors’ model is the most popular of the car-following theories because of the

following reasons:

1. Agreement with field data; the simulation models developed based on General motors’

car following models shows good correlation to the field data.

2. Mathematical relation to macroscopic model; Greenberg’s logarithmic model for speed-

density relationship can be derived from General motors car following model.



In car following models, the motion of individual vehicle is governed by an equation, which

is analogous to the Newton’s Laws of motion. In Newtonian mechanics, acceleration can be

regarded as the response of the particle to stimulus it receives in the form of force which includes

both the external force as well as those arising from the interaction with all other particles in

the system. This model is the widely used and will be discussed in detail later.

14.2.5 Optimal velocity model

The concept of this model is that each driver tries to achieve an optimal velocity based on the

distance to the preceding vehicle and the speed difference between the vehicles. This was an

alternative possibility explored recently in car-following models. The formulation is based on

the assumption that the desired speed vndesireddepends on the distance headway of the nth

vehicle. i.e.vtndesired

= vopt(∆xtn) where vopt is the optimal velocity function which is a function

of the instantaneous distance headway ∆xtn. Therefore at

n is given by

atn = [1/τ ][V opt(∆xt

n) − vtn] (14.1)

where 1

τis called as sensitivity coefficient. In short, the driving strategy of nth vehicle is that,

it tries to maintain a safe speed which in turn depends on the relative position, rather than

relative speed.

14.3 General motor’s car following model

14.3.1 Basic Philosophy

The basic philosophy of car following model is from Newtonian mechanics, where the acceler-

ation may be regarded as the response of a matter to the stimulus it receives in the form of

the force it receives from the interaction with other particles in the system. Hence, the basic

philosophy of car-following theories can be summarized by the following equation

[Response]n α [Stimulus]n (14.2)

for the nth vehicle (n=1, 2, ...). Each driver can respond to the surrounding traffic conditions

only by accelerating or decelerating the vehicle. As mentioned earlier, different theories on car-

following have arisen because of the difference in views regarding the nature of the stimulus.

The stimulus may be composed of the speed of the vehicle, relative speeds, distance headway

etc, and hence, it is not a single variable, but a function and can be represented as,

atn = fsti(vn, ∆xn, ∆vn) (14.3)



where fsti is the stimulus function that depends on the speed of the current vehicle, relative

position and speed with the front vehicle.

14.3.2 Follow-the-leader model

The car following model proposed by General motors is based on follow-the leader concept. This

is based on two assumptions; (a) higher the speed of the vehicle, higher will be the spacing

between the vehicles and (b) to avoid collision, driver must maintain a safe distance with the

vehicle ahead.

Let ∆xtn+1 is the gap available for (n+1)th vehicle, and let ∆xsafe is the safe distance, vt

n+1

and vtn are the velocities, the gap required is given by,

∆xtn+1 = ∆xsafe + τvt

n+1 (14.4)

where τ is a sensitivity coefficient. The above equation can be written as

xn − xtn+1 = ∆xsafe + τvt

n+1 (14.5)

Differentiating the above equation with respect to time, we get

vtn − vt

n+1 = τ.atn+1

atn+1 =

1

τ[vt

n − vtn+1]

General Motors has proposed various forms of sensitivity coefficient term resulting in five gen-

erations of models. The most general model has the form,

atn+1 =

[

αl,m(vtn+1)

m

(xtn − xt

n+1)l

]

[

vtn − vt

n+1

]

(14.6)

where l is a distance headway exponent and can take values from +4 to -1, m is a speed exponent

and can take values from -2 to +2, and α is a sensitivity coefficient. These parameters are to

be calibrated using field data. This equation is the core of traffic simulation models.

In computer, implementation of the simulation models, three things need to be remembered:

1. A driver will react to the change in speed of the front vehicle after a time gap called the

reaction time during which the follower perceives the change in speed and react to it.

2. The vehicle position, speed and acceleration will be updated at certain time intervals

depending on the accuracy required. Lower the time interval, higher the accuracy.

3. Vehicle position and speed is governed by Newton’s laws of motion, and the acceleration

is governed by the car following model.



Therefore, the governing equations of a traffic flow can be developed as below. Let ∆T is

the reaction time, and ∆t is the updation time, the governing equations can be written as,

vtn = vt−∆t

n + at−∆tn × ∆t (14.7)

xtn = xt−∆t

n + vt−∆tn × ∆t +

1

2at−∆t

n ∆t2 (14.8)

atn+1 =

[

αl,m(vtn+1)

m

(xt−∆Tn − xt−∆T

n+1 )l

]

(vt−∆Tn − vt−∆T

n+1 ) (14.9)

The equation 14.7 is a simulation version of the Newton’s simple law of motion v = u + at and

equation 14.8 is the simulation version of the Newton’s another equation s = ut + 1

2at2. The

acceleration of the follower vehicle depends upon the relative velocity of the leader and the

follower vehicle, sensitivity coefficient and the gap between the vehicles.

Numerical Example

Let a leader vehicle is moving with zero acceleration for two seconds from time zero. Then he

accelerates by 1 m/s2 for 2 seconds, then decelerates by 1m/s2for 2 seconds. The initial speed

is 16 m/s and initial location is 28 m from datum. A vehicle is following this vehicle with initial

speed 16 m/s, and position zero. Simulate the behavior of the following vehicle using General

Motors’ Car following model (acceleration, speed and position) for 7.5 seconds. Assume the

parameters l=1, m=0 , sensitivity coefficient (αl,m) = 13, reaction time as 1 second and scan

interval as 0.5 seconds.

Solution The first column shows the time in seconds. Column 2, 3, and 4 shows the accel-

eration, velocity and distance of the leader vehicle. Column 5,6, and 7 shows the acceleration,

velocity and distance of the follower vehicle. Column 8 gives the difference in velocities between

the leader and follower vehicle denoted as dv. Column 9 gives the difference in displacement

between the leader and follower vehicle denoted as dx. Note that the values are assumed to be

the state at the beginning of that time interval. At time t=0, leader vehicle has a velocity of

16 m/s and located at a distance of 28 m from a datum. The follower vehicle is also having the

same velocity of 16 m/s and located at the datum. Since the velocity is same for both, dv =

0. At time t = 0, the leader vehicle is having acceleration zero, and hence has the same speed.

The location of the leader vehicle can be found out from equation as, x = 28+16×0.5 = 36

m. Similarly, the follower vehicle is not accelerating and is maintaining the same speed. The

location of the follower vehicle is, x = 0+16×0.5 = 8 m. Therefore, dx = 36-8 =28m. These

steps are repeated till t = 1.5 seconds. At time t = 2 seconds, leader vehicle accelerates at the

rate of 1 m/s2 and continues to accelerate for 2 seconds. After that it decelerates for a period



Follower

Leader

Time(seconds)

Vel

ocity

15 20 25 10 5 0

17

18

19

20

16

15

30

Figure 14:2: Velocity vz Time

FollowerLeader

25 20 15 10 5 0

−0.5

−1

0

0.5

1

1.5

−1.5 30

Acc

eler

atio

n

Time(seconds)

Figure 14:3: Acceleration vz Time

of two seconds. At t= 2.5 seconds, velocity of leader vehicle changes to 16.5 m/s. Thus dv

becomes 0.5 m/s at 2.5 seconds. dx also changes since the position of leader changes. Since the

reaction time is 1 second, the follower will react to the leader’s change in acceleration at 2.0

seconds only after 3 seconds. Therefore, at t=3.5 seconds, the follower responds to the leaders

change in acceleration given by equation i.e., a = 13×0.528.23

= 0.23 m/s2. That is the current ac-

celeration of the follower vehicle depends on dv and reaction time ∆ of 1 second. The follower

will change the speed at the next time interval. i.e., at time t = 4 seconds. The speed of the

follower vehicle at t = 4 seconds is given by equation as v= 16+0.231×0.5 = 16.12 The location

of the follower vehicle at t = 4 seconds is given by equation as x = 56+16×0.5+1

2×0.231×0.52

= 64.03 These steps are followed for all the cells of the table.

The earliest car-following models considered the difference in speeds between the leader and

the follower as the stimulus. It was assumed that every driver tends to move with the same



Table 14:1: Car-following examplet a(t) v(t) x(t) a(t) v(t) x(t) dv dx

(1) (2) (3) (4) (5) (6) (7) (8) (9)

t a(t) v(t) x(t) a(t) v(t) x(t) dv dx

0.00 0.00 16.00 28.00 0.00 16.00 0.00 0.00 28.00

0.50 0.00 16.00 36.00 0.00 16.00 8.00 0.00 28.00

1.00 0.00 16.00 44.00 0.00 16.00 16.00 0.00 28.00

1.50 0.00 16.00 52.00 0.00 16.00 24.00 0.00 28.00

2.00 1.00 16.00 60.00 0.00 16.00 32.00 0.00 28.00

2.50 1.00 16.50 68.13 0.00 16.00 40.00 0.50 28.13

3.00 1.00 17.00 76.50 0.00 16.00 48.00 1.00 28.50

3.50 1.00 17.50 85.13 0.23 16.00 56.00 1.50 29.13

4.00 -1.00 18.00 94.00 0.46 16.12 64.03 1.88 29.97

4.50 -1.00 17.50 102.88 0.67 16.34 72.14 1.16 30.73

5.00 -1.00 17.00 111.50 0.82 16.68 80.40 0.32 31.10

5.50 -1.00 16.50 119.88 0.49 17.09 88.84 -0.59 31.03

6.00 0.00 16.00 128.00 0.13 17.33 97.45 -1.33 30.55

6.50 0.00 16.00 136.00 -0.25 17.40 106.13 -1.40 29.87

7.00 0.00 16.00 144.00 -0.57 17.28 114.80 -1.28 29.20

7.50 0.00 16.00 152.00 -0.61 16.99 123.36 -0.99 28.64

8.00 0.00 16.00 160.00 -0.57 16.69 131.78 -0.69 28.22

8.50 0.00 16.00 168.00 -0.45 16.40 140.06 -0.40 27.94

9.00 0.00 16.00 176.00 -0.32 16.18 148.20 -0.18 27.80

9.50 0.00 16.00 184.00 -0.19 16.02 156.25 -0.02 27.75

10.00 0.00 16.00 192.00 -0.08 15.93 164.24 0.07 27.76

10.50 0.00 16.00 200.00 -0.01 15.88 172.19 0.12 27.81

11.00 0.00 16.00 208.00 0.03 15.88 180.13 0.12 27.87

11.50 0.00 16.00 216.00 0.05 15.90 188.08 0.10 27.92

12.00 0.00 16.00 224.00 0.06 15.92 196.03 0.08 27.97

12.50 0.00 16.00 232.00 0.05 15.95 204.00 0.05 28.00

13.00 0.00 16.00 240.00 0.04 15.98 211.98 0.02 28.02

13.50 0.00 16.00 248.00 0.02 15.99 219.98 0.01 28.02

14.00 0.00 16.00 256.00 0.01 16.00 227.98 0.00 28.02

14.50 0.00 16.00 264.00 0.00 16.01 235.98 -0.01 28.02

15.00 0.00 16.00 272.00 0.00 16.01 243.98 -0.01 28.02

15.50 0.00 16.00 280.00 0.00 16.01 251.99 -0.01 28.01

16.00 0.00 16.00 288.00 -0.01 16.01 260.00 -0.01 28.00

16.50 0.00 16.00 296.00 0.00 16.01 268.00 -0.01 28.00

17.00 0.00 16.00 304.00 0.00 16.00 276.00 0.00 28.00

17.50 0.00 16.00 312.00 0.00 16.00 284.00 0.00 28.00

18.00 0.00 16.00 320.00 0.00 16.00 292.00 0.00 28.00

18.50 0.00 16.00 328.00 0.00 16.00 300.00 0.00 28.00

19.00 0.00 16.00 336.00 0.00 16.00 308.00 0.00 28.00

19.50 0.00 16.00 344.00 0.00 16.00 316.00 0.00 28.00

20.00 0.00 16.00 352.00 0.00 16.00 324.00 0.00 28.00

20.50 0.00 16.00 360.00 0.00 16.00 332.00 0.00 28.00



speed as that of the corresponding leading vehicle so that

atn =

1

τ(vt+1

n − vtn+1) (14.10)

where τ is a parameter that sets the time scale of the model and 1

τcan be considered as a

measure of the sensitivity of the driver. According to such models, the driving strategy is to

follow the leader and, therefore, such car-following models are collectively referred to as the

follow the leader model. Efforts to develop this stimulus function led to five generations of

car-following models, and the most general model is expressed mathematically as follows.

at+∆Tn+1 =

αl,m [vt−∆Tn+1 ]m

[xt−∆Tn − xt−∆T

n+1 ]l(vt−∆T

n − vt−∆Tn+1 ) (14.11)

where l is a distance headway exponent and can take values from +4 to -1, m is a speed exponent

and can take values from -2 to +2, and α is a sensitivity coefficient. These parameters are to

be calibrated using field data.

14.4 Summary

Microscopic traffic flow modeling focuses on the minute aspects of traffic stream like vehicle to

vehicle interaction and individual vehicle behavior. They help to analyze very small changes

in the traffic stream over time and space. Car following model is one such model where in the

stimulus-response concept is employed. Optimal models and simulation models were briefly

discussed.

14.5 References


New Delhi, 1987.

2. L J Pignataro. Traffic Engineering: Theory and practice. Prentice-Hall, Englewoods

Cliffs,N.J., 1973.


Transportation Systems Engineering 15. Lane Changing Models

Chapter 15

Lane Changing Models

15.1 Overview

The transfer of a vehicle from one lane to next adjacent lane is defined as lane change. Lane

changing has a significant impact on traffic flow. Lane changing models are therefore an im-

portant component in microscopic traffic simulators, which are increasingly the tool of choice

for a wide range of traffic-related applications at the operational level. Modeling the behaviour

of a vehicle within its present lane is relatively straightforward, as the only considerations of

any importance are the speed and location of the preceding vehicle. Lane changing, however,

is more complex, because the decision to change lanes depends on a number of objectives, and

at times these may conflict. Gap acceptance models are used to model the execution of lane-

changes. The available gaps are compared to the smallest acceptable gap (critical gap) and a

lane-change is executed if the available gaps are greater. Gaps may be defined either in terms

of time gap or free space.

15.2 Basic Lane changing model

The basic lane change model is described using the framework shown in Figure 15:1. The

subject vehicle in the current lane tries to change direction either to its left or to its right. If

the gap in the selected lane is acceptable the lane change occurs or else it will remain in the

current lane

15.3 Classification of Lane change

The classification of lane changes is done based on the execution of the lane change and ac-

cordingly two type of lane changs exists.



Left Current Right

NO CHANGE CHANGE LEFT NO CHANGE CHANGE RIGHT

NO CHANGE

Change direction

Gap acceptance

Figure 15:1: Basic Lane Change Model

Start

MLC MLC

Drivingconditions notsatisfactory

Drivingconditions

satisfactory

current lanesother

lanes

Left lane Right laneLeft lane Right lane

GapAccept

GapReject Accept

Gap GapGap Gap Gap GapAccept AcceptReject Reject Reject

Left lanecurrent lanes Right lane current

lanes Left lanecurrent lanes Right lane current

lanescurrent lanes

current lanes

Figure 15:2: Discretionary Lane change model

Mandatory Lane Change (MLC): Mandatory lane change (MLC) occurs when a driver

must change lane to follow a specified path Suppose if a driver wants to make a right turn at

the next intersection the he changes to the right most lane which is referred as Mandatory Lane

change.

Discretionary Lane Change (DLC): Discretionary lane change (DLC) occurs when a

driver changes to a lane perceived to offer better traffic conditions, he attempts to achieve

desired speed, avoid following trucks, avoid merging traffic, etc. Suppose if a driver perceives

better driving conditions in the adjacent lane then he makes a Discretionary Lane change.

15.3.1 MLC and DLC Model

The lane changing model structure is shown in Figure 15:2. The MLC branch in the top level

corresponds to the case when a driver decides to respond to the MLC condition. Explanatory

variables that affect such decision include remaining distance to the point at which lane change



must be completed, the number of lanes to cross to reach a lane connected to the next link,

delay (time elapsed since the MLC conditions apply), and whether the subject vehicle is a

heavy vehicle (bus, truck, etc..,). Drivers are likely to respond to the MLC situations earlier if

it involves crossing several lanes. A longer delay makes a driver more anxious and increases the

likelihood of responding to the MLC situations. And finally, due to lower maneuverability and

larger gap length requirement of heavy vehicles as compared to their non heavy counterparts,

they have a higher likelihood of responding to the MLC conditions.

15.3.2 Decision making

The MLC branch corresponds to the case where either a driver does not respond to an MLC

condition, or that MLC conditions do not apply. A driver then decides whether to perform a

discretionary lane change (DLC). This comprises of two decisions: whether the driving condi-

tions are satisfactory, and if not satisfactory, whether any other lane is better than the current

lane. The term driving conditions satisfactory implies that the driver is satisfied with the driv-

ing conditions of the current lane. Important factors affecting the decision whether the driving

conditions are satisfactory include the speed of the driver compared to its desired speed, pres-

ence of heavy vehicles in front and behind the subject, if an adjacent on ramp merges with the

current lane, whether the subject is tailgated etc.

If the driving conditions are not satisfactory, the driver compares the driving conditions

of the current lane with those of the adjacent lanes. Important factors affecting this decision

include the difference between the speed of traffic in different lanes and the driver’s desired

speed, the density of traffic in different lanes, the relative speed with respect to the lag vehicle

in the target lane, the presence of heavy vehicles in different lanes ahead of the subject etc. In

addition, when a driver considers DLC although a mandatory lane change is required but the

driver is not responding to the MLC conditions, changing lanes opposite to the direction as

required by the MLC conditions may be less desirable.

If a driver decides not to perform a discretionary lane change (i.e., either the driving con-

ditions are satisfactory, or, although the driving conditions are not satisfactory, the current is

the lane with the best driving conditions) the driver continues in the current lane. Otherwise,

the driver selects a lane from the available alternatives and assesses the adjacent gap in the

target lane.. When trying to perform a DLC, factors that affect drivers’ gap acceptance be-

havior include the gap length, speed of the subject, speed of the vehicles ahead of and behind

the subject in the target lane, and the type of the subject vehicle (heavy vehicle or not). For

instance, a larger gap is required for merging at a higher travel speed. A heavy vehicle would

require a larger gap length compared to a car due to lower maneuverability and the length of



the heavy vehicle.

15.4 Lane changing models

Most models classify lane changes as either mandatory or discretionary lane change. This sepa-

ration implies that there are no trade-offs between mandatory and discretionary considerations.

For example, a vehicle on a freeway that intends to take on of-ramp will not overtake a slower

vehicle if the distance to the off-ramp is below a threshold, regardless of the speed of that ve-

hicle. Furthermore, in order to implement MLC and DLC model separately, rules that dictate

when drivers begin to respond to MLC conditions need to be defined. However, this point

is unobservable, and so only judgment-based heuristic rules, which often are defined by the

distance from the point where the MLC must be completed, are used. Just like the judgement

based lane changing models ,there also exist lot of other models like general acceleration based

lane changing models and gap acceptance based lane changing models

15.4.1 Forced merging model

If the gap on the target lane is not acceptable then the subject vehicle forces the lag vehicle on

the target to decelerate until the gap is acceptable. This process is known as Forced merging.

At every discrete point in time, a driver is assumed to (a) evaluate the traffic environment in

the target lane to decide whether the driver intends to merge in front of the lag vehicle in the

target lane and (b) try to communicate with the lag vehicle to understand whether the driver’s

right of way is established. If a driver intends to merge in front of the lag vehicle and right

of way is established, the decision process ends and the driver gradually move into the target

lane. We characterize this instant by state M, where M denotes start forced merging. This

process may last from less than a second to a few seconds. If right of way is not established,

the subject continues the evaluation/communication process (i.e., remains in state M) during

the next time instant.

15.4.2 Cooperative Merging

The models discussed so far assume that lane changing is executed through gap acceptance.

However, in congested traffic conditions acceptable gaps may not be available, and so other

mechanisms for lane changing are needed. For example, drivers may change lanes through

courtesy and cooperation of the lag vehicles on the target lane that will slow down in order to

accommodate the lane change. In other cases, some drivers may become impatient and decide



Lane 1

Lane 2

Lane 3

Figure 15:3: Process of lane change

to force in to the target lane and compel the lag vehicle to slow down.

15.5 Discretionary lane changng process

The discretionary lane changing process is modeled as a sequence of the following three steps:

1. Decision to consider a lane change,

2. Check for the feasibility,

3. Gap acceptance

Lane changing process is explained using the example which is shown in Figure 15:3. The

subject vehicle in lane 2 makes a decision to consider a lane change and then it selects a target

lane which may be either lane 1 or lane 3. Then it checks for the feasibility of lane change.

Now this subject vehicle accepts the gap in the target lane to make a lane change.

15.5.1 Desire to change the lane

Decision to change the lane in discretionary lane change conditions may be taken due to a

number of factors but basically what the driver has in mind should be higher utility in the

target lane which may be for example higher speed. Here we use the equation suggested by

Gipps (1986) to find if it is possible for the driver to attain his desired speed within the existing

space difference between his vehicle and the preceding vehicle in the current lane. If required

space difference is not available, the driver is assumed to decide lane change. The relation is

given as:

Vn(t + T ) = bn T +√

b2n T 2 − bn (2Dx(t) − Vn(t) T − Vn−1(t)2/b) (15.1)



where, Vn(t + T ) is the maximum safe speed for vehicle n with respect to the preceding vehicle

at time (t+T), Vn(t) is the velocity nth vehicle, Vn−1(t) is the velocity n-1th vehicle, bn (< 0) is

the most severe braking the driver is prepared to undertake, T is the time between consecutive

calculations of speed and position, b is an estimate of bn−1 employed by the driver of vehicle n,

and Dx(t) is the distance between front of subject vehicle and rear of leading vehicle at t. The

driver is assumed to decide to change lane if Dx is more than the existing space gap between

the subject vehicle and preceding vehicle in current lane.

15.5.2 Check for feasibility

The lane change is said to be feasible if the chance that the subject vehicle would collide at

the rear of preceding vehicle in the target lane and the chance that the lag vehicle in the

target lane would collide at the rear of the subject vehicle is avoided. To check if the subject

vehicle would collide at the rear of preceeding vehicle in the target lane we consider the subject

vehicle as n and preceding vehicle in the target lane as n-1.Then we substitute the values in the

equation 15.1. If the maximum safe speed can be attained in the time T with a deceleration less

than the maximum possible deceleration of the vehicle we say that the lane change is feasible.

To check if the lag vehicle after sighting the subject vehicle in the target lane, would collide

at the rear of subject vehicle in the target lane. For this we consider the lag vehicle as N and

subject vehicle in the target lane as n-1. Also we have to consider that the space difference

available will be changed as both the vehicles would have moved a distance during the lane

change. Then we substitute the values in the equation 15.1. If the maximum safe speed can be

attained in the time T by the lag vehicle with a deceleration less than the maximum possible

deceleration of the vehicle we say that the lane change is feasible

15.5.3 Gap acceptance

A gap is defined as the gap in between the lead and lag vehicles in the target lane (see Fig-

ure 15:4). For merging into an adjacent lane, a gap is acceptable only when both lead and lag

gap are acceptable. Drivers are assumed to have minimum acceptable lead and lag gap lengths

which are termed as the lead and lag critical gaps respectively. These critical gaps vary not only

among different individuals, but also for a given individual under different traffic conditions.

Most models also make a distinction between the lead gap and the lag gap and require that

both are acceptable. The lead gap is the gap between the subject vehicle and the vehicle ahead

of it in the lane it is changing to. The lag gap is defined in the same way relative to the vehicle

behind in that lane. The critical gap lengths are assumed to be log normally distributed The



critical gap for driver n at time t is assumed to have the following relation.

Gg,crn = e[X

g

nβ+αVn+εn]

where, Gg,crn (t) is the critical gap measure for gap G perceived by driver n at time step t, Xg

n(t)

is the explanatory variable used to characterize mean Gg,crn (t), εn is the random term follows

log normal distribution, and αg is the parameter of driver specific random term vn. Assuming

X

X Y

Y

lead vehicle

front vehicle

lag vehicle

subject

lag gap lead gaptotal clear gap + vehicle length

Figure 15:4: Definition of gaps

εgn(t) ≈ N(0, σ2

εg) the conditional probability of acceptance of a gap p(g) considering that the

probability of lead gap acceptance (p(lead)) and lag gap (p(lag)) acceptance as two independent

events is probability that the lead and lag gaps are accepted. That is:

P (g) = p(lead) × p(lag)

= p(Gleadtn ≥ log(Glead

cr,tn) and Gtagtn ≥ log(Gtag

cr,tn))

= p(log(Gleadtn ) ≥ log(Glead

cr,tn)) × P (log(Gtagtn ) ≥ log(Gtag

cr,tn))

= Φ

[

log(Gleadtn ) − βleadX

leadtn − αleadVn

σε,lead

]

×

Φ

[

log(Glagtn ) − βlagX

lagtn − αleadVn

σε,lag

]

(15.2)

where (X) means X follows standard normal distribution ,N(0,1)

Numerical Example

For the given state of traffic predict if the subject vehicle in the figure 5 would initiate a

lane change.if yes what is the feasibility and probability of lane change. Given is the midblock

section of 2 lane highway with no other blocks in either of the lane. Neglect lateral acceleration.



Consider update time 1 sec. Maximum deceleration driver ready to apply is -2 m/s2 and

maximum acceleration feasible is -2.2 m/s2 Assume that lane change take 1 second. Given:

σlead =2, σlead = 3 ,Glead =40m, Glag =50m ,βlead = βlag = 1 ,Xnlead = Xnlag = 0.8, V leadn =

V lagn = 0.7 , αlead =αlag = 1.2

N−1

y

YX

X

lag vehicle

DIRECTION OF TRAFFIC FLOW

20.83 m/s

18 m/s

18 m/s

N

19.4 m/s

lead vehicle

30 m

40m50 m

Subject

Solution Step 1. Decision to change the lane: In the case of discretionary lange change,

the decision to change the lane is taken by the driver when he finds higher utility in any other

lane. Here, we consider higher speed or desired speed as higher utility. Let the desired speed

be 25 m/s2. Considering the subject vehicle as vehicle n and the vehicle preceding it in the

current lane as vehicle n-1, we calculate the minimum distance required by the subject vehicle

to attain the desired speed in a time T

Dx = xn−1(t) − Sn−1 − xn(t)

Vn(t + T ) = bn T +√

b2nT

2 − bn (2Dx − VnT − Vn − 12/b)

25 = −2 × 1 +√

−22 + (2 Dx − 19.4 + 182/2.5)

The Dx in this problem is 155 m, which means that the subject vehicle requires at least 155 m

to reach his desired speed. But the gap available is 30 m. So decision is to change the lange or

trigger DLC.

Step 2. Check for the feasibility of lane change: A lane change is said to be

feasible if the subject vehicle is able to maintain maximum safe speed with respect to the

preceding vehicle in the target line. In order to find the maximum safe speed possible for the

subject vehicle to avoid collision we consider the subject vehicle as N and preceding vehicle in

the target lane as N-1. Then we substitute the values in the second equation. Vn(t + T ) =

−2× 1 + [−22 + 22(40) − 19.4 + 182/2.5]1/2 = 17.6m/s And the deceleration required = (17.6-

19.4)/1 = -1.79 m/s2 Since -1.79 m/s2 less than -2.2 m/s2 the lane change feasible to avoid




30 m

18m/s19.4 m/s

18m/s

N−1

N

20.83 m/s

50 m 40 m

X

X Y

Y

lag vehicle lead vehicle

subject

collision with the lead vehicle in the target lane. Now we have to check if the lag vehicle

in the target line would be able to avoid the collision with the subject vehicle after the lane

change. For this we take lag vehicle as N th vehicle and subject vehicle as N − 1th vehicle Here,

N N−1

19.4 m/s 18 m/s

20.83 m

50 m 40 m

18 m/s

19.4 m

30 m

Y

Y

20.83 m/s


Lag vehiclelead vehicle

X

X

Dx = 50+19.4−20.83 = 48.5m as the lag vehicle and subject vehicle would have moved some

distance during the lane change duration of 1 second. These distances are 20.83 m and 19.4

m respectively. Vn(t + T ) = −2x1 + [−22 + 22(48.5) − 20.83 + 19.42/2.5]1/2 = 19.38m/s The

deceleration required to be applied by the lag vehicle in the target lane to avoid collision with

the subject vehicle = (19.38 − 20.83)/1 = −1.44m/s2. Since -1.44 m/s2 ¡ -2.2 m/s2 the lane

change feasible to avoid collision of the lag vehicle in the target lane.

Step 3. Check for the gap acceptance of lane change in the given state of

traffic: Here we find that the lag gap that was available is 50 m and the lead gap is 40



m.using the equation 2 we get,

p(g) = Φ

[

log(Gleadtn ) − βleadX

leadtn − αleadVn

σε,lead

]

×

Φ

[

log(Glagtn ) − βlagX

lagtn − αleadVn

σε,lag

]

= Φ(log(40) − 0.8 − 0.84)/2 × Φ(log(50) − 0.8 − 0.84)/2

= Φ(1.02) × Φ(0.75) = 0.8212 × 0.7734 = 0.635.

This means that a given driver would opt for a lane change in the the given condition with a

probability of 0.635.

15.6 Average Delay for Lane change

The blockage length and the average delay for the lane change are calculated based on the

following formulae.

BL =T × V s

N

Average delay =1

2×

BL

V r

where, T = Total time of headways rejected, BL = blockage length, Vs = stream velocity, Vr

= relative velocity, N = number of acceptable gap

Numerical Example

In a two lane, one way stream of 1000 vph with 360 vehicles in Lane A and the remaining

vehicles in lane B. 8% of the vehicles in lane A have gaps less than 1 sec and 18% of the

vehicles in lane A have gaps less than 2 sec. Compute the time during which vehicles in Lane

B may not change to Lane A in 1 hour. Assume driver requires one second ahead and behind

in making a lane change.

Solution Total acceptable time for lane change in an hour = 3600 - total rejected headway

- total clearance time. Given that 0 to 1 second Gaps is 8% of 360 = 29 and 1 to 2 second

Gaps is (18-8) % of 360 = 36. Total = 65 Gaps. Time spent in Gaps 0 to 1 second = 29 x

.5 = 14.5 sec, and Time spent in Gaps 1 to 2 second = 36 x 1.5 = 54.0 sec. As 65 Gaps are

rejected, Acceptable Gaps are (360-65) = 295 Gaps. In this 295 Gaps clearance time = 295

x 2 = 590 sec. Time lost in rejected gap = 14.5+54=68.5. Therefore, Total time left in one



Lane A (360 vph)

Lane B (640 vph)

Figure 15:5: Numerical example

gAgR gA

gR gA

car car


hour to accept Gap=(3600 - 590 - 68.5) = 2941 sec. Vehicle can change lane in (2941/3600) =

81.7% of the Total time. Vehicle is prevented from changing lane in 18.3% of the time.

Numerical Example

In a two lane, one way stream of 1000 vph with 360 vehicles in Lane A and the remaining

vehicles in lane B. 8% of the vehicles in lane A have gaps less than 1 sec and 18% of the

vehicles in lane A have gaps less than 2 sec. Compute the average waiting for the driver to

make a lane change. Assume driver velocity in lane B = 40 kmph and stream velocity = 50

kmph. Solution: The average length of headways and portions of head ways of insufficient

length for a lane change, which may be considered as general blockages moving in the stream.

Division of this Blockage length by the relative speed determines potential total delay time of

the blockade. Finally since a delayed vehicle is as likely to be at the head as at the tail of

such a blockade at the moment of desired lane change, the total delay must be divided by 2 for

average delay time.

Average delay =1

2×

BL

V r

BL =T ∗ V s

N

where T = 3600× 18.3% = 658.8, Vs = 50 kmph, N = acceptable gaps. So 0 to 2 second Gaps

= 18 % of 360 = 65. Therefore N = 360-65 = 295. BL = 658.8×50

295= 111.6. In the above figure

the vertical lines are the centre line of the cars and gr, ga represents the acceptable and rejected

gaps respectively.

Average delay =1

2×

BL

V r

Average delay =1

2×

111.6

(50 − 40)= 5.58sec



15.7 Summary

Lane changing is an important component of microscopic traffic simulation model, and has

significant impact on the results of analysis that uses these tools. In recent years, interest in

the development of lane changing models and their implementation in traffic simulators have

increased dramatically. There is a lot of scope for the improvement of these lane change models

like integrating acceleration behavior, impact of the buses, bus stops, traffic signals and queues

that form due to lane change maneuver.

15.8 References

1. K I Ahmed. Modeling drivers’ acceleration and lane changing behaviors. PhD thesis,

Department of Civil and Environmental Engineering, MIT, 1999.

2. C F Choudhury. Modeling driving decisions with Latent plans. PhD thesis, Department

of Civil and Environmental Engineering, MIT, 2007.

3. D R Drew. Traffic flow theory and control. McGraw-Hill Book Company, New York,

1968. IITB–.

4. P G Gipps. A model for the structure of lane-changing decisions. Transportation

Research Part B: Methodological, Volume 20, Issue 5, 1986.



Transportation Systems Engineering 16. Microscopic Traffic Simulation

Chapter 16

Microscopic Traffic Simulation

16.1 Overview

The complexity of traffic stream behaviour and the difficulties in performing experiments with

real world traffic make computer simulation an important analysis tool in traffic engineering.

The physical propagation of traffic flows can be specifically described using traffic flow models.

By making use of different traffic simulation models, one can simulate large scale real-world

situations in great detail. Depending on the level of detailing, traffic flow models are classified

into macroscopic, mesoscopic and microscopic models. Macroscopic models view the traffic flow

as a whole whereas microscopic ones gives attention to individual vehicles and their interactions

while the mesoscopic models fall in between these two. This chapter gives an overview of the

basic concepts behind simulation models and elaboration about the microscopic approach for

modelling traffic.

A microscopic model of traffic flow attempts to analyse the flow of traffic by modelling

driver-driver and driver-road interactions within a traffic stream which respectively analyses

the interaction between a driver and another driver on road and of a single driver on the

different features of a road. Many studies and researches were carried out on driver’s behavior

in different situations like a case when he meets a static obstacle or when he meets a dynamic

obstacle. Among these, the pioneer development of car following theories paved the way for

the researchers to model the behaviour of a vehicle following another vehicle in the 1950s and

1960s.

16.2 Traffic Simulation Models

Simulation modelling is an increasingly popular and effective tool for analysing a wide variety of

dynamical problems those associated with complex processes which cannot readily be described

in analytical terms. Usually, these processes are characterized by the interaction of many system



components or entities whose interactions are complex in nature. Specifically, simulation models

are mathematical/logical representations of real-world systems, which take the form of software

executed on a digital computer in an experimental fashion. The most important advantage is

that these models are by no means exhaustive.

16.2.1 Need for simulation

Traffic simulation models have a large variety of applications in the required fields. Now-a-days

they become inevitable tools of analysis and interpretation of real world situations especially in

Traffic Engineering. The following are some situations where these models can find their scope.

1. When mathematical or analytical treatment of a problem is found infeasible or inadequate

due to its complex nature.

2. When there is some doubt in the mathematical formulation or results.

3. When there is a need of an animated view of flow of vehicles to study their behaviour.

It is important to note that simulation can only be used as an auxiliary tool for evaluation and

extension of results provided by other conceptual or mathematical formulations or models.

16.2.2 Applications

Traffic simulations models can meet a wide range of requirements:

1. Evaluation of alternative treatments

2. Testing new designs

3. As an element of the design process

4. Embed in other tools

5. Training personnel

6. Safety Analysis



16.2.3 Classifications

Traffic simulation models can be classified based on different criteria. Figure 16:1 shows various

types of classification. In a broader sense, they can be categorized into continuous and discrete

ones according to how the elements describing a system change their states. The latter is again

classified into two.

• Discrete time based models

• Discrete event based models

Traffic simulation models

Macroscopic

Mesoscopic

Microscopic

Discrete

StochasticDeterministic

Continuous

Figure 16:1: Classification of Traffic simulation models

The first, divides time into fixed small intervals and within each interval the simulation model

computes the activities which change the states of selected system elements. For some specific

applications, considerable savings in computational time can be achieved by the use of event

based models where scanning is performed based on some abrupt changes in the state of the

system (events). However the discrete time models could be a better choice where the model

objectives require more realistic and detailed descriptions.

According to the level of detailing, simulation models can be classified into macroscopic,

mesoscopic and microscopic models. A macroscopic model describes entities and their activities

and interactions at a low level of detail. Traffic stream is represented in an aggregate measure

in terms of characteristics like speed, flow and density. A mesoscopic model generally repre-

sents most entities at a high level of detail but describes their activities and interactions at a

much lower level of detail. A microscopic model describes both the system entities and their

interactions at a high level of detail. Car following models and lane changing models are some

significant examples. The choice of a particular type of model depends on the nature of the

problem of interest.

Depending on the type of processes represented by the model, there are deterministic and

stochastic models. Models without the use of any random variables or in other words, all entity

interactions are defined by exact mathematical/logical relationships are called deterministic

models. Stochastic models have processes which include probability functions.



16.3 Building Traffic Simulator

The basic steps involved in the development are same irrespective of the type of model. The

different activities involved are the following.

1. Define the problem and the model objectives

2. Define the system to be studied - Roadway, Vehicle and Driver characteristics

3. Model development

4. Model calibration

5. Model verification

6. Model validation

7. Documentation

The most significant steps among the above are described with the help of stating the procedure

for developing a microscopic model.

16.3.1 Model development

The framework of a model consists of mainly three processes as mentioned below.

1. Vehicle generation

2. Vehicle position updation

3. Analysis

The flow diagram of a microscopic traffic simulation model is given in Figure 16.2. The basic

structure of a model includes various component models like car following models like car

following models, lane changing models etc. which come under the vehicle position updation

part. In this chapter, the vehicle generation stage is explained in detail. The vehicles can

be generated either according to the distributions of vehicular headways or vehicular arrivals.

Headways generally follow one of the following distributions.

1. Negative Exponential Distribution (Low flow rate)

2. Normal Distribution (High flow rate)

3. Erlang Distribution (Intermediate flow rate)



The generation of vehicles using negative exponential distribution is demonstrated here. The

probability distribution function is given as follows.

f(x) = λe−λx (16.1)

From the above equation, the expression for exponential variate headway X can be derived as:

X = µ(− loge R) (16.2)

where, µ is the mean headway, R is the random number between 0 and 1 Random number

Start

Input and Initialization

Headway generationfor first vehicle

Iscurrenttime=

multiple of scaninterval

Iscurrenttime=cumulativeheadway

vehicle generation andnext headway generation

Is

over?

End

Vehicle position updation

Time stepupdation

Simulation timeNo

Yes

Yes

No

No

Yes

Figure 16:2: Flow diagram of a Microscopic traffic simulation model

generation is an essential part in any stochastic simulation model, especially in vehicle genera-

tion module. Numerous methods in terms of computer programs have been devised to generate

random numbers which appear to be random. This is the reason why some call them pseudo-

random numbers. Therefore headways can be generated using the above expression by giving

a random number and the mean headway as the input variables.



In a similar way, the vehicular arrival pattern can be modeled using Poisson’s distribution.

The probability mass function is given as:

p(x) =λxe−λ

x!(16.3)

where, p(x) is the probability of x vehicle arrivals in an interval t, λ is the mean arrival rate of

vehicles If the probability of no vehicle in the interval t is given as p(0), then this probability

is same as the probability that the headway greater than or equal to t.

Numerical example

Given flow rate is 900 veh/hr. Simulate the vehicle arrivals for 1 min using negative exponential

distribution.

Solution Step 1: Calculate the mean headway µ = 1(900/3600)

= 4sec. Step 2: Generate the

random numbers between 0 and 1. Step 3: Calculate the headways and then estimate the

cumulative headways. The calculations are given in Table 16:1

X = µ(−logeR)

Numerical example

The hourly flow rate in a road section is 900 veh/hr. Use Poisson distribution to model this

vehicle arrival for 10 min.

Solution Step 1: Calculate the no. of vehicles arriving per min. λ = 900/60 = 15 veh/min.

Step 2: Calculate the probability of 0, 1, 2, ... vehicles per minute using Poisson distribution

formula. Also calculate the cumulative probability as shown below.

p(x) =λxe−λ

x!

Step 3: Generate random numbers from 0 to 1. Using the calculated cumulative probability

values, estimate the no. of vehicles arriving in that interval as shown in Table below. Here

the total number of vehicles arrived in 10 min is 143 which is almost same as the vehicle arrival

rate obtained using negative exponential distribution.



Veh. No. R X Arrival time (sec)

1 0.73 1.23 1.23

2 0.97 0.14 1.37

3 0.27 5.26 6.63

4 0.44 3.25 9.88

5 0.52 2.63 12.51

6 0.77 1.05 13.55

7 0.43 3.39 16.94

8 0.81 0.84 17.79

9 0.08 9.96 27.75

10 0.74 1.18 28.93

11 0.53 2.58 31.51

12 0.81 0.83 32.34

13 0.15 7.46 39.80

14 0.44 3.26 43.06

15 0.29 5.02 48.08

16 0.68 1.56 49.63

17 0.05 12.09 61.72

Table 16:1: Vehicle arrivals using Negative exponential distribution



n p(x=n) p(x¡=n)

0 0.000 0

1 0.000 0.000

2 0.000 0.000

3 0.000 0.000

4 0.001 0.001

5 0.002 0.003

6 0.005 0.008

7 0.010 0.018

8 0.019 0.037

9 0.032 0.070

10 0.049 0.118

11 0.066 0.185

12 0.083 0.268

13 0.096 0.363

14 0.102 0.466

15 0.102 0.568

16 0.096 0.664

17 0.085 0.749

18 0.071 0.819

19 0.056 0.875

20 0.042 0.917

Table 16:2: Calculation of probabilities using Poisson distribution



t (min) R n

1 0.231 11

2 0.162 10

3 0.909 19

4 0.871 18

5 0.307 12

6 0.008 6

7 0.654 15

8 0.775 17

9 0.632 15

10 0.901 20

143

Table 16:3: Vehicle arrivals using Poisson distribution

16.3.2 Model calibration

The activity of specifying data to the model that describes traffic operations and other features

which are site specific is called calibration of the model. In other words, calibration is the

process of quantifying model parameters using real-world data. This data may take the form

of scalar elements and of statistical distributions. Calibration is a major challenge during the

implementation stage of any model. The commonly used methods of calibration are regression,

optimization, error determination, trajectory analysis etc. A brief description about various

errors and their significance is presented in this section. The optimization method of calibration

is also explained using the following example problem.

Numerical example

The parameters obtained in GM car-following model simulation are given in Table below. Field

observed values of acceleration of follower is also given. Calibrate the model by finding the value

of α. Assume l=1 and m=0. Use optimization method to solve the problem.

Solution Step 1: Formulate the objective function (z).

Minimize z =4

∑

i=1

(

aobsi − acal

i

)2.



Observed Acceleration (aobs) Velocity difference, dv Distance headway, dx

0.23 1.5 29.13

0.46 1.88 29.97

0.67 1.16 30.73

0.82 0.32 31.10

Table 16:4: Parameters of GM Model

Step 2: Express acali in terms of α. As per GM model (since l=1 and m=0),

acali =

α × dv

dx

Step 3: Therefore the objective function can be expressed as:

z = (0.23 − 0.05α)2 + (0.46 − 0.06α)2 + (0.67 − 0.04α)2 + (0.82 − 0.01α)2

Step 4: Since the above function is convex, differentiating and then equating to zero will give

the solution (as stationary point is the global minimum). Differentiating with respect to and

equating to zero,dz

dα= 0

Then, value of α is obtained as 9.74.

16.3.3 Determination of Errors

Most of the available commercial traffic simulation software provides advanced user-friendly

graphic user interfaces with flexible and powerful graphic editors to assist analysts in the model-

building process. This reduces the number of errors. There are a number of manual ways to

quantify the error associated with every parameter while calibrating them. Some of the common

measures of error and their expressions are discussed below.

1. Root mean square error

RMSE =

√

1

NΣi=1N(xi − yyi)2 (16.4)

2. Root mean squared normalized error

RMSNE =

√

1

NΣi=1N(

xi − yi

yi

)2 (16.5)



3. Mean error

ME =1

NΣi=1N(xi − yi) (16.6)

4. Mean normalized error

MNE =1

NΣi=1N(

xi − yi

yi) (16.7)

where, xi is the ith measured or simulated value, yi is the ith observed value

The above error measures are useful when applied separately to measurements at each

location instead of to all measurements jointly. They indicate the existence of systematic bias

in terms of under or over prediction by the simulation model. Taking into account that the series

of measurements and simulated values can be collected at regular time intervals, it becomes

obvious that they can be interpreted as time series and, therefore, used to determine how close

the simulated and the observed values are. Thus it can be determined that how similar both

time series are. On the other hand, the use of aggregated values to validate a simulation seems

contradictory if one takes into account that it is dynamic in nature, and thus time dependent.

Theil defined a set of indices aimed at this goal and these indices have been widely used for that

purpose. The first index is Theil’s indicator, U (also called Theil’s inequality coefficient), which

provides a normalized measure of the relative error that reduces the impact of large errors:

U =

√

1N

Σi=1N(xi − yi)2

√

1N

Σi=1N(xi)2 +√

1N

Σi=1N(yi)2(16.8)

The global index U is bounded, 0 ≤ U ≤ 1, with U = 0 for a perfect fit and xi = yi for i = 1 to

N, between observed and simulated values. For U ≤ 0.2, the simulated series can be accepted

as replicating the observed series acceptably well. The closer the values are to 0, the better will

be the model. For values greater than 0.2, the simulated series is rejected.

Numerical example

The observed and simulated values obtained using Model 1 and Model 2 are given in Table

below.

1. Comment on the performance of both the models based on the following error measures

- RMSE, RMSNE, ME and MNE.

2. Using Theil’s indicator, comment on the acceptability of the models.



Table 16:5: Observed and Simulated values

Simulated values, x

Observed values, y Model 1 Model 2

0.23 0.2 0.27

0.46 0.39 0.5

0.67 0.71 0.65

0.82 0.83 0.84

Table 16:6: Error calculations for Model 1

Model 1

(x − y) (x−yy

) (x − y)2 (x−yy

)2

-0.030 -0.130 0.0009 0.0170

-0.070 -0.152 0.0049 0.0232

0.040 0.060 0.0016 0.0036

0.010 0.012 0.0001 0.0001

ǫ = -0.050 ǫ = -0.211 ǫ = 0.0075 ǫ = 0.0439

ME = 0.013 MNE = 0.053 RMSE = 0.043 RMSNE = 0.105

Solution

1. Using the formulas given below (Equations 16.4, 16.5, 16.6, 16.7), all the four errors can

be calculated. Here N = 4.

RMSE =

√

1

NΣi=1N(xi − yyi)2

RMSNE =

√

1

NΣi=1N(

xi − yi

yi

)2

ME =1

NΣi=1N(xi − yi)

MNE =1

NΣi=1N(

xi − yi

yi)

Tabulations required are given below. Comparing Model 1 and Model 2 in terms of

RMSE and RMSNE, Model 2 is better. But with respect to ME and MNE, Model 1 is

better.



Table 16:7: Error calculations for Model 2

Model 2

(x − y) (x−yy

) (x − y)2 (x−yy

)2

0.040 0.174 0.0016 0.0302

0.040 0.087 0.0016 0.0076

-0.020 -0.030 0.0004 0.0009

0.020 0.024 0.0004 0.0006

ǫ = 0.080 ǫ = 0.255 ǫ= 0.0040 ǫ = 0.0393

ME = 0.020 MNE = 0.064 RMSE = 0.032 RMSNE = 0.099

Table 16:8: Theil’s indicator calculation

x2

Model 1 Model 2 y2

0.04 0.0729 0.0529

0.1521 0.25 0.2116

0.5041 0.4225 0.4489

0.6889 0.7056 0.6724

ǫ = 1.3851 ǫ = 1.451 ǫ = 1.3858

2. Theil’s indicator

U =

√

1N

Σi=1N(xi − yi)2

√

1N

Σi=1N(xi)2 +√

1N

Σi=1N(yi)2

The additional tabulations required are as follows: The value of Theil’s indicator is ob-

tained as: For Model 1, U = 0.037 which is ≤ 0.2, and For Model 2, U = 0.027 which is

≤ 0.2. Therefore both models are acceptable.

16.3.4 Model Verification

Following de-bugging, verification is a structured regimen to provide assurance that the soft-

ware performs as intended. Since simulation models are primarily logical constructs, rather

than computational ones, the analyst must perform detailed logical path analyses. When com-

pleted, the model developer should be convinced that the model is performing in accord with



expectations over its entire domain of application.

16.3.5 Model Validation

Validation is the process to determine whether the simulation model is an accurate represen-

tation of the system under study. This establishes that the model behaviour accurately and

reliably represents the real-world system being simulated, over the range of conditions antici-

pated and it involves the following major steps.

1. Acquiring and formatting real world data

2. Establishing the validation criteria - Hypotheses, Statistical tests etc.

3. Experimental design for validation including a variety of scenarios

4. Perform validation study

5. Identify the causes of failure if any and repair the model accordingly

The methodological scheme for validation is shown in the following Figure 16:3.

16.4 Simulation Packages

Now a days, traffic simulation packages like CORSIM and VISSIM are frequently used as tools

for analysing traffic. VISSIM is a microscopic, time step and behaviour based simulation model

developed to analyse the full range of functionally classified roadways and public transporta-

tion operations. Since all these are commercial software packages, it is not possible to make

sufficient changes in the internal parameters used in these models according to the specific

requirements. Common applications of these packages include freeway and arterial corridor

studies, subarea planning studies, evacuation planning, freeway management strategy devel-

opment, environmental impact studies, Intelligent Transportation Systems (ITS) assessments,

current and future traffic management schemes etc.

Results of simulation can be interpreted in different ways. Animation displays of extracting

the sought information and insights from the mass of the traffic environment (if available) are

a most powerful tool for analysing simulation results. If the selected traffic simulation lacks

an animation feature or if questions remain after viewing the animation, then the following

procedures may be adopted:



AcceptYes No

Are

Close?

CompareSystem DataMeasured Values

Simulation Model

DataOutput:Collected

Simulation Model

System Data

System DataCollection

Analysis andCompletion

Data Filtering

Model input toSimulator

Significantly

Figure 16:3: Methodological scheme for validation

1. Execute the model to replicate existing real-world conditions and compare its results with

observed behaviour. This ”face validation” can be done to identify model or implemen-

tation deficiencies.

2. Perform ”sensitivity” tests on the study network by varying key variables and observing

model responses in a carefully designed succession of model executions.

3. Plot these results. A review will probably uncover the perceived anomalies

Statistical analysis of the simulation results are also conducted to present point estimates of

effectiveness and to form the confidence intervals. Through these processes, one can establish

that which simulation system is the best among the different alternatives.

16.5 Conclusion

It can be observed from the study that using different microscopic simulation models, large scale

real-world situations can be simulated in great detail. New applications of traffic simulation

can contribute significantly to various programs in ITS. Calibration and validation are the



major challenges to be tackled. It is expected that further exploration would open up better

opportunities for better utilization and further development of these models.

16.6 References

1. J Barcelo. Fundamentals of Traffic Simulation. Springer, 2010.

2. R Kitamura and M Kuwahara. Simulation Approaches in Transportation Analysis.

Springer, 2005.

3. E Lieberman and A K Rathi. Traffic simulation, Traffic flow theory. 1997.

4. L J Pignataro. Traffic Engineering: Theory and practice. Prentice-Hall, Englewoods

Cliffs,N.J., 1973.


Transportation Systems Engineering 17. Traffic Flow Modeling Analogies

Chapter 17

Traffic Flow Modeling Analogies



Contents

17 Traffic Flow Modeling Analogies 1

17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

17.2 Model framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

17.2.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

17.2.2 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

17.2.3 Derivation of the Conservation equation . . . . . . . . . . . . . . . . . . 5

17.3 Analytical Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

17.3.1 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

17.3.2 Method of Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . 7

17.3.3 Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

17.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

17.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

17.1 Introduction

If one looks into traffic flow from a very long distance, the flow of fairly heavy traffic appears

like a stream of a fluid. Therefore, a macroscopic theory of traffic can be developed with the

help of hydrodynamic theory of fluids by considering traffic as an effectively one-dimensional

compressible fluid. The behaviour of individual vehicle is ignored and one is concerned only

with the behaviour of sizable aggregate of vehicles. The earliest traffic flow models began by

writing the balance equation to address vehicle number conservation on a road. Infact, all

traffic flow models and theories must satisfy the law of conservation of the number of vehicles

on the road.



17.2 Model framework

17.2.1 Assumptions

The traffic flow is similar to the flow of fluids and the traffic state is described based on speed,

density and flow. However the traffic flow can be modelled as a one directional compressible

fluid. The two important assumptions of this modelling approach are:

• The traffic flow is conserved, or in other words vehicles are not created or destroyed. The

continuity or conservation equation can be applied.

• There is one to one relationship between speed and density as well as flow and density.

The difficulty with this assumption is that although intuitively correct, in some cases this can

lead to negative speed and density. Further, for a given density there exists many speed values

are actually measured. These assumptions are valid only at equilibrium condition, that is, when

the speed is a function of density. However, equilibrium can be rarely observed in practice and

therefore hard to get Speed-density relationship. These are some of the limitations of continuous

modelling. The advantages of the continuous modelling are:

• Better than input output models because flow and density are set as a function of time

and distance.

• Compressibility: ie., flow is assumed to be a function of density.

• Solving the continuity equation (or flow conservation equation) and the state equation

(speed-density and flow-density) are basic traffic flow equations (q = k.v). By using the

equation that define q, k, and v at any location x and time t, we can evaluate the system

using measures of effectiveness such as delays, travel time etc.

17.2.2 Formulation

Assuming that the vehicles are flowing from left to right, the continuity equation can be written

as∂k(x, t)

∂t+

∂q(x, t)

∂x= 0 (17.1)

where x denotes the spatial coordinate in the direction of traffic flow, t is the time, k is the

density and q denotes the flow. However, one cannot get two unknowns, namely k(x, t) by

and q(x, t) by solving one equation. One possible solution is to write two equations from two



regimes of the flow, say before and after a bottleneck. In this system the flow rate before and

after will be same, or

k1v1 = k2v2 (17.2)

From this the shockwave velocity can be derived as

v(to)p =q2 − q1

k2 − k1

(17.3)

This is normally referred to as Stock’s shockwave formula. An alternate possibility which

Lighthill and Whitham adopted in their landmark study is to assume that the flow rate q is

determined primarily by the local density k, so that flow q can be treated as a function of only

density k. Therefore the number of unknown variables will be reduced to one. Essentially this

assumption states that k(x,t) and q (x,t) are not independent of each other. Therefore the

continuity equation takes the form

∂k(x, t)

∂t+

∂q(k(x, t))

∂x= 0 (17.4)

However, the functional relationship between flow q and density k cannot be calculated from

fluid-dynamical theory. This has to be either taken as a phenomenological relation derived from

the empirical observation or from microscopic theories. Therefore, the flow rate q is a function

of the vehicular density k; q = q(k). Thus, the balance equation takes the form

∂k(x, t)

∂t+

∂q(k(x, t))

∂x= 0 (17.5)

Now there is only one independent variable in the balance equation, the vehicle density k. If

initial and boundary conditions are known, this can be solved. Solution to LWR models are

kinematic waves moving with velocitydq(k)

dk(17.6)

This velocity vk is positive when the flow rate increases with density, and it is negative when

the flow rate decreases with density. In some cases, this function may shift from one regime to

the other, and then a shock is said to be formed. This shockwave propagate at the velocity

vs =q(k2) − q(k1)

k2 − k1

(17.7)

where q(k2) and q(k1) are the flow rates corresponding to the upstream density k2 and down-

stream density k1 of the shockwave. Unlike Stock’s shockwave formula there is only one variable

here.



(1) (2)

N2N1

q1 q2

∆x

17.2.3 Derivation of the Conservation equation

Consider a unidirectional continuous road section with two counting station. Let N1 : number

of cars passing (1) in time ∆t; q1 : the flow; N2 : number of cars passing (2) in time ∆t; and

q2 : the flow; Assume N1 > N2, then queuing between (1) and (2)

q1 =N1

∆t, q2 =

N2

∆t

∆q = q2 − q1 =N2 − N1

∆t=

−∆N

∆t

Note that q2 < q1 and therefore ∆q is negative. Therefore,

∆N = −∆q.∆t (17.8)

Similarly (k2 > k1),

∆k = k2 − k1 =N1 − N2

∆x=

+∆N

∆x,

Therefore

∆N = ∆k∆x

From the above two equations:

∆k ∆x + ∆q ∆t = 0

Dividing by ∆t ∆x∆k

∆t+

∆q

∆x= 0

Assuming continuous medium (ie., taking limits) limt→0

∂q

∂x+

∂k

∂t= 0



If sink or source is considered∂q

∂x+

∂k

∂t= g(x, t)

where, g(x, t) is the generation or dissipation term (Ramp on and off). Solution to the above

was proposed by Lighthill and Whitham (1955) and Richard (1956) popularly knows as LWR

Model.

17.3 Analytical Solution

17.3.1 Formulation

The analytical solution, popularly called as LWR Model, is obtained by defining the relationship

between the fundamental dependant traffic flow variable (k and q) to the independent variable

(x and t). However, the solution to the continuity equation needs one more equation: by

assuming q = f(k) , ie., q = k.v. Therefore:

∂q

∂x+

∂k

∂t= 0, becomes

∂f(k)

∂k+

∂k

∂t= 0

∂k

∂t+

∂(k.v)

∂x= 0

∂k

∂t+

∂[k.f(k)]

∂x= 0, v = f(k)

Therefore,

∂[k.f(k)]

∂x=

∂k

∂x.f(k) + k.

∂f(k)

∂x

=∂k

∂xf(k) + k.

df

dk.∂k

∂x

=∂k

∂x

[

f(k) + k.df

dk

]

Continuity equation can be written as

∂k

∂t+

∂k

∂x

[

f(k) + k.df

dk

]

= 0



where f(k) could be any function relating density and speed. Eg: Assuming the Greenshield’s

leinear model:

v = vf −

vf

kj

k

Therefore, f(k) + kdf(k)

dk= vf −

vf

kj

k + k−vf

kj

= vf − 2vf

kj

k

Therefore,∂k

∂t+

∂k

∂x

[

vf − 2vf

kj

k

]

= 0 (17.9)

The equation 17.9 is first order quasi-linear, hyperbolic, partial differential equation (a special

kind of wave equation).

17.3.2 Method of Characteristics

Consider k(x, t) at each point of x and t, and ∂k∂t

+ ∂k∂x

[f(k) + df

dkk] = 0 in the total derivative of

k along a curve which has slope ∂x∂t

= f(k) + df

dkk. ie., Along any curve in (x, t), consider x, k

as function of t.

x0 x

(k)

t

Total derivative of k will be

dk

dt=

∂k

∂t+

∂k

∂x.dx

dt

=∂k

∂t+

∂k

∂x

[

f(k) +df

dkk

]

At the solution, dkdt

= 0, k is constant along the curve, f(k) + k. df

dkis constant along the curve.

That is,

x(t) = x0 +

[

dx

dt

]

t

= x0 +

[

f(k) + k.dt

dk

]

t



Note that the solution is to construct some curve e so that: (a) kt+c(k).kx is the total derivative

of k along the curve (ie., directional derivative) and (b) slope of the curve dxdt

= c(k). We know

k(x, t). Therefore directional derivative k(x, t) along t

dk(x, t)

dt=

∂k

∂t+

dx

dt.∂k

∂x

=∂k

∂t+

[

f(k) + k.df

dk

]

∂k

∂x

= 0

ie.,dk

dt= 0

That is k is constant along the curve e or dxdt

= f(k) + k df

dkis constant along curve e. Therefore

e must be straight line.

x(t) = x0 +

[

f(k) + k.df

dk

]

t

If k(x, 0) = k0 is initial condition

x(t) = x0 +

[

f(k0) + k0.df

dk

∣

∣

∣

∣

k=k0

]

t

This function is plotted below along with a fundamental q-k diagram.

17.3.3 Inference

1. Density k is constant along characteristic lines

2. Characteristic lines are straight lines emanating from the boundaries of x − t plane

3. The slope of the characteristic line is

dx

dt= f(k) + k.

df

dk≡

dq

dk

ie., Characteristic curve has the slope equal to the tangent of the flow density curve.

4. When two Characteristic lines intersect (ie., 2 k values at a given x,t) shockwaves are

generated; and characteristic line terminate.

5. Shockwave represent mathematical discontinuity ie., abrupt changes to k, q, v.

6. Speed of the Shockwave is ratio of the time storage rate to space storage rate; that is:

vw =qd − qu

kd − kv

.



A

wave velocity

wave velocity

B

k = 0 kB kA kj

k

q = kv = k(vf −vf

kjk)

dqdk

= vf − 2vf

kjk ∼= dx

dt

Characteristic lines

A

BShockwave

uw = dxdt

∼= dqdx

x

t

Vehicle trajectories

x

t

17.4 Conclusion

The advantages of the continuous modelling is that it gives good insight into the understanding

of the behaviour of traffic. It can also be applied to platoon movement, signal control, etc.

Finally, it also paves the way for the development of higher order models. However, it also

has some serious limitations. The first one is the difficulty in getting solutions for realistic

problems(initial boundary conditions). Second, the q − k and u − k relationship are complex.

It may also cause unrealistic abrupt changes in the system. Finally acceleration-deceleration

characteristics are not directly modelled in the system.



17.5 References

[1] D Chowdhury, L Santen, and A Schadschneider. Statistical physics of vehicular traffic

and some related systems. Physics Report 329, 2000. 199-329.


New Delhi, 1987.


Transportation Systems Engineering 18. Cell Transmission Models

Chapter 18

Cell Transmission Models

18.1 Introduction

Models are necessary to simulate the real world scenario to some extent, or in some cases,

they can even provide the exact scenario. Characteristics of traffic changes with time, place,

human behavior etc. The models in traffic engineering are necessary to predict the behavior

of traffic in proper planning and design of the road network. The models can be microscopic

and macroscopic. In the present chapter, a macroscopic model has been discussed known as

cell transmission model which tries to simulate the traffic behavior.

In the classical methods to explain macroscopic behaviour of traffic, like hydrodynamic

theory, differential equations need to be solved to predict traffic evolution. However in situations

of sudden high density variations, like bottlenecking, the hydrodynamic model calls for a shock

wave (an ad-hoc). Hence these equations are essentially piecewise continuous which are difficult

to solve. Cell transmission models are developed as a discrete analogue of these differential

equations in the form of difference equations which are easy to solve and also take care of high

density changes.

In this lecture note the hydrodynamic model and cell transmission model and their equiv-

alence is discussed. The cell transmission model is explained in two parts, first with only a

source and a sink, and then it is extended to a network. In the first part, the concepts of

basic flow advancement equations of CTM and a generalized form of CTM are presented. In

addition, the phenomenon of instability is also discussed. In the second segment, the network

representation and topologies are established, after which the model is discussed in terms of a

linear program formulation for merging and diverging.



18.2 Single source and sink CTM model

18.2.1 Basic Premise

The cell transmission model simulates traffic conditions by proposing to simulate the system

with a time-scan strategy where current conditions are updated with every tick of a clock. The

road section under consideration is divided into homogeneous sections called cells, numbered

from i = 1 to I. The lengths of the sections are set equal to the distances travelled in light

traffic by a typical vehicle in one clock tick. Under light traffic condition, all the vehicles in a

cell can be assumed to advance to the next with each clock tick. i.e,

ni+1(t + 1) = ni(t) (18.1)

where, ni(t) is the number of vehicles in cell i at time t. However, equation 18.1 is not reasonable

when flow exceeds the capacity. Hence a more robust set of flow advancement equations are

presented in a later section.

18.2.2 Flow Advancement Equations

First, two constants associated with each cell are defined, they are: (i) Ni(t) which is the

maximum number of vehicles that can be present in cell i at time t, it is the product of the

cell’s length and its jam density. (ii) Qi(t) : is the maximum number of vehicles that can flow

into cell i when the clock advances from t to t + 1 (time interval t), it is the minimum of the

capacity of cells from i− 1 and i. It is called the capacity of cell i. It represents the maximum

flow that can be transferred from i − 1 to i. We allow these constants to vary with time to be

able to model transient traffic incidents. Now the flow advancement equation can be written

as, the cell occupancy at time t + 1 equals its occupancy at time t, plus the inflow and minus

the outflow; i.e.,

ni(t + 1) = ni(t) + yi(t) − yi+1(t) (18.2)

where, ni(t + 1) is the cell occupancy at time t + 1, ni(t) the cell occupance at time t, yi(t)

is the inflow at time t, yi+1(t) is the outflow at time t. The flows are related to the current

conditions at time t as indicated below:

yi(t) = min [ni−1(t), Qi(t), Ni(t) − ni(t)] (18.3)

where, ni−1(t): is the number of vehicles in cell i − 1 at time t, Qi(t): is the capacity flow into

i for time interval t, Ni(t) - ni(t): is the amount of empty space in cell i at time t.



t

Qi−1(t), Ni−1(t) Qi(t), Ni(t) Qi+1(t), Ni+1(t)

ni−1(t) ni(t) ni+1(t)

t + 1 ni(t + 1)

Figure 18:1: Flow advancement

18.2.3 Boundary conditions

Boundary conditions are specified by means of input and output cells. The output cell, a sink

for all exiting traffic, should have infinite size (NI+1 = ∞) and a suitable, possibly time-varying,

capacity. Input flows can be modeled by a cell pair. A source cell numbered 00 with an infinite

number of vehicles (n00(O) = ∞) that discharges into an empty gate cell 00 of infinite size,

N0(t) = ∞. The inflow capacity Q0(t) of the gate cell is set equal to the desired link input flow

for time interval t + 1.

18.2.4 Equivalence with Hydrodynamic theory

Consider equations 18.2 & 18.3, they are discrete approximations to the hydrodynamic model

with a density- flow (k-q) relationship in the shape of an isoscaled trapezoid, as in Fig.18:2.

This relationship can be expressed as:

q = min [vk, qmax, v(kj − k)], for 0 ≤ k ≤ kj, (18.4)

Flow conservation is given by,∂q(x, t)

∂x=

∂k(x, t)

∂t(18.5)

To demonstrate the equivalence of the discrete and continuous approaches, the clock tick set

to be equal to ∂t and choose the unit of distance such that v∂t = 1. Then the cell length is 1,

v is also 1, and the following equivalences hold: x ≡ i, kj ≡ N , qmax ≡ Q, and k(x, t) ≡ ni(t)

with these conventions, it can be easily seen that the equations 18.4 & 18.3 are equivalent.

Equation 18.6 can be equivalently written as:

yi(t) − yi+1(t) = −ni(t) + ni+1(t + 1) (18.6)

This represents change in flow over space equal to change in occupancy over time. Rearranging

terms of equation 18.7 we can arrive at equation 18.3, which is the same as the basic flow

advancement equation of the cell transmission model.



ka

qmax

vkj/2

-v

kb

Figure 18:2: Flow-density relationship for the basic cell-transmission model

Flo

w

Densityka kb

−w

qmax

kj1v+ 1

w

Figure 18:3: Flow-density relationship for the generalized CTM

18.3 Generalized CTM

Generalized CTM is an extension of the cell transmission model that would approximate the

hydrodynamic model for an equation of state that allows backward waves with speed w ≤ v

(see Fig. 18:3 ). This is a realistic model, since on many occassions speed of backward wave

will not be same as the free flow speed.

yi(t) = min [ni−1(t), Qi(t), w/v{Ni(t) − ni(t)}] (18.7)

A small modification is made in the above equation to avoid the error caused due to numerical

spreading. Equation 18.7 is rewritten as

yi(t) = min [ni−1(t), Qi(t), α{Ni(t) − ni(t)}] (18.8)

where, α = 1 if ni−1(t) ≤ Qi(t), and α = w/v if ni−1(t) > Qi(t).



18.3.1 Numerical example

Consider a 1.25 km homogeneous road with speed v = 50 kmph, jam density kj = 180 veh/km

and qmax = 3000 veh/hr. Initially traffic is flowing undisturbed at 80% of capacity: q =

2400 veh/hr. Then, a partial lane blockage lasting 2 min occurs on 1/3rd of the distance from

the end of the road. The blockage effectively restricts flow to 20% of the maximum. Clearly, a

queue is going to build and dissipate behind the restriction. After 2 minutes, the flow in cell

3 is maximum possible flow. Predict the evolution of the traffic. Take one clock tick as 30

seconds.

Solution The main purpose of cell transmission model is to simulate the real traffic conditions

for a defined stretch of road. The speed and cell length is kept constant and also the cell lengths

in cell transmission model. The solution has been divided into 4 steps as follows:

Step 1: Determination of cell length and number of cells Given clock tick, t =

30sec = 1/120th of an hour. So, cell length = distance travelled by vehicle in one clock tick

= v × t = 50 × (1/120) ≈ 5/12 km. Road stretch given = 1.25 km. Therefore, no of cells =

1.25/(5/12) = 3 cells

Step 2: Determination of constants (N & Q) N = maximum numberof vehicles that

can be at time t in cell i, = cell length x jam density, = 180 x (5/12) = 75 vehicles, Q =

maximum number of vehicles that can flow into cell I from time t to t+1, = 3000 x (1/120) =

25 vehicles. Now, to simulate the traffic conditions for some time interval, our main aim is to

find the occupancies of the 3 cells (as calculated above) with the progression of clock tick. This

is easily showed by creating a table. First of all, the initial values in the tables are filled up.

Step 3: Determination of cell capacity in terms of number of vehicles for various

traffic flows. For 20% of the maximum = 600 × (1/120) vehicles. For 80% of the maximum =

2400 × (1/120) vehicles.

Step 4: Initialization of the table The table has been prepared with source cell as a

large capacity value and a gate is there which connects and regulates the flow of vehicles from

source to cell 1 as per the capacity of the cell for a particular interval. The cell constants (Q

and N) for the 3 cells are shown in the table. Note that the sink can accommodate maximum

number of vehicles whichever the cell 3 generates. Q3 is the capacity in terms of number of

vehicls of cell 3 . The value from H5 to H7 (i.e 5) corresponds to the 2min time interval with 4

clock ticks when the lane was blocked so the capacity reduced to 20% of the maximum (i.e. 600

× (1/120) vehicles). After the 2 min time interval is passed vehicles flows with full capacity

in cell 3. So the value is 25 (i.e 3000 × (1/120) vehicles).

Step 5: Computation of Occupancies Simulation need not be started in any specific



Source(00) Gate(0) Cell1 Cell2 Cell3 Cell4

Q 20 25 25 25

N 999 75 75 75 999

Time Q3

1 999 20 20 20 20 5

2 999 20 5

3 999 20 5

4 999 20 5

5 999 20 25

6 999 20 25

7 999 20 25

8 999 20 25

9 999 20 25

10 999 20 25

11 999 20 25

12 999 20 25

13 999 20 25

14 999 20 25

15 999 20 25

16 999 20 25

17 999 20 25

18 999 20 25

Table 18:1: Entries at the start of the simulation.



Q=25,N=75 Q=25,N=75 Q=5,N=75

t=1 2020

205

20

35t=2

t=1

t=2

2020 2020 20

20

Q=20,N=75 Q=25,N=75 Q=25,N=75

order, it can be started from any cell in the row corresponding to the current clock tick. Now,

consider cell circled (cell 2 at time 2) in the final table. Its entry depends on the cells marked

with rectangles. By flow conservation law: Occupancy = Storage + Inflow - Outflow. Note

that the Storage is the occupancy of the same cell from the preceding clock tick. Also outflow

of one cell is equal to the inflow of the just succeeding cell. Here, Storage = 20. For inflow use

equation 18.3 Inflow= min [20,min(25,25),(75-20)]= 20. Outflow= min [20,min(25,5),(75-20)]=

5. Occupancy= 20+20-5=35. Now, For cell 1 at time 2, Inflow= min [20,min(25,25),(75-20)]=

20, Outflow= min [20,min(25,25),(75-20)]= 20, Occupancy= 20+20-20=20. Now, For cell 3 at

time 2, Inflow= min [20, min (25,5),(75-20)]= 5. Outflow= 20 (:.sink cell takes all the vehicles

in previous cell) Occupancy= 20+5-20=5. Similarly, rest of the entries can be filled and the

final result is shown in Table below. From the table it can be seen that the occupancy i.e. the

number of vehicles on cell 1 and 2 increases and then decreases simulating the effect of lane

blockage in cell 3 on cell 1 and cell 2. The lane blockage lasts 2 minutes in this problem, after

that there is no congestion taken into account. So as the time passes by, the occupancy in cell

1 and cell 2 also gets reduced.

t=1

t=2

2020 2020

Q=25,N=75Q=25,N=75 Q=5,N=75

5

5



Source(00) Gate(0) Cell 1 Cell 2 Cell 3 Cell 4

Q 20 25 25 25

N 999 75 75 75 999

Time Q3

1 999 20 20 20 20 5

2 999 20 20 35 5 5

3 999 20 20 50 5 5

4 999 20 20 65 5 5

5 999 20 30 70 5 25

6 999 20 45 50 25 25

7 999 20 40 50 25 25

8 999 20 35 50 25 25

9 999 20 30 50 25 25

10 999 20 25 50 25 25

11 999 20 20 50 25 25

12 999 20 20 45 25 25

13 999 20 20 40 25 25

14 999 20 20 35 25 25

15 999 20 20 30 25 25

16 999 20 20 25 25 25

17 999 20 20 20 25 25

18 999 20 20 20 20 25

Table 18:2: Final entries simulating the traffic



|Λ−1(j)| = 0 |Λ(j)| = 1

Figure 18:4: Source Cell


Consider a 1.25 km homogeneous road with speed v = 50 kmph, jam density kj = 180 veh/km

and qmax = 3000 veh/hr. Initially traffic is flowing undisturbed at 80% of capacity: q = 2400

VPH. Then, a partial lane blockage lasting 2 min occurs l/3 of the distance from the end of

the road. The blockage effectively restricts flow to 20% of the maximum. Clearly, a queue is

going to build and dissipate behind the restriction. Predict the evolution of the traffic. Take

one clock tick as 6 seconds.

Solution This problem is same as the earlier problem, only change being the clock tick.

This problem has been solved in Excel. The simulation is done for this smaller clock tick; the

results are shown in Fig. 18:3 One can clearly observe the pattern in which the cells are getting

updated. After the decrease in capacity on last one-third segment queuing is slowly building up

and the backward wave can be appreciated through the first arrow. The second arrow shows

the dissipation of queue and one can see that queue builds up at a faster than it dissipates.

This simple illustration shows how CTM mimics the traffic conditions.

18.4 CTM: Network Traffic

18.4.1 General

As sequel to his first paper on CTM, Daganzo (1995) published first paper on CTM applied to

network traffic. In this section application of CTM to network traffic considering merging and

diverging is discussed. Some basic notations: (The notations used from here on, are adopted

from Ziliaskopoulos (2000)) Γ−1 = Set of predecessor cells. Γ = Set of successor cells.

18.4.2 Network topologies

The notations introduced in previous section are applied to different types of cells, as shown in

Figures 18:4, 18:5 & 18:6. Some valid and invalid representations in a network are shown in

Fig 18:10 & Fig 18:9.



clock tick 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

1 4 4 4 4 4 4 4 4 4 6 4 4 4 4 4

2 4 4 4 4 4 4 4 4 4 7 1 4 4 4 4

3 4 4 4 4 4 4 4 4 4 10 1 1 4 4 4

4 4 4 4 4 4 4 4 4 5 13 1 1 1 4 4

5 4 4 4 4 4 4 4 4 6 14 1 1 1 1 4

6 4 4 4 4 4 4 4 4 9 14 1 1 1 1 1

7 4 4 4 4 4 4 4 4 12 14 1 1 1 1 1

8 4 4 4 4 4 4 4 4 14 14 1 1 1 1 1

9 4 4 4 4 4 4 4 5 14 14 1 1 1 1 1

10 4 4 4 4 4 4 4 8 14 14 1 1 1 1 1

11 4 4 4 4 4 4 6 11 14 14 1 1 1 1 1

12 4 4 4 4 4 4 7 14 14 14 1 1 1 1 1

13 4 4 4 4 4 4 10 14 14 14 1 1 1 1 1

14 4 4 4 4 4 5 13 14 14 14 1 1 1 1 1

15 4 4 4 4 4 6 14 14 14 14 1 1 1 1 1

16 4 4 4 4 4 9 14 14 14 14 1 1 1 1 1

17 4 4 4 4 4 12 14 14 14 14 1 1 1 1 1

18 4 4 4 4 5 14 14 14 14 14 1 1 1 1 1

19 4 4 4 4 8 14 14 14 14 14 1 1 1 1 1

20 4 4 4 4 11 14 14 14 14 14 1 1 1 1 1

21 4 4 4 6 14 14 14 14 14 14 1 1 1 1 1

22 4 4 4 7 14 14 14 14 14 10 5 1 1 1 1

23 4 4 4 10 14 14 14 14 10 10 5 5 1 1 1

24 4 4 4 13 14 14 14 10 10 10 5 5 5 1 1

25 4 4 8 14 14 14 10 10 10 10 5 5 5 5 1

26 4 4 9 14 14 10 10 10 10 10 5 5 5 5 5

27 4 4 12 14 10 10 10 10 10 10 5 5 5 5 5

28 4 8 14 10 10 10 10 10 10 10 5 5 5 5 5

29 4 7 10 4 10 10 10 10 10 10 5 5 5 5 5

30 4 4 10 4 10 10 10 10 10 10 5 5 5 5 5

31 4 4 10 4 10 10 10 10 10 10 5 5 5 5 5

32 4 4 10 4 10 10 10 10 10 10 5 5 5 5 5

33 4 4 10 4 10 10 10 10 10 10 5 5 5 5 5

34 4 4 9 4 10 10 10 10 10 10 5 5 5 5 5

Table 18:3: Illustration of traffic simulation in CTMDr. Tom V. Mathew, IIT Bombay 18.10 January 31, 2014


|Λ(j)| = 0|Λ−1(j)|=1

Figure 18:5: Sink Cell

Cell j

|Λ−1(j)| = 1 |Λ(j)| = 1

Figure 18:6: Ordinary Cell

Cell j

|Λ−1(j)| > 1 |Λ(j)| = 1

Figure 18:7: Merging Cell

Cell j

|Λ−1(j)| = 1 |Λ(j)| > 1

Figure 18:8: Diverging Cell

kk

Figure 18:9: Invalid representations



Figure 18:10: Valid representations

E_{k}

B_{k}k

Figure 18:11: Ordinary Link

18.4.3 Ordinary link

Consider an ordinary link with a beginning cell and ending cell, which gives the flow between

two cells is simplified as explained below.

yk(t) = min(nBk(t), min[QBk(t), QEk(t)], δEk[NEk(t) − nEk(t)]) (18.9)

where, δ = w/v. yk(t) is the inflow to cell Ek in the time interval (t,t + 1). Defining the

maximum flows that can be sent and received by the cell i in the interval between t to t + 1 as

SI(t) = min(QI, nI), and RI(t) = min(QI , δI , [NI − nI ]). Therefore, yk(t) can be written in a

more compact form as: yk(t) = min(SBk, REk). This means that the flow on link k should be

the maximum that can be sent by its upstream cell unless prevented to do so by its end cell. If

blocked in this manner, the flow is the maximum allowed by the end cell. From equations one

can see that a simplification is done by splitting yk(t) in to SBk and REk terms. ’S’ represents

sending capacity and ’R’ represents receiving capacity. During time periods when SBk < REk

the flow on link k is dictated by upstream traffic conditions-as would be predicted from the

forward moving characteristics of the Hydrodynamic model. Conversely, when SBk > REk, flow

is dictated by downstream conditions and backward moving characteristics.

18.4.4 Merging and Diverging

Consider two cells merging, here we have a beginning cell and its complimentary merging into

ending cell, the constraints on the flow that can be sent and received are given by equation 18.10

and equation 18.10.

yk(t) ≤ SBk; yck(t) ≤ SCkyk(t) + yck(t) ≤ REk (18.10)



Ek

Bk

Ck

k

ck

where, SI(t) = (QI , nI), and RI(t) = (QI , δI, [NI − nI ]). A number of combinations of yk(t) +

yck(t) are possible satisfying the above said constraints. Similarly for diverging a number of

possible outflows to different links is possible satisfying corresponding constraints, hence this

calls for an optimization problem. Ziliaskopoulos (2000), has given this LP formulations for

both merging and diverging, this has been discussed later

18.5 CTM Software - NETCELL

• NETCELL is a freeway network simulation program based on the cell transmission model

developed by Cay ford, Lin and Daganzo.

• It consists of two components,

– NETCELL

– NETVIEW(a graphical postprocessor)

• This is a free software and can be downloaded from the link below http://www.ce.berkeley.edu/ da-

ganzo/software and data.htm

• NETCELL is a macroscopic simulation program in which vehicle quantities are treated as

continuous variables. Vehicles are advanced in a way consistent with the hydrodynamic

theory of traffic flow.

18.6 Conclusion

18.6.1 Summary

• CTM is a discrete approximation of hydrodynamic model. System evolution is based on

difference equations.



• Unlike hydrodynamic model, it explains the phenomenon of Instability.

• Lesser the time per clock tick lesser are the size of cells and more accurate results would

be obtained. But a compromise is needed between accuracy and computational effort.

Largest possible cell size which would sufficiently give the details needed must be chosen.

• CTM has many applications in DTA, NDP, traffic operations, emergency evacuations etc.

• There is a vast scope for improvement and applications of this model.

18.6.2 Advantages and applications

• CTM is consistent with hydrodynamic theory, which is a widely used model for studying

macroscopic behavior of the traffic.

• It is simple and sufficiently accurate for planning purposes.

• CTM can be used to provide ”real time” information to the drivers.

• CTM has been used in developing a system optimal signal optimization formulation.

• CTM based Dynamic Traffic Assignment have shown good results.

• CTM has its application in Network Design Problems.(NDP)

18.6.3 Limitations

• CTM is for a ”typical vehicle” in network traffic, work is needed for the multi-modal

representation of traffic.

• Cell length cannot be varied. For this the methods like Modified Cell Transmission Model

is to be used.

• CTM is largely deterministic, stochastic variables are needed to be introduced to represent

the random human behavior.

18.7 References

1. C D Alexandru. A stochastic mesoscopic cell transmission model for operational analy-

sis of large-scale transportation networks. A dissertation submitted to Louisiana State

University, 2006.



2. C F Daganzo. The cell transmission model Part I: A simple dynamic representation

of highway traffic. Research Report UCB-ITS-PATH-RR-93-7, University of California,

Berkeley, 1993.

3. C F Daganzo. The cell transmission model: A dynamic representation of highway traffic

consistent with the hydrodynamic theory. Transportation Research B, 28(4):269-287,

1994.

4. C F Daganzo. The cell transmission model. Part II: Network Traffic. Transportation

Research B, 29(2):79-93, 1995.

5. A K Ziliaskopoulos. A Linear Programming Model for the Single Destination System

Optimum Dynamic Traffic Assignment Problem. Transportation Science, Vol.34,No. 1,

2000.


Transportation Systems Engineering 19. Traffic Progression Models

Chapter 19

Traffic Progression Models

19.1 Introduction

A majority of the metro cities in India are facing the problem of traffic congestion, delays,

which have further resulted in pollution. The delays are caused mainly due to the isolated

functioning of the traffic signals at closely located intersections. For better regulation of traffic

flow at these intersections, the traffic signals need to be coordinated or linked. For the linking

of signals, the vehicle movement characteristics from upstream signal to downstream signal

need to be considered and simulated. Traffic Progression Models model the vehicle movement

characteristics and help in the linking of signals. First, the concept of platoon, platoon variables

is discussed and then platoon ratio is defined which is required for determination of arrival type.

Then, the phenomenon of platoon dispersion and platoon dispersion model is introduced for

understanding dispersion behavior of the vehicles. Finally, one of the platoon dispersion models

i.e., Roberson’s platoon dispersion model is discussed, which estimates the vehicle arrivals at

downstream locations based on an upstream departure profile.

19.2 Characterising Platoon

A vehicle Platoon is defined as a group of vehicles travelling together. A vehicle Platoon is

shown in Fig. 19:1.

19.2.1 Variables describing platoon

The various vehicle platoon characteristics or variables include platoon size, platoon headway,

platoon speed and inter-arrival headway. Platoon behaviour and distribution patterns could be

identified with respect to these parameters. The various platoon characteristics are illustrated

in Fig. 19:2.



VehicleVehicle

Vehicle Vehicle Vehicle

Vehicle

VehicleVehicleVehicle

Vehicle Vehicle Vehicle Vehicle Vehicle Vehicle

Figure 19:1: A vehicle Platoon

StopLine

PlatoonDetector Direction of traffic

1 2 3 4 n 1 m

IAhhLP 1 2

Figure 19:2: Illustration of Platoon Variables

• Platoon Size (Np): It is the number of vehicles in a platoon.

• Platoon Headway (hp): It is the average value of headways within a platoon.

• Platoon Speed (Vp): It is the average speed of all the vehicles within a platoon.

• Inter-Arrival (IA): It is the headway between the last vehicle of the preceding platoon

and the first vehicle of the following platoon.

Various values of platoon headway and inter-arrival between consecutive platoons can be used

to determine appropriate critical headway for platoon identification and detection. Once the

critical headway is determined, platoon size and platoon speed can be detected to calculate

the signal timing adjustment to accommodate the approaching vehicle platoon. It is of great

importance to select a proper value of the critical headway since a small change in the critical

headway will generate tremendous changes in the resultant platoon characteristics. Use of a

large critical headway will result in a large average platoon size and require a large detection

area in order to detect large vehicle platoons. Consequently, a large detection area leads to

an increase of detector installation and maintenance costs. On the other hand, use of a small

critical headway will result in a small average platoon size, but may not provide sufficient

vehicle platoon information. Therefore, it is desired to find an appropriate critical headway so



Table 19:1: Relationship between Arrival Type and Platoon Ratio

Arrival Range of platoon Default value(Rp) Progression quality

type ratio(Rp)

1 ≤ 0.50 0.333 Very poor

2 > 0.50 − 0.85 0.667 Unfavorable

3 > 0.85 − 1.15 1.000 Random arrivals

4 > 1.15 − 1.50 1.333 Favorable

5 > 1.5 − 2.00 1.667 Highly favorable

6 > 2 2.000 Exceptional

that sufficient platoon information can be obtained within a proper detection area. Research

has shown that headways are rarely less than 0.5 seconds or over 10 seconds at different traffic

volumes. Many investigations have been done on finding the effects of critical headways of

1.2, 1.5, 2.1 and 2.7 seconds on platoon behaviour and these investigations have shown that a

critical headway of 2.1 seconds corresponding to a traffic volume of 1500 vehicles per hour per

lane (vphpl) can be taken for data collection.

19.2.2 Platoon Ratio

The platoon ratio denoted as Rp, is a numerical value used to quantify the quality of progression

on an approach. The platoon ratio represents the ratio of the number of vehicles arriving during

the green phase to the proportion of the green interval of the total cycle. This is given by

Rp = PC

g(19.1)

where, P = Proportion of all vehicles during green time, C = Cycle length, g = Effective green

time. Its value ranges from 0.5 to 2.0. It is used in the calculation of delays, capacity of an

approach. The arrival types range from 1 (worst platoon condition) to 6 (the best platoon

condition). The platoon ratio approximates the arrival type and the progression quality. For

example HCM (2000) has suggested the following relationship between platoon ratio and arrival

which is as shown in Table 19:1.

19.3 Platoon Dispersion

As a platoon moves downstream from an upstream intersection, the vehicles disperse i.e., the

distance between the vehicles increase which may be due to the differences in the vehicle speeds,



Dire

ctio

n of

traf

fic fl

ow

0 m

200 m

300 m

4

2

0

0 m

200 m

300 m

0

2

4

4

2

0

2 18 34 50 66 82

2 18 34 50 66 82

2 18 34 50 66 82

Figure 19:3: A simple case of Platoon Dispersion

vehicle interactions (lane changing and merging) and other interferences (parking, pedestrians,

etc.,). This phenomenon is called as Platoon Dispersion.

Dispersion has been found to be a function of the travel time from a signal to a downstream

signal (or other downstream location) and the length of the platoon. The longer the travel

time between signals, the greater the dispersion. This is intuitively logical since the longer

the travel time, the more time (opportunity) there is for different drivers to deviate from the

average travel time. A simple case of Platoon Dispersion is as shown in Fig. 19:3. From the

figure, it can be observed that, initially the peak of the platoon is high and the length of the

platoon is comparatively small, but as the platoon progresses downstream, the peak of the

platoon decreases and the length increases.

Various traffic engineering software like TRANSYT (Traffic Network Study Tool) and

SCOOT (Split Cycle Offset Optimization Technique) have employed the phenomenon of Pla-

toon Dispersion for the prediction of Arrival Types. A flow profile obtained from TRANSYT-7F

is as shown in the Fig. 19:4. From this figure also, it can be observed that, initially the peak

of the platoon is high and the length of the platoon is small, but as the platoon progresses

downstream, the peak of the platoon decreases and the length increases.

19.3.1 Platoon Dispersion Models

Platoon dispersion models simulate the dispersion of a traffic stream as it travels downstream

by estimating vehicle arrivals at downstream locations based on an upstream vehicle depar-

ture profile and a desired traffic-stream speed. There are two kinds of mathematical models

describing the dispersion of the platoon, namely:



10 20 30 40 50 60 70 80 900

1600

1400

1200

1000

800

600

400

200

0

2000

Flo

wra

te

Time

50100

5001000

Figure 19:4: A TRANSYT-7F Flow Profile

1. Normal Distribution Model - proposed by Pacey

2. Geometric Distribution Model - proposed by Robertson

One of the geometric distribution models is the Robertson’s platoon dispersion model, which

has become a virtually universal standard platoon dispersion model and has been implemented

in various traffic simulation softwares. Research has already been conducted on the applicability

of platoon dispersion as a reliable traffic movement model in urban street networks. Most of

the research has shown that Robertson’s model of platoon dispersion is reliable, accurate, and

robust.

19.3.2 Robertson’s Platoon Dispersion Model

The basic Robertson’s recursive platoon dispersion model takes the following mathematical

form

qdt = Fn ∗ qt−T + (1 − Fn) ∗ qd

t−n (19.2)

where, qdt = arrival flow rate at the downstream signal at time t, qt−T = departure flow rate at

the upstream signal at time t-T, T = minimum travel time on the link (measured in terms of

unit steps T =βTa), Ta = average link travel time, n = modeling time step duration, Fn is the

smoothing factor given by:

Fn =1

1 + αnβnTa

(19.3)

αn = platoon dispersion factor (unitless) βn = travel time factor (unitless) Equation shows

that the arrival flows in each time period at each intersection are dependent on the departure



All inflowin vehicles

q1q1*F

q2*Fq2

q3q#*F

q4t+ki

t+2i

t+i

t

Figure 19:5: Graphical Representation of Robertson’s Platoon Dispersion Model

flows from other intersections. Note that the Robertson’s platoon dispersion equation means

that the traffic flow qdt , which arrives during a given time step at the downstream end of a link,

is a weighted combination of the arrival pattern at the downstream end of the link during the

previous time step qdt−n and the departure pattern from the upstream traffic signal T seconds

ago qt−T .

Fig. 19:5 gives the graphical representation of the model. It clearly shows that predicated

flow rate at any time step is a linear combination of the original platoon flow rate in the

corresponding time step (with a lag time of t) and the flow rate of the predicted platoon in the

step immediately preceding it. Since the dispersion model gives the downstream flow at a given

time interval, the model needs to be applied recursively to predict the flow. Seddon developed

a numerical procedure for platoon dispersion. He rewrote Robertson’s equation as,

qdt =

∞∑

i=T

Fn(1 − Fn)i−T ∗ qt−i+T (19.4)

This equation demonstrates that the downstream traffic flow computed using the Robertson’s

platoon dispersion model follows a shifted geometric series, which estimates the contribution of

an upstream flow in the (t−i)th interval to the downstream flow in the tth interval. A successful

application of Robertson’s platoon dispersion model relies on the appropriate calibration of the

model parameters. Research has shown that the travel-time factor (βn) is dependent on the

platoon dispersion factor (αn). Using the basic properties of the geometric distribution of

Equation 19:5, the following equations have been derived for calibrating the parameters of the

Robertson platoon dispersion model.

βn =1

1 + αn

OR αn =1 − βn

βn

(19.5)



Equation 19.5 demonstrates that the value of the travel time factor (β) is dependent on the

value of the platoon dispersion factor (α) and thus a value of 0.8 as assumed by Robertson

results in inconsistencies in the formulation. Further, the model requires calibration of only

one of them and the other factors can be obtained subsequently.

βn =2Ta + n −

√n2 + 4σ2

2Ta

(19.6)

where, σ is the standard deviation of link travel times and Ta is the average travel time between

upstream and downstream intersections. Equation demonstrates that travel time factor can be

obtained knowing the average travel time, time step for modeling and standard deviation of

the travel time on the road stretch.

Fn = n

√n2 + 4σ2 − n

2σ2(19.7)

Equation 19.7 further permits the calculation of the smoothing factor directly from the standard

deviation of the link travel time and time step of modeling. Thus, both βn and Fn can be

mathematically determined as long as the average link travel time, time step for modeling and

its standard deviation are given.

Numerical Example 1

In a case study, the average travel time for a particular stretch was found out to be 22.8 seconds,

standard deviation is 5.951 and model time step duration is 10 sec. Find out the Robertson’s

model parameters and also the flow at downstream at different time steps where the upstream

flows are as given as: q10 sec = 20, q20 sec = 10, q30 sec = 15, q40 sec = 18, q50 sec = 14, q60 sec = 12.



Solution Given, The model time step duration n=10sec, average travel time (Ta)=22.8sec,

standard deviation (σ)=5.951. From equations above.

βn =2Ta + n −

√n2 + 4σ2

2Ta

=2 ∗ 22.8 + 10 −

√102 + 4 ∗ 5.9512

2 ∗ 22.8= 0.878

αn =1 − βn

βn

=1 − 0.878

0.878= 0.139

Fn = n

√n2 + 4σ2 − n

2σ2

= 10

√102 + 4 ∗ 5.9512 − 10

2 ∗ 5.9512

= 0.783

Upstream Flows: Since the modelling time step duration is given as n=10 sec, the given

upstream flows can be written as follows:

q10 sec = q1

q20 sec = q2

q30 sec = q3

On simmilar lines , q4, q5, q6 can be written.

Downstream Flows: On the downstream, at 10 sec the flow will be zero since the modelling

step duration is 10 sec. Hence the downstream flows can be written as follows.

qd20 sec = qd

1

qd30 sec = qd

2

qd40 sec = qd

3



Simmilarly, downstreams flows can be written till 80 sec. Note that since n=10 sec, T is taken

in units of n. The minimum travel time (T) is given as

T = βTa = 0.878 ∗ 22.8 = 20 sec = 2

qdt =

∞∑

i=T

Fn(1 − Fn)i−T ∗ qt−i+T

qd1 = F ∗ (1 − F )2−2 ∗ q1−2+2

= F ∗ q1

= 0.783 ∗ 20 = 15.66 ≈ 16 veh

qd2 = F ∗ (1 − F )2−2 ∗ q2−2+2 + F ∗ (1 − F )3−2 ∗ q2−3+2

= F ∗ q2 + F ∗ (1 − F )1 ∗ q1

= 0.783x10 + 0.783 ∗ (1 − 0.783)1 ∗ 20

= 7.83 + 3.39 = 11.22 ≈ 11 veh

qd3 = F ∗ (1 − F )2−2 ∗ q3−2+2 + F ∗ (1 − F )3−2 ∗ q3+2 + F ∗ (1 − F )4−2 ∗ q3−4+2

= F ∗ q3 + F ∗ (1 − F )1 ∗ q2 + F ∗ (1 − F )2 ∗ q1

= 0.783 ∗ 15 + 0.783 ∗ (1 − 0.783)1 ∗ 10 + 0.783 ∗ (1 − 0.783)2 ∗ 20

= 11.75 + 1.69 + 0.737 = 14.18 ≈ 14 veh

Calculating on similar lines, we get

qd4(50 sec) = 17 veh



qd7(80 sec) = 3 veh

The total upstream vehicles in 60 sec is 89. And total downstream vehicles in 80 sec is 89. That

is, all 89 vehicles coming from upstream in 6 intervals took 7 intervals to pass the downstream.

Numerical Example 2

In a case study, the average travel time from the upstream point to 1st downward point (point

in between upstream and downstream) was found out to be 22.8 seconds and from upstream

point to downward point (end point) was found out to be 32.8 seconds , standard deviation



is 5.951 and model time step duration is 10 sec. Find out the Robertson’s model parameters

and also the flow at downstream at different time steps where the upstream flows are as given

below. q10 sec = 20, q20 sec = 10, q30 sec = 15, q40 sec = 18, q50 sec = 14, q60 sec = 12.

Solution This problem is simmilar to the earlier problem. Only there are 2 downstream

points given in this. For the first downstream point, upstream values of flow given in the

problem will be used, whereas for the 2nd downstream point, the flow from the 1st downstream

point is to be used. Hence at 1st downstream point, flow in the first interval is zero and at

the 2nd downstream value, flow is zero for first 2 intervals. The calculations have been done in

excel and the following shows the results.

Upstream Vol. for (in sec.) No. of Vehicles

10 20

20 10

30 15

40 18

50 14

60 12

0

0

0

0

89

Smoothing Factor F 0.783

Lag Time(For In Between Point) 20 sec

Lag Time(For End Point) 30 sec

Four graphs are plotted below. The first graph shows the upstream profile, the second shows

the downstream profile at in between point, the third shows the downstream profile at the end

point. The last graph shows the comparison of all the three.

19.4 Conclusion

Initially, the concept of platoon and platoon variables was discussed. The platoon variables are

required for the determination of critical headway which further helps in platoon identification.

Then, the platoon ratio was defined which helps us in identifying the arrival type. Later,



Downstream Volume Downstream Volume

At in between Point At End Point

(in seconds) (in seconds)

10 0 10 0.00

20 15.66 20 0.00

30 11.23 30 12.26

40 14.18 40 11.45

50 17.17 50 13.59

60 14.69 60 16.39

70 12.58 70 15.06

80 2.73 80 13.12

90 0.59 90 4.99

100 0.13 100 1.55

0.00 110 0.44

88.96 120 0.09

88.84

120 140100806040200

UpstreamtrafficDownstreamtraffic in between Downstreamtraffic at end point

20

15

10

5

25

0



platoon dispersion model was discussed which model the departure profile of the downstream

vehicles based on the upstream departure profile. Finally, Robertson’s platoon dispersion model

is discussed with the help of numerical examples. The Robertson’s platoon dispersion model

estimates the downstream volume at different time intervals which can be used for the linking

of the signals and optimization of signal timings.

19.5 References



2. Y Jiang, L Shou, and E Daniel. A Platoon-based Traffic Signal Timing Algorithm for

Major-Minor Intersection Types. Transportation Research Part B 40, 2006.

3. A Manar and K G Baass. Traffic Flow Theory and Traffic flow simulation models.

Transportation Research Record: 1566, 1996.

4. F Qiao, H Yang, and W Lam. Intelligent simulation and prediction of traffic flow disper-

sion. Transportation Research Part B: Methodological, 35(9), 2001.

5. H Rakha and M Farzaneh. Calibration of TRANSYT Traffic Dispersion Model: Issues

and Proposed Solutions. Virginia Tech Transportation Institute, 2004.

6. R H Showers. Investigation and Enhancement of models that describe the flow of traffic

on arterial streets. A Ph.D. Thesis submitted to the University of Florida,4,73,97, 2002.

7. W Wey. Model formulation and solution algorithm of traffic signal control in an urban

network. Computers, Environment and Urban Systems, 24, 2000.


Transportation Systems Engineering 20. Discrete Simulation Models

Chapter 20

Discrete Simulation Models

20.1 Introduction

In the field of traffic flow modelling, microscopic simulation involves the detailed models that

describe the behaviour of individual vehicles so it is always a time consuming and a complex

process. So, approximately a decade ago new microscopic models have been developed and

they are based on Cellular Automata programming. The main advantage was an efficient and

fast performance when used in computer simulations, due to their rather low accuracy on a

microscopic scale. These so-called traffic cellular automata (TCA) are dynamical systems that

are discrete in nature, in the sense that time advances with discrete steps and space is coarse-

grained (e.g., the road is discretised into cells of 7.5m wide, each cell being empty or containing

a vehicle).

A Cellular Automata is an n-dimensional array of simple cells where each cell may be in

any one of k-states. At each tick of the clock a cell will change its state based on the states of

the cells in a local neighborhood. Typically, the rule for updating the state does not change

over time, and is applied to the whole grid simultaneously. Due to its simplicity the CA rules

are used to solve the complex behaviour. Through the use of powerful computers, these models

can encapsulate the complexity of the real world traffic behavior and produces clear physical

patterns that are similar to those we see in everyday life. One more advantage of cellular

automata models is their efficiency in showing the clear transition from the moving traffic to

jamming traffic. CA models have the distinction of being able to capture micro-level dynamics

and relate these to macro level traffic flow behavior.

20.2 Cellular Automata

20.2.1 Components of Cellular Automata

There are four components, which play a major role in cellular automata.



Figure 20:1: Physical environment as different types of cells

i−1 i i+1

Figure 20:2: Neighbourhoods of the present cell i

The physical environment

The term physical environment indicates the physical platform on which CA is computed. It

normally consists of discrete lattice of cells with rectangular, hexagonal etc shown in Fig. 20:1.

All these cells are equal in size. They can be finite or infinite in size and its dimensionality can

be 1 (a linear string of cells called an elementary cellular automaton or ECA).

The cells states

Every cell can be in a particular state where typically an integer can determine the number of

distinct states a cell can be in, eg (binary state). Generally, the cell is assigned with an integer

value or a null value based upon its state. The states of cells collectively are called as “Global

configuration”. This convention clearly indicates that states are local and refer to cells, while

a configuration is global and refers to the whole lattice.

The cells’ neighbourhoods

The future state of a cell is mainly dependent on its state of its neighbourhood cell, so neighbour-

hood cell determines the evolution of the cell. So generally, the lattices vary as one-dimensional

and two-dimensional. In one dimensional lattice, the present cell and the two adjacent cells

forms its neighbourhoods ( shown in Fig. 20:2), whereas in the context of two dimensional

lattice there are four adjacent cells which acts as the neighbourhoods. Therefore, it is clear

that as the dimensionality increases the no of adjacent cells also increases.



A local transition rule

This rule (also called function) acts upon a cell and its direct neighbourhood, such that the

cell’s state changes from one discrete time step to another (i.e., the system’s iterations). The

CA evolves in time and space as the rule is subsequently applied to all the cells in parallel.

Typically, the same rule is used for all the cells (if the converse is true, then the term hybrid

CA is used). When there are no stochastic components present in this rule, we call the model

a deterministic CA, as opposed to a stochastic (also called probabilistic) CA.

20.2.2 Road and physical environment

When the cellular automaton analogy is applied to vehicular road traffic flows, the physical

environment of the system represents the road on which the vehicles are been driving. In a

general single-lane setup for traffic cellular automata, this layout consists of a one-dimensional

lattice that is composed of individual cells (our description here mainly focuses on unidirec-

tional, single-lane traffic). Every cell either can be empty, or occupied by exactly one vehicle.

We use the term single-cell models to describe these systems. Multi-cell models are those mod-

els, where the vehicle has a possibility to span several consecutive cells. Because vehicles move

from one cell to another, TCA models are also called particle-hopping models.

An example of the tempo-spatial dynamics of such a system is depicted in the below Fig.4,

where two consecutive vehicles i and j are driving on a one-dimensional lattice. Here we assume

T = 1 s and X = 7.5m, corresponding to speed increments of V =X/T =27 km/h. The spatial

discretisation corresponds to the average length a conventional vehicle occupies in a closely jam

packed (and as such, its width is neglected), whereas the temporal discretisation is based on a

typical driver’s reaction time and we implicitly assume that a driver does not react to events

between two consecutive time steps.

20.2.3 Vehicle movements

In traffic stream, the movement of the individual vehicles is described by means of a rule

set that reflects the car-following and lane-changing behaviour of a traffic cellular automaton

evolving in time and space. The TCAs local transition rule actually comprises this set of rules.

These rules are applied to all the vehicles in parallel (where in that case it is called as parallel

update). Therefore, in a classic setup, the system’s state is changed through synchronous

position updates of all the vehicles.

For each vehicle, the new speed is computed, after which its position is updated according

to this speed and a possible lane-change manoeuvre. Note that there are other ways to perform



this update procedure, e.g., a random sequential update. It is assumed that a driver does not

react to events between consecutive time steps. For single-lane traffic, we assume that vehicles

act as anisotropic particles, i.e., they only respond to frontal stimuli. So typically, the car-

following part of a rule set only considers the direct frontal neighbourhood of the vehicle to

which the rules are applied.

The radius of this neighbourhood should be taken large enough such that vehicles are able

to drive collision-free. In most cases, this radius is equal to the maximum speed a vehicle can

achieve, expressed in cells per time step. From a microscopic point of view, the process of a

vehicle following its predecessor is typically expressed using a stimulus-response relation. This

response is the speed or the acceleration of a vehicle in TCA models. A vehicle’s stimulus is

mainly composed of its speed and the distance to its leader, with the response directly being a

new (adjusted) speed of the vehicle.

20.2.4 Mathematical notations

CA model represents a discrete dynamic system, consisting of four ingredients namely, the

physical environment denoted as (£), the set of possible states denoted as (Σ), the associated

neighbourhood cells of ith cell represented as (Ni) and the set of the possible future update

cells is denoted by the notation (δ). So the CA is the function of the four ingredients and is

formulated mathematically as CA = (£, Σ, N, δ). The physical environment (£) is a discrete

lattice with the neighbourhood of radius 1 in normal case where as it changes with the user

based upon his usage of the different cells sizes. The set of possible states denoted as (Σ) takes

the values as ( 0,1) where 1 indicates the presence of vehicle in the cell or 0 for the empty

condition. So, for every time step t the ith cell of a lattice has a state i(t) which belongs to Σ.

In normal case of one-dimensional, lattice the neighbourhood cells of i are Ni = i − 1, i, i + 1,

where (i− 1) is the left hand side cell and (i+1) is the right hand side cell. The set of possible

future update cells is represented as i − 1(t), i(t), i + 1(t) → i(t + 1), where left hand side are

the present cell and the neighbourhood cells and the right hand side part is the state of the cell

i at time t + 1.

Converting between TCA and real world units seems straightforward, as we only need

to suitably multiply with or divide by the temporal and spatial discretisation ∆T and ∆X,

respectively. The conversions for the macroscopic traffic stream characteristics densities, flows,

and space-mean speeds, as well as the microscopic vehicle speed, are as follows:

k = k′ ∗ 1000/∆X (20.1)

q = q′ ∗ 3600/∆T (20.2)

v = v′ ∗ 3.6 ∗ ∆X/∆T (20.3)



where k′, v′, q′ are the values of density, speed, flow in the units of CA, and k, q, v are the real

world values of density, flow and speed.

The length of our cell is 7.5 m and if our stretch of road is 1000m (i.e., 1 km ) then the

no of cells in CA turns out to be 1000/7.5 =133.333 cells. So, for a single cell model if the

density turns out to be “one unit” (i.e., one vehicle per cell) then in the real world its density

(Kj) is 1*1000/7.5 = 133vehicles/km as per the equation. 20.1. The speed increment of the

vehicles is the ratio of distance and time. In our case the distance is the length of one cell and

time interval is one unit (sec) so the speed in km/hr is 7.5*3600/1000 =27km/hr as per the

equation. 20.3.

20.2.5 Wolfram 184 rule

In this section, we shall discuss about the Wolfram rule 184, which is used to determine the

new state of the cell. In a single lane highway, rule 184 is used as a simple model for traffic

flow and it forms the basis for many cellular automaton models of traffic flow.

In this model, vehicles move in a single direction, stopping and starting depending on the

vehicles in front of them. The number of vehicles remains unchanged throughout the simulation.

Because of this application, Rule 184 is sometimes called the “traffic rule”. Rule 184 in a simpler

way can be understood as a system of particles moving both leftwards and rightwards through

a one-dimensional medium. The rule set for Rule 184 is described as; At each step, if a cell

with value 1 has a cell with value 0 immediately to its right, the 1 moves rightwards leaving a

0 behind. A 1 with another 1 to its right remains in place, while a 0 that does not have a 1 to

its left stays a 0. This description is most apt for the application to traffic flow modeling.

The truth table for rule 184 is shown in Table. 20:1. The operation of the rule is easily

summarized as: “if the center cell is at state zero, shift the state of the left neighbor into the

center cell, else shift the state of the right neighbor into the center cell” (equation. 20.4).

σt+1

i =

σti−1 : σt

i = 0

σti+1 : σt

i = 1 (20.4)

The first three columns are the neighborhood and the rightmost column is the state of the

center cell that results from applying the transition function on the neighborhood.

The name for this rule, Rule 184, is the Wolfram code describing the state in the Fig. 20:3:

the bottom row of the figure, 10111000, when viewed as a binary number, is equal to the

decimal number 184. All 8 possible configurations for the local neighbourhood are sorted in

descending order, expressing the local transition rule (i, t) as explained by Fig. 20:3.



Table 20:1: Operation of Wolfram rule 184

Sti−1 St

i Sti+1 St+1

i

0 0 0 0

0 0 1 0

0 1 0 0

0 1 1 1

1 0 0 1

1 0 1 1

1 1 0 0

1 1 1 1

1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 0

00011101

1 ∗ 27 + 0 ∗ 26 + 1 ∗ 25 + 1 ∗ 24 + 1 ∗ 23 + 0 ∗ 22 + 0 ∗ 21 + 0 ∗ 20

128 + 0 + 32 + 16 + 8 + 0 + 0 + 0 = 184

Figure 20:3: New state of each cell as a function of the previous state

20.2.6 Single cell models

Till now we have discussed the physical and mathematical aspects of cellular automata and TCA

models in particular, we shall now focus on single-cell models. As explained before each cell can

either be empty, or is occupied by exactly one vehicle all vehicles have the same length li =1

cell. Traffic is also considered homogeneous, so all vehicles characteristics are assumed the same.

In earlier section, 2.5 we had discussed the wolfram rule 184 which is actually a deterministic

model but in the realistic traffic scenario there is stochastic term coming into picture so Wolfram

rule proved to inefficient in explaining such cases and hence stochastic models are have been

emerged. In the subsequent sections, we look at such stochastic TCA models (accompanied

by their suggested abbreviations). In summary, Wolfram’s rule 184 (CA-184) falls under the

deterministic model and the stochastic models have emerged when Nagel with the help of

Schreckenberg proposed a TCA model which is the well known cellular automata in the traffic

perspective.

Models that allow for the spontaneous emergence of phantom jams are called stochastic

models. In 1992, Nagel and Schreckenberg proposed a TCA model that was able to reproduce

several characteristics of real-life traffic flows, e.g., the spontaneous emergence of traffic jams.

Their model is called the NaSch TCA, but is more commonly known as the Stochastic traffic



cellular automaton (STCA).

20.2.7 Stochastic Cellular Automata (STCA)

We shall now discuss stochastic TCA models (i.e., these are probabilistic CAs) that allow for the

spontaneous emergence of phantom jams. All these models explicitly incorporate a stochastic

term in their equations, in order to accomplish this kind of real-life behaviour.

In 1992, Nagel and Schreckenberg proposed. A TCA model that was able to reproduce

several characteristics of real-life traffic flows, e.g., the spontaneous emergence of traffic jams.

Their model is called the NaSch TCA, but is more commonly known as the stochastic traffic

cellular automaton (STCA). It explicitly includes a stochastic noise term in one of its rules,

which we present in the same fashion as those of the previously discussed deterministic TCA

models. The space is divided into cells (cell may contain vehicle or can be empty). The length of

a cell is the minimum space headway available between vehicles in times of jam, and numerically

it is reciprocal of jam density and is set to 7.5 m( Kj=133veh/km).

The STCA then comprises the following three rules (note that in Nagel and Schreckenberg’s

original formulation, they decoupled acceleration and braking, resulting in four rules). Here we

shall discuss about the NaSch model based upon its rules. There are four rules, mainly rules

for acceleration, rules of deceleration, rules for randomization and lastly the vehicle updation

step.

Step 1: Rule for acceleration

if(vn < vmax), then vn −→ min(vn + 1, vmax) (20.5)

This step reflects the general tendency of the drivers to drive as fast as possible without crossing

the maximum speed limit. If the present speed is smaller than the desired maximum speed, the

vehicle is accelerated. The desired speed vmax can be assumed to be distributed by a statistical

distribution function where the values of vmax are only allowed to be 1, 2,..., 5 cell/∆t.

Step 2: Rule for deceleration

if(dn ≤ vn), then vn −→ min(vn, dn − 1) (20.6)

This step ensures that the driver doesnt collide with any vehicle ahead of him so that deceler-

ation is applied to those vehicles which may collide. If the present speed is larger than the gap

in the front, set v = gap. This rule avoids rear end collisions between vehicles. Note that here

a very unrealistic braking rule allowing for arbitrarily large decelerations is involved. This rule

forces minimum time headway of ∆t s.



velocity

2 1 1 0

Step 3: Rule for randomization

if(vn > 0), then vn −→ max(vn − 1, 0) (20.7)

This step of randomization takes into account the different behavioral patterns of the individual

drivers, especially, overreaction while slowing down and nondeterministic acceleration where

overreaction while slowing down will be mostly responsible for the formation of traffic jams.

This rule introduces a random element into the model. This randomness models the uncer-

tainties of driver behavior, such as acceleration noise, inability to hold a fixed distance to the

vehicle ahead. Fluctuations in maximal speed, and assign different acceleration values to differ-

ent vehicles. If present velocity of a vehicle is greater than zero then the velocity of the vehicle

reduces by a single unit with a probability Pbrake. This rule has no theoretical background

and is introduced quite heuristically.

Step 4: Vehicle updation

xn −→ xn + vn (20.8)

After the above three steps the position of vehicles are updated according to their respective

velocities. Even changing the precise order of the steps of the update rules stated above would

change the properties of the model.

Numerical Example

Assume a single lane stretch road divided into 8 cells and vehicles are present in the first, third,

sixth, seventh cells with 2, 1, 1, 0 as their velocities respectively. Apply the rules of cellular

automata.

Solution Apply the CA rules (equation. 20.5 - 20.8) in a sequential way as per the require-

ments of acceleration, deceleration, randomization and vehicle updation. The rules are applied

step wise as shown below.

Solution Step 1: Acceleration stage (according to equation. 20.5)

if(vn < vmax), then vn −→ min(vn + 1, vmax)



3 2 2 1

1 2 0 1

Here the velocity of the present vehicle is 2 where the maximum velocity is 5 so the vehicle gets

accelerated and acquires the new velocity based upon the min of the (present velocity (2) +1,

or the maximum velocity).

• First vehicle: (2 < 5) so min(2 + 1, 5) = 3. Similarly applying the same rule for the rest

of the vehicles the velocities acquired are as follows.

• Second vehicle: (1 < 5) so min(1 + 1, 5) = 2

• Third vehicle: (1 < 5) so min(1 + 1, 5) = 2

• Fourth vehicle: (0 < 5) so min(0 + 1, 5) = 1

Step 2: Deceleration stage ( according to equation. 20.6)

if(dn ≤ vn), then vn −→ min(vn, dn − 1)

In this step the vehicle decelerates if it doesnt find enough gap ahead of it in its lane. The new

velocity of the first vehicle is 3 where as the gap ahead of it 2 so it needs to decelerate by an

amount of gap minus one i.e., (2-1)=1.

• First vehicle : ( 2 3) , min ( 2-1, 3) = 1

Similarly applying it to remaining vehicles the updated velocities are obtained and are

shown below.

• Second vehicle : (3 > 2), no deceleration.

• Third vehicle : (1 < 2), (1 − 1, 2) =0

• Fourth vehicle : (2 > 1), no deceleration.



0 2 0 1

0 2 0 1

Step 3: Randomization stage ( according to equation. 20.7)

if(vn > 0), then vn −→ max(vn − 1, 0)

This step is generally a randomly applied rule for a particular number of vehicles in a set of

total n vehicles. This number depends upon the probability ratio p that the user defines. But

in our case as we are working with a limited number of vehicles so we cannot use the probability

function so for the simplicity of the rule we shall apply this rule ( additional deceleration) to all

the those vehicles which undergo deceleration stage. So in our case the first vehicle undergoes

randomization stage and acquires a new velocity of 0.

• First vehicle : (1 > 0), max(1 − 1, 0) = 0

Step 4: Vehicle updation: ( according to equation. 20.8)

xn −→ xn + vn

The velocity of the first vehicle after undergoing the three rules has been reduced from two to

zero, so the position of the vehicle is not changed in the next time step.

• First vehicle : Xn = 1 + 0 = 1

Similarly applying the rule to the rest of the vehicles in the same way will obtained the

following results as below.

• Second vehicle :Xn = 3 + 2 = 5

• Third vehicle : Xn = 6 + 0 = 6

• Fourth vehicle :Xn = 7 + 1 = 8

The figure below gives the reader a clear overview if all the four stages at a glance.



0 2 0 1

0 2 0 1

1 2 0 1

3 2 2 1

2 1 1 0

Decelerationstage

Vehicleupdation

Randomization

Actualposition

Accelerationstage

20.2.8 Limitations

• Every model has some limitations and as such this cellular automata for single lane traffic

has also some limitations which are stated below.

• A single lane model doesn’t suit the realistic traffic where it has vehicle types of different

velocities. So here in single lane model if such vehicles are entertained the result is the

platooning effect and the average velocity of the stream becomes the velocity of slow

moving velocity.

• So, two lane models are introduced to meet the requirement and four more additional

rules are included for the exchange of vehicles between the lanes.

20.3 Lane changing

The concept of lane changing came into picture with the disadvantage of the single lane model of

unexplained realistic traffic conditions. The reason behind this disadvantage is that a realistic

traffic is usually composed of vehicle types of different desired velocities.

The presence of such vehicles will result in platooning effect. The generic two lane model is

the combination of two parallel single lane models with periodic boundary conditions with some

additional rules as stated in the below sections. The update step is split into two sub-steps. In



first sub-step the exchange of vehicles in the two lanes, take place according to the new rule

set. Vehicles are moved only sideways. They do not advance in one go. However, in reality

this does not happen and this is step is also not seen. This step has a meaning when it is

coordinated with the second step. In the second step, the independent single-lane updates on

both lanes according to the single lane update rules.

20.3.1 STCA models of two lane traffic:

Nagatani has formulated an oversimplified model for two-lane traffic. There are some assump-

tions in this model, one of which is that the maximum allowable speed of each vehicle is

identical. Therefore, the model turns out to be a homogeneous type model and hence cannot

explain heterogeneous traffic consisting of different types of vehicles. Some of the notations,

which will be used to indicate the gaps in the lanes, are

• ∆Xfp (n) = gaps in front of nth vehicle in its present lane.

• ∆Xfo (n) = gaps in front of nth vehicle in other lane.

• ∆Xbo(n) =gap in the other lane behind the site.

All lane-changing rules consist of two parts: Trigger criterion (“Do I want to change the lane”)

and Safety criterion (“Is it safe if I change the lane”). Once if both the criteria are fulfilled,

the vehicle will change the lane.

In a two lane model proposed by Rickert, a vehicle changes its lane with a probability p,

provided there is not enough gap in the current lane in front of the vehicle, if the gap in the

front of the vehicle in the target lane is adequate, if it is possible without collision and finally

when the lane changing activity doesn’t block someone else’s way. The above sentences are

formulated in form of rules from equations. 20.9 to 20.11

• The vehicle does not find enough gap in its current lane ahead of it.

∆Xfp (n) < V (n) + 1 (20.9)

• The gap in the target lane ahead of it is adequate.

∆Xfo (n) > V (n) + 1 (20.10)

• No collision takes place (i.e.,The cell where the vehicle is intending to change should be

empty)



1 1

1 1 2 1

Figure 20:4: CA Example

2 2

2 2 3 2

Figure 20:5: CA Example

• It should not block some others way.

∆Xbo(n) > Vmax (20.11)

Rules 9 and 10 are called the trigger criterion and the rule 11 is called the safety criterion.

These rules are applicable for both left to right and right to left lane changes and it changes

the lane with probability.

Numerical Example

Assume a two-lane road divided into nine cells in each of its lane. In first lane vehicles are

present in first (1), third (1), fourth (2), eight (1) cells and in second lane vehicles are present

in fifth (1) and sixth (1) cells. The numbers in the brackets indicate the present velocities of

the respective velocities. Apply the lane changing rules and determine which vehicles fulfilled

the lane changing requirements.

Solution Initially the solution starts with the acceleration stage of the vehicles, where the

vehicles are applied with the acceleration rule (equation. 20.5). In the acceleration stage, a

single unit increase in every vehicle, which possesses a velocity less than the maximum velocity.

So stage of the vehicles after the acceleration are shown in the Fig. 20:5. Lane changing is

required for L1(1), L1(2), L2(1) where “L1(1)” indicates number in the subscript as its lane

number and the superscript as it vehicle number in respective lanes.

Rule 1: ∆Xpp (n) < V (n)+ 1 The first vehicle has a velocity two and the gap ahead of it in

its current lane is 2 so according to the rule (velocity +1 > gap). Therefore, the vehicle satisfied

the rule so that it can change the lane. L1(1) = (2 < 2 + 1) . . . satisfied. Similarly checking



for all the other vehicles. L1(2) = (1 < 2 + 1) . . . satisfied, L2(1) = (1 < 2 + 1) . . . satisfied.

The term gap is generally referred in two different ways, where it is explained as the distance

between bumper to bumper of the vehicles. The other way to state, the term gap is the number

of empty cells in front of a vehicle”. Here in the present discussion it is taken as the earlier one

but anyways it depends on the reader of choosing it where a slight modification (i.e., addition

of ± 1on the other side of the equations).

Rule 2 : (∆Xfo (n) > V (n) + 1 ) (as per the rule 10) The velocity of the first vehicle is

two and the gap in the target lane ahead of it is four so the rule ( gap ( target lane ) > velocity

+ one ) is satisfied for the first vehicle. L1(1) = (4 > 2 + 1) . . . satisfied. Similarly checking

for other vehicles also will obtain the following results. L1(2) = (2 6> 2 + 1) . . . rejected, and

L2(1) = (34 6> 2 + 1) . . . rejected.

Rule 3: No collision of vehicles is observed as per the pattern given.

Rule 4: (∆Xbo(n) > Vmax ) (as per the rule 11)

The maximum velocity of any vehicle is given as four and the gap behind the first vehicle

in the target lane is five which is greater than the maximum velocity so the vehicle satisfied

the rule and subjected to lane change. L1(1) = (5 > 4). Therefore the first vehicle in the first

lane satisfied all the four rules.

20.3.2 Limitations

In real world traffic the vehicles dont have unique velocities but it was an assumption in the

model. So the vehicles are further divided into two types of different Vmax, namely Vfmax, Vsmax,

corresponding to fast vehicles and a slow vehicles. Introduction of “symmetric two lane model”

for inhomogeneous traffic.

20.4 Extensions

20.4.1 Types of updates

There are two types

Sequential update : This updating procedure considers each cell in the lattice one at a

time. If all cells are considered consecutively, two updating directions are possible, left-to-right

and right-to-left. There is also a third possibility, called random sequential update. Under this

scheme and with N particles in the lattice, each time step is divided in N smaller sub steps.



3 2 1

2 1 2

t

v

Figure 20:6: Without randomization

3 2 1

2 2

v

t

0

Figure 20:7: With randomization

At each of these sub steps, a random cell (or vehicle) is chosen and the CA rules are applied

to it.

Parallel update: This type of update is the classic update procedure generally used in all

the models. For a parallel update, all cells in the system are updated in one and the same time

step. Compared to a sequential updating procedure, this one is computationally more efficient

(note that it is equivalent to a left-to-right sequential update).

20.4.2 Effect of Randomization

The Fig. 20:6 shows the updation without randomization and the Fig. 20:7 is with randomiza-

tion where an extra deceleration is observed in second vehicle and then updation.

20.4.3 Totally asymmetric simple exclusion principle

The simple exclusion process is a simplified well-known particle transport model from non-

equilibrium statistical mechanics, defined on a one-dimensional lattice. In the case of open

boundary conditions (i.e., the bottleneck scenario), particles enter the system from the left side

at an entry rate α , move through the lattice, and leave it at an exit rate β. The term ‘simple



v

1 2 1αδ γ

β

Figure 20:8: Total asymmetric exclusion process

Global density [vehicles/cell]

TASEP (vMax = 1)TASEP (vMax = 5)

CA−184 (vMax = 1)STCA (vMax = 1, p = 0.1)

Glo

bal s

pace

−mea

n sp

eed

[cel

ls/ti

me

step

]

0 0.2 0.4 0.6 0.8 1

1

0.8

0.6

0.4

0.2

0

Figure 20:9: Speed-density relation

exclusion’ refers to the fact that a cell in the lattice can only be empty, or occupied by one

particle.

When moving through the lattice, particles move one cell to the left with probability, and

one cell to the right with probability γ. When γ = δ, the process is called the symmetric simple

exclusion process (SSEP); if γ = δ then it is called the asymmetric simple exclusion process

(ASEP). Finally, if we set γ = 0 and δ = 1, the system is called the totally asymmetric simple

exclusion process (TASEP). If we consider the TASEP as a TCA model, then all vehicles move

with Vmax = 1 cell/time step to their direct right-neighbouring cell, on the condition that this

cell is empty. The process is shown in the below Fig. 20:8.

20.4.4 Comparisons

The above Fig. 20:9 gives a differentiation between four types of models and interestingly it is

observed that the TASEP with Vmax = 1 has a trend of the Greenshield model and following a



Glo

bal f

low

[veh

icle

s/tim

e st

ep]

Global density [vehicles/cell]

CA−184 (vMax = 1)STCA (vMax =1, p = 0.1)TASEP (vMax =5)TASEP (vMax = 1)

10.80.60.40.200

0.1

0.2

0.3

0.4

0.5

0.45

0.35

0.25

0.15

0.05

Figure 20:10: Flow density relation

linearity in the speed-density relation. The same trend is also observed in the below Fig. 20:10

flow density curve.

20.5 References

1. Sven Maerivoet and Bart De Moor. Cellular automata models of road traffic, 2005.

2. K Nagel and M Schreckenberg. A cellular automaton model for freeway traffic. France,

1992.

3. M Rickert, K Nagel, M Schreckenberg, and A Latour. Two lane traffic simulations using

cellular automata. 1996.

4. Debashish Chowdhury Ludger Santen and Andreas Schadschneider. Statistical physics

of vehicular traffic and some related systems, 2000.

5. Andreas Schadschneider. Statistical physics of traffic flow, 2000.

6. Christopher Stone and Larry Bull. Solving the Density Classification Task Using Cellular

Automaton 184 with Memory. Complex Systems Publications,Inc., 2009.


Transportation Systems Engineering 21. Capacity and Level of Service LOS

Chapter 21

Capacity and Level of Service LOS

21.1 Introduction

Often it is required to ascertain how much a transport facility can accommodate. Such in-

formation is useful in the design of traffic facility. Capacity analysis helps in answering the

question. It is a quantitative assessment of the ability of a traffic facility to handle vehicles or

people for which it is designed.

A related question is, what is the performance level of the system at various operating

conditions. Or in other words, how good is the operation of the traffic facility. Level of Service

analysis tries to answer this question which is essentially a qualitative analysis. Capacities and

Level of Services are therefore closely related analysis of a traffic facility.

21.2 Concepts

21.2.1 Capacity

Capacity of a transport facility is defined as the maximum number of vehicles, passengers, or

the like, per unit time which can be accommodated under given conditions with a reasonable

expectation of occurrence. The Highway Capacity Manual(2010) defines the capacity as the

maximum howdy rate at which persons or vehicles can be reasonably expected to traverse a

point or a uniform segment of a lane or roadway during a given time period, under prevailing

roadway, traffic and control conditions. Several observations can be made from the above defi-

nition. Although capacity is the maximum howdy rate, in many situations the break 15 minute

flow rate is expressed as the capacity. The above definition also contains the term “reasonably

expected” to account for the variation in traffic and driving habit at various location. However,

it can be termed as a probabilistic measure. Further, analytical derivations are possible for

getting the maximum flow rate, seldom it is achieved in the field. However, capacity measures



are often empirically derived. Capacity is usually defined for a point or a uniform segment

where operating conditions do not vary.

The capacity measure depends on these operating conditions. The first is the traffic condi-

tions and the factors that influence the capacity includes vehicle composition, turning, move-

ments, etc. The second factor is the roadway conditions and it includes geometrical character-

istics such as lane width, shoulder width, horizontal alignment, vertical alignment. The third

factor is the control conditions such as the traffic signal timings, round-about characteristics.

It is also to be noted that the above capacity definition holds good for a point or at a section

of the road having uniform control conditions. Another aspect of the above capacity definition

is the expression that the maximum flow rate which accounts for the worst 15 minutes traffic

within the peak hour traffic. Lastly the term reasonable expectancy indicates that the capac-

ity measure is probabilistic and not an analytically derived deterministic value. The capacity

measure is probabilistic, for it accounts for the unexplainable variation in traffic and diverse

driving characteristics.

21.2.2 Level of service

Level-of-Service(LOS) of a traffic facility is a concept introduced to relate the quality of traffic

service to a given flow rate. Level-of-Service is introduced by HCM to denote the level of quality

one can derive from a local under different operation characteristics and traffic volume. HCM

proposes LOS as a letter that designate a range of operating conditions on a particular type of

facility. Six LOS letters are defined by HCM, namely A, B, C, D, E, and F, where A denote

the best quality of service and F denote the worst. These definitions are based on Measures of

Effectiveness(MoE) of that facility. Typical measure of effectiveness include speed, travel-time,

density, delay etc. There will be an associated service volume for each of the LOS levels. A

service volume or service flow rate is the maximum number of vehicles, passengers, or the like,

which can be accommodated by a given facility or system under given conditions at a given

LOS.

21.2.3 Type of Facilities

HCM has developed the capacities standard and LOS measure for various facilities. Each traffic

facility has its own unit for the capacity and measure of effectiveness for each item will also vary.

The traffic facilities can be divided into three, namely: the uninterrupted facilities, interrupted

facilities, and others. Interrupted facilities include freeway (basic freeway, weaving sections,

and ramps), multi-lane highways (unidirectional), two-lane highways(bidirectional). Freeways

normally have density as the measure of effectiveness, while multi-lane and two-lane highways



have delay/speed as the MoE. Interrupted facilities include un-signalized intersection, signalized

intersection, and arterials or corridors. They have respectively control delay, total delay and

average travel speed as the measure of effectiveness. Other facilities may include pedestrian

pathways, bicycle tracks, bus-transit system, rail-transit system and air-transportation system.

Each of them have facility specific measure of effectiveness.

21.3 Illustrations

For a typical freeway mid block section the capacity and LOS can be defined for an ideal section.

An ideal section has uninterrupted flow from both sides and has only passenger cars and the

drivers are regular travelers who are familiar with the facility. The lane width is 3.65m wide

with proper shoulder and 1.8m lateral clearance is available from the edge of the pavement.

The free flow speed of 115kmph is achievable on the multi-lane and 100kmph on the two-lane

highway.

21.3.1 Capacity

Such a facility is considered as an ideal facility and for such facilities the following values can

be taken as capacity.

1. A capacity of 2000 vehicle per hour per lane for a speed of 115kmph

2. A capacity of 1900 vehicles per hour per lane for a speed of 80kmph

3. A capacity of 2800 vehicle per hour for both direction at 100kmph

Note that the above values are not analytical or experimentally derived, but, statistically de-

rived from the observed field values from large number of such sections. Needly to say that it

is possible to have a flow higher than this capacity measure, but not necessary.

21.3.2 Level of service

The above capacity value drop due to various ‘non-ideal condition’ which includes changes in

speed or travel time, traffic interruptions or restriction etc. Accordingly HCM has defined

various levels of services for the traffic facility. Assigning quality value is based on several user

surveys capturing the perception of drivers on the quality of the traffic under various operating

condition. The Fig. 21:1 illustrate the quality of services or Level-of-Services (A to F) and the

various operating conditions. The same can be shown in the form of a table ??.



1.0V/C Ratio

E

F

DCBA

Op

erat

ing

Sp

eed

Figure 21:1: The LOS of a Mid Block Section

Table 21:1: The LOS of a Mid Block SectionLOS Quality Speed V/C Description

(kmph)

A Free-flow 80 0.6 High level of physical

and psychological comfort

B Reasonable 70 0.7 Reasonable level of

free-flow physical and psychological comfort

C Near 60 0.8 Local deterioration

free-flow possible with blockages

D Medium 50 0.85 Non-recoverable

flow local disruptions

E At capacity 40 0.9 Minor disturbances

flow resulting breakdown

F Congested 15 1.0 Break down of flow

flow capacity drops



21.4 Conclusion

In this lecture the concepts of capacity and LOS is presented. Capacity is a quantitative

measure, whereas LOS is a qualitative measure. Capacity defined for various traffic facilities

considering the traffic, geometric and control condition and obtained from field observation.

LOS on the other side is assigning quality levels of traffic based on performance measure like

speed, density, etc. Together, the concepts gave planner a valuable tool in designing and

evaluating various traffic facilities.

21.5 References

1. James H Banks. Introduction to transportation engineering. Tata Mc-Graw Hill, 2004.

2. W R McShane and P R Roger. Traffic Engineering. Prentice Hall Publication, 1990.


Delhi, 1987.


Transportation Systems Engineering 22. Urban Streets

Chapter 22

Urban Streets

22.1 Introduction

Cities and traffic have developed hand-in-hand since the earliest large human settlements and

forcing inhabitants to congregate in large urban areas and in turn enforcing need of urban

transportation. To develop efficient street transportation, to serve effectively various land use

in an urban area, and ensure community development, it is desirable to establish a network of

streets divided into systems, each system serving a particular function or particular purpose.

Accordingly, a community should develop an ultimate street-classification in which each system

has a specific transportation service function to perform. There are several operational perfor-

mance measures and level of services (LOS) which have to be taken into account to evaluate

the system of streets. Increasing population of urban areas due to shifting of people from rural

to urban areas and thus certainly increasing vehicular population on urban streets, have caused

problems of congestion in urban areas. Road traffic congestion poses a challenge for all large

and growing urban areas. This document provides a summary of urban street with respect

to their classification, related operational performance measures and level of services (LOS)

involved in each class of urban street and it also provides strategies necessary for any effective

congestion management policy to curb the congestion.

22.2 Classification of urban streets

There are three ways of classifying urban streets

• Functional based

• Design based

• Combination of functional and design based



Mobility Arterials

Collectors

LocalsLand access

Figure 22:1: Relationship of functionally classified systems in service traffic mobility and land

access

22.2.1 Function based

Functional classification is the process by which streets and highways are grouped into classes,

or systems, according to the character of service they are intended to provide. Basic to this

process is the recognition that individual roads and streets do not serve travel independently in

any major way. Rather, most travel involves movement through a network of roads. It becomes

necessary then to determine how this travel can be channelized within the network in a logical

and efficient manner. Functional classification defines the nature of this channelization process

by defining the part that any particular road or street should play in serving the flow of trips

through a highway network. The four functional systems for urbanized areas are:

1. Principal Arterial streets

2. Minor Arterial streets

3. Collector street

4. Local roads

General idea of various streets as per their mobility and land use is shown in the Fig. 22:1.



Principal arterial system

Arterial streets are basically meant to carry longer and through traffic. Function of arterial

is to provide access to commercial and residential land uses. A downtown street not only

carries through traffic but also turning traffics and it resembles arterials. As shown in Fig. ??

mobility of principal arterials is high but land access is very low. Major arterial serves as

principal network for through traffic flow. This should be connected with principal traffic

generations, important rural highways entering the city. It should be well coordinated with

existing and proposed expressway system for good distribution and circulation of through traffic

and continuity of routes should be maintained. In every urban environment there exists a

system of streets and highways which can be identified as unusually significant to the area

in which it lies in terms of the nature and composition of travel it serves. In smaller urban

areas (population under 50,000) these facilities may be very limited in number and extent and

their importance may be primarily derived from the service provided to travel passing through

the area. In larger urban areas their importance also derives from service to rural oriented

traffic, but equally or even more important, from service for major movements within these

urbanized areas. The principal arterial system should carry the major portion of trips entering

and leaving the urban area, as well as the majority of through movements desiring to bypass

the central city. In addition, significant intra-area travels, such as between central business

districts and outlying residential areas between major inner city communities or between major

suburban centers should be served by this system. Frequently the principal arterial system will

carry important intra urban as well as intercity bus routes. Finally, this system in small urban

and urbanized areas should provide continuity for all rural arterials which intercept the urban

boundary.

Minor arterials

The minor arterial street system should interconnect with and augment the urban principal

arterial system and provide service to trips of moderate length at a somewhat lower level of

travel mobility than principal arterials. This system also distributes travel to geographic areas

smaller than those identified with the higher system. The minor arterial street system includes

all arterials not classified as a principal and contains facilities that place more emphasis on

land access than the higher system, and offer a lower level of traffic mobility. Such facilities

may carry local bus routes and provide intra-community continuity, but ideally should not

penetrate identifiable neighborhoods. This system should include urban connections to rural

collector roads where such connections have not been classified as urban principal arterials.

The spacing of minor arterial streets may vary from half to one km in the central business



City

TownVillageArterialsCollector StreetsLocalStreets

Figure 22:2: Schematic illustration of functional classification of rural highway network

Legend

Arterial street Collector street

PublicCommercial

Figure 22:3: Schematic illustration of a portion of urban street network

district to 4 to 5 km in the suburban fringes, but should normally be not more than 2 km in

fully developed areas.

Collector streets

This system of streets includes all distributer and collector streets. Function of this system

is serving between major arterials and local streets to connect adjacent neighborhood areas

placed approximately at half miles intervals to accommodate local through traffic movements

and interconnect local streets with the major arterial street system. Unlike arterials their

operation is not always dominated by traffic signals.

Local Street

Local streets are primarily meant for direct access to residential commercial, industrial or other

abutting property. All through traffics should be discouraged on local streets. Land access is

very high but mobility is very low for local streets.



22.2.2 Design based Classification

This classification basically depends upon speed limits, signal density, driveways / access point

density etc.

1. High speed

2. Suburban

3. Intermediate

4. Urban

High speed streets

These are the streets with very low driveway or access point density. These are provided with

separate right turn lanes and; no parking is permitted on street. Streets may be multilane

divided or undivided or two lane facility with shoulders. Signals are infrequent and spaced at

long distances. Road side development is very low. A speed limit on these roads is 75 to 90

kmph.

Sub-urban streets

They represent streets with a low driveway/access-point density,separate or continuous right

turn lane and some portions where parking is permitted. These roads possess comparatively

higher density of roadside development than that on high speed streets. It has about three

signals per Km. and speed limit on these roads is 65 to 75 kmph.

Intermediate design streets

They represent urban streets with moderate driveway/access point density. Like sub-urban

streets they also have some separate or continuous right turn lane and some portions where

parking is permitted. These roads possess comparatively higher roadside development than

that on sub-urban streets. It has about two to six signals per Km. and speed limit on these

roads is 50 to 60 Kmph.

Urban streets

They represent urban streets with high driveway/access point density. These are usually pro-

vided with road side parking. It has highest road side development density among all above

stated four classes. Signal density is about four to eight per Km. Speed limit is 40 to 55 Kmph.



Table 22:1: Combined classification of urban streetsDesign category Functional category

Principal arterial Minor arterial

High speed I NA

Suburban II II

Intermediate II III or IV

Urban III or IV IV

Table 22:2: Specifications of street classes

Urban Street Class Signal density Free flow

(signals/km) speed(kmph)

I 0.2 80

II 2 65

III 4 55

IV 6 45

22.2.3 Combination of functional and design based

This type of classification considers for combination of functional and design classes divided

into four classes viz. I, II, III, IV which reflects a unique combination for of street function and

Design, as shown in table 1 and related signal densities are shown in table 2.

22.3 Operational performance measures

Engineer has to quantify how well the ’system’ or ’facility is working’. The facilities will usually

assembled by specific qualitative and quantitative index of flow characteristics termed as Level

of Service (LOS), in this regard engineer has to do following works.

1. Assessing the existing condition

2. Evaluating alternative improvements

3. Quantifying associated cost and benefits

4. Communicating results to both technical and non technical people



As far as operational performance of urban streets is considered we are interested in determining

arterial level of service which is discussed in succeeding section.

22.3.1 Arterial LOS

Urban streets LOS is mainly based on average travel speed for the segment or for the entire

street under consideration. The average travel speed is computed from the running times

on the urban street and the control delay of through movements at signalized intersections.

The control delay is the portion of the total delay for a vehicle approaching and entering a

signalized intersection. Control delay includes the delays of initial deceleration, move-up time

in the queue, stops, and reacceleration, these delays are also known as intersection approach

delays.

The LOS for urban streets is influenced both by the number of signals per kilometer and

by the intersection control delay. Inappropriate signal timing, poor progression, and increasing

traffic flow can degrade the LOS substantially. Streets with medium-to-high signal densities

(i.e., more than one signal per kilometer) are more susceptible to these factors, and poor LOS

might be observed even before significant problems occur. On the other hand, longer urban

street segments comprising heavily loaded intersections can provide reasonably good LOS,

although an individual signalized intersection might be operating at a lower level. The term

through vehicle refers to all vehicles passing directly through a street segment and not turning.

Considering all the above aspects, HCM provides a seven step methodology to determine the

level of service of an arterial which will be discussed in following section.

22.3.2 HCM Method of performance measurement

HCM method of arterial performance measurement involves seven steps which aim to compute

’average travel speed’ of arterial to measure the Level of Service. These seven steps are as

follows,

1. Establish arterial to be considered

2. Determine arterial class by free flow speed

3. Define arterial section

4. Compute running time

5. Compute intersection approach delay

6. Compute average travel speed



Table 22:3: Range and typical values of FFS for different arterial classes

Free flow Arterial Class

speed (kmph) I II III IV

Speed range 90 to 70 70 to 55 55 to 50 55 to 40

Typical value 80 65 55 45

7. Estimate the LOS.

The above flow chart shows the steps to determine LOS in a schematic form. Further in this

section we are going to discuss these seven steps in detail.

22.3.3 Step 1: Establish arterial to be considered

Establishing the arterial is the very first step in the process of determining the LOS. In this

step, an engineer has to define arterial segment or entire arterial whose LOS is to be determined.

Arterial may be established by arterial class, its flow characteristics and signal density. Arterial

class may be defined as per its free flow speed as explained in step 2 as follows.

22.3.4 Step 2: Determine arterial class by free flow speed

Free flow speed is the speed on the arterial which most of the drivers choose if they had green

indication and they are alone in the direction of movement are not the part of platoon) but

have to be conscious about all other prevailing conditions. (e.g. Block spacing, contiguous

land use, right of way, characteristic, pedestrian activity, parking, etc.) Free flow speed should

be measured at just the time when the entire factors are present except for the prevailing

traffic levels and red indication. An arterial can be classified on the basis of its free flow speed

as explained under the section design based classification and combined classification . The

following table 3 can be used to determine the arterial class.

22.3.5 Step 3: Define arterial section

After determining the arterial class it is required to be more specific about the particular section

of an arterial for which LOS is to be determined. The arterial section may be mid block or

intersection. Generally signalized intersection is taken into account to determine intersection

approach delays which are further required to determine level of service.



22.3.6 Step 4: Arterial running time

There are two principal components for the total time that a vehicle spends on a segment of an

urban street. These are running time and control delay at signalized intersections. To compute

the running time for a segment, the analyst must know the street’s classification, its segment

length, and it’s free flow speed. Arterial running time can be obtained by Travel time studies,

information of running times from local data and intersection delays etc.

22.3.7 Step 5: Intersection Approach Delay

Intersection approach delay is the correct delay which is to be used in arterial evaluation. It

gives consideration not only for absolute stopped delay but also for the delay in retarding the

vehicle approaching at signal for stopping and reaccelerating on starting of green. It is longer

than the stopped delay. This can be related to intersection stopped delay and is computed by,

D = 1.3 d (22.1)

where, D = intersection approach delay (sec/veh), and d = intersection stopped delay (sec/veh).

Delay at intersection approach is of special interest because it is a Measure of Effectiveness

(MOE) used to quantify LOS. To determine intersection approach (or control) delay it is nec-

essary to calculate stopped delay which is discussed below.

Stopped Delays

Stopped vehicles on intersection are counted for intervals of 10 to 20 seconds. It is assumed

that vehicles counted as ’stopped’ during one of these intervals will be stopped for the length

of the interval. Measuring the stopped delays involves following steps.

1. Maximum extent of queue length on intersection approach during the study period must

be observed in advance (observer must be able to count all stopped vehicles in the longest

possible queue).

2. Count intervals are set at 10, 15, or 20 seconds stopped vehicles within the queuing area

observed and recorded at each interval.

3. Discharge volumes are separately counted for the study period.



Table 22:4: Data observed at an intersection for stopping vehicles

Seconds into minute

Minute 0 sec 15 sec 30 sec 45 sec

5.00 pm 2 4 1 3

5.01 pm 4 5 3 0

5.02 pm 6 3 2 1

5.03 pm 2 5 4 3

5.04 pm 4 2 6 4

5.05 pm 5 4 1 1

5.06 pm 1 2 5 5

5.07 pm 4 3 3 3

5.08 pm 2 5 2 2

5.09 pm 3 1 4 2

Total 33 34 31 24

Numerical example

In an intersection the following data was observed for stopping times for vehicles as tabulated

in table 4. Calculate intersection approach delay for the given data set. Total exiting vehicles:

100.

Solution: Total of stopped-vehicle counts (density counts) for study sample is: 33+34+31+24=122

veh. Each of the vehicle interval is 15 seconds. Aggregate delay for the 10 minutes study period

is, 122× 15 sec=1830 veh-sec. Average stopped delay per vehicle for study period of 10 minutes

is, 1830/100 =18.3 sec per vehicle. That is, d=18.3 sec per vehicle. We use this in the first

equation. So, intersection approach (or control) delay D

D = 1.3 × d = 1.3 × 18.3 = 23.79 sec/veh.

22.3.8 Step 6: Average travel speed

Arterial LOS is based on the ’average travel speed’ for segment, section or entire arterial under

consideration. Arterial average travel speed is given by

vavg =3600L

Tr × L + D(22.2)



Table 22:5: Urban Street LOS by Class and Average Travel Speed

LOS Average Travel Speed (km/h)

I II III IV

A > 72 > 59 > 50 > 41

B > 56 > 46 > 39 > 32

C > 40 > 33 > 28 > 23

D > 32 > 26 > 22 > 18

E > 26 > 21 > 17 > 14

F > 26 < 21 < 17 < 14

where, vavg = arterial or segmental average travel speed (Kmph), L = arterial or segmental

length (Km), Tr = total of the running time per kilometer on all segments in the arterial or

section (seconds), D = total of the approach delay at all intersections within the defined arterial

(seconds). It is the actual speed in consideration with the additional effect of control and all

stop delays. It is the measure by which LOS is defined.

22.3.9 Step 7: Estimate the LOS

This is the last step of determination of LOS. After calculation of average travel speed we can

determine the level of service of an arterial by using Table 22:5.

Numerical example

Consider an arterial which has free flow speed of 65 kmph and average running time of vehicles

is 145 sec/km determine LOS for this arterial.

Solution: From Table 22:5 we can find LOS of an arterial. As free flow speed is 65 kmph

by using table 3 we can classify this as Arterial Class II, Now we should know average travel

speed, to find out LOS. Delay is determined in problem 1. Hence D=23.79sec/veh.

vavg =3600L

Tr × L + D=

3600 × 1

145 + 23.79= 21.32 km/hr

As average travel speed is 21.32 kmph we can have LOS as ’E’ from Table 22:5.



22.4 Congestion Management

When demand on a facility exceeds the capacity Congestion takes place. The travel time or

delay is in excess of that normally incurred under light or free flow traffic condition. The

travel time or delay is in excess of agreed upon norm which may vary by type of transport

facility, travel mode, geographical location, and time of day. In the procedure for congestion

management initially we have to find out the root cause of congestion and finding out the

remedies for managing the congestion, updating the signalization if it is needed. It is always

better to use good signalization for minimizing impact of congestion. We can provide more

space by making use of ’turn bays’ if geometry permits. Parking restrictions also help in

congestion management on urban streets. Now we will discuss some important strategies to

manage the congestion on urban streets.

22.4.1 Managing surface street congestion

Basically at street level congestion can be encountered by following ways,

1. Signal based

2. Non-signal based

22.4.2 Signal based remedies

Signal based remedies for congestion management can be achieved by implementing following

two strategies,

1. Metering plans

2. Reasonably shorter cycle lengths

Metering plans

It is the congestion management policy for street congestion to limit the volumes arriving at

critical locations. It uses some control strategies within the congestion networks by storing

vehicles at links defined to be part of system under control. It should be noted that metering

concept does not explicitly minimize delays and stops but manages queue formation. There are

three types of metering strategies,

1. Internal metering: It is the management policy which makes use of control strategies

within the congested network by influencing the distribution of vehicles arriving at and



Figure 22:4: g/C is reduced to limit discharge

departing from critical locations as shown in Fig. 22:4 Limit the upstream or downstream

blockage by limiting the turn in flows as shown in Fig. 22:5. It deals with upstream

control by creating moving storage situation on upstream link. It manages congestion by

limiting turn-in flows from cross streets and preserving arterials for their through flow by

metering from face of back up from outside as shown in Fig. 22:6

2. External metering: Control of major access points shown in Fig. 22:7 (e.g. river crossing,

downtown surrounded by water from three sides, a system that receives limited no. of

arterials etc.) so as to limit inflow rates. It is conceptually convenient because the storage

of problem vehicles belongs to somebody else outside the system. But while metering it

should be noted that metering should not be upto such extent that other areas.

3. Release metering: It uses policy of controlling the release of vehicles from the places

where vehicles are stored such as parking, garages etc. they are stored off-street so as to

reduce their spillback potential. This type of metering can be used in shopping centers,

mega center, etc. by lowering the discharge rates of vehicles.

Shorter cycle length

If on any intersection higher cycle time is provided then it will certainly create problems like

increase in queue length and platoon length discharged and it will lead to increase in blockage



Figure 22:5: g/C is reduced to preserve through flow

critical intersection

undersaturated

internally metered

Figure 22:6: Internal metering



external metering plansinnerbound routes that are metered

Figure 22:7: External metering

of intersection, with substantial adverse impact on system capacity. This is particularly when

short link lengths are involved. Length of downstream space should be greater than queue

length to store the vehicles. Note that a critical lane flow of Vi nominally discharges Vi*C/3600

vehicles in a cycle. If each vehicle requires D meters of storage space, the downstream link would

be(

ViC

3600

)

D ≤ L (22.3)

where, ViC3600

= no. of vehicles per cycle, D= storage space required for each vehicle, L= available

downstream space in m. (This may be set by some lower value to keep the queue away from

the discharging intersection, or to allow for turn-ins.) Equation may be re-arranged as,

C ≤

(

L

D

) (

3600

Vi

)

(22.4)

Note that Vi in this case is the discharge volume per downstream lane, which may differ from

the demand volume, particularly at the fringes of the system being considered. Note that only

rather high flows (maximum f > 800 veh per hour per lane (vphpl)) and short blocks will create

very severe limits on the cycle length. However, these are just the situations of at most interest

for extreme congestion situations. An illustratise example to show the requirement of shorter

cycle length is given below.

Numerical example

Flow on an critical lane is 300 veh/h, cycle time is 80 seconds, suppose storage space required

per lane vehicle is 6m as an average and space available on downstream is 30 m, find whether

the space is sufficient and comment on the result and suggest some remedy if required.



Solution: Given: Vi = 300 veh/h, C = 80 sec, and L = 30 m. Vehicles discharged by a

critical lane per cycle to be found out and which is given by, ( ViC3600

) = 300 * 80/3600 = 60/9

=6.6 veh/cycle. Therefore, space required for storing these vehicles for cycle time is, = 6.6 *

D, = 6.6 * 6, = 39.6 m. ≈ 40 m. So, 40 m > 30 m (length of downstream storage i.e. space

available), So length is inadequate. As the length is fixed the only possible variable is ’cycle

time’ so we will reduce the cycle time, let the new cycle time be, 40 seconds instead of 80

seconds. Space required will be get reduced to half i.e. 20m which is lesser than the available

space i.e. 30m so it is feasible to reduce the cycle length to manage the congestion.

22.4.3 Non-signal based remedies

If the problem of congestion does not get resolved by signalization the next set of actions are

summarized in two words more space means there is need of provision of additional lanes or

some other facility. It can be achieved by adding left turn bays / right turn bays, removing

obstructions to through flows by adding more space and free movements Some non-signal based

remedies are given below,

1. Two way turn lanes

2. Reversible lanes

3. Kerb parking prohibition

4. Lane marking

Two way turn lanes

On suburban and urban arterials dedication of a central laneas shown in Fig. 22:8 for turns in

either direction is provided. This also allows for storage and vehicles to make their maneuvers

in two distinct steps. Leaving the arterial and entering it is separated into two distinct

steps. Vehicles leaving (Fig. 22:9) the arterial do not have to block a moving lane while waiting

for a gap in the opposing flow. Entering vehicles (Fig. 22:10) do not have to wait for a gap

simultaneously in both directions. The Figure 22:8 shown above is the road sign for two way left

turn lane which indicates that the center lane is provided exclusively for two way left turning

traffic.

Reversible lane

Reversible lanes shown in Figure 8 have great advantage of matching lane availability to the

peak demand. Lanes are reversible means can be split into various combinations for different



2 way sign

Figure 22:8: Two way left-turn lane on arterial

Vehicle

1

2

Figure 22:9: A vehicle leaving arterial in two steps

2

1Vehicle

Figure 22:10: A vehicle entering arterial in two steps



Reversible lane

Figure 22:11: Lane marking and associated signal /signs for reversible lane

times of day to match the demand. E.g. eight lanes can be split into 6:2 or 5:3 and so forth

if required to match up for the demand. It should be noted that some jurisdictions have

combined two-way lanes and reversible lanes on same arterial ’because combination of peak-

period congestion and increased road side development’. The concerns with reversible lanes

and relates to the misuse and lanes by the driver (particularly the unfamiliar driver), despite

the signalization over the lanes.

HOV lanes

High occupancy vehicle (HOV) lanes are designed to help move more people through congested

areas. HOV lanes offer users a faster, more reliable commute, while also easing congestion in

regular lanes - by moving more people in fewer vehicles. HOV lanes on provincial highways are

reserved for any of the following passenger vehicles carrying at least two people (often referred

to as 2+):

1. Car

2. Commercial truck less than 6.5 metres long

3. Minivan

4. Motorcycle

5. Taxi or limousine

In addition, vehicles with a special green licence plate (plug-in hybrid electric or battery electric

vehicle) A bus of any type can use an HOV lane, even without passengers. This helps buses

keep to their schedules and provide reliable, efficient service. Emergency vehicles are permitted

to use the HOV lanes at all times.



Kerb Parking Prohibition

Congestion can be managed by prohibiting the kerb parking. Kerb parking means on street

parallel parking. If such parking is avoided it implies oblique and right angled parking is also

prohibited and hence provides more space for traffic flow so congestion is minimized.

Lane marking

Longitudinal lane markings such solid white lines and broken white lines restricts overtak-

ing maneuver of vehicles which encourages mix through traffic flow unobstructed resulting in

reducing the congestion.

Equity offsets

This topic can be read in reference to congestion management by signal based remedies. Offset

on an arterial are usually set to move vehicles smoothly along the arterial, as is logical. Equity

offset allows the congested arterial to have its green at upstream intersection until the vehicle

just begin to move , then switch the signal, so that these vehicles flush out the intersection,

but no new vehicles continue to enter.

Imbalanced split

This topic can be referred under signal based congestion management remedies. It is the pro-

cedure of allocating the ’available green’ in proportion to the relative demands. It is sometimes

desirable to split green as per demand of various routes to meet peak hour demands of respective

routes.

HOV Lanes

This topic can be referred as non signal based remedies On provincial highways HOV lanes are

developed by adding a new inside (leftmost) lane to existing corridors. Where the HOV lane

begins, signs on the left side of the highway inform carpools and buses to move left into the

new lane. An overhead sign indicates the beginning of the HOV lane. In some locations, where

a highway on-ramp used to end, the on-ramp lane has been extended as the new HOV lane.

In this situation, motorists not permitted to use the HOV lane have to exit that lane before

the start of the HOV lane designation. Overhead signs at 1 kilometre and again at 500 metres

before the start of the HOV lane designation advise drivers to exit the lane. Overhead signing

and closely spaced white broken lines and diamond symbol pavement markings indicate the

beginning of the HOV lane (Figure 22:12).



��

Figure 22:12: High Occupancy Vehicle Lane

22.5 Conclusion

It can be understood that urban streets are integral part of transportation system. Urban

streets plays vital role in development of country. These are classified on their function, design

for various considerations taking into account. Performance measures are to be worked out

to determine LOS. Congestion is a huge problem which can be curbed by some preventive

measures and design strategies. Signalized remedies are more efficient than any other measures

of street congestion management. Non signalized remedies can be used to manage congestion

by providing more space in terms of extra lanes.

22.6 References




New Delhi, 1987.

3. W R McShane and P R Roger. Traffic Engineering. Prentice Hall Publication, 1990.

4. C D Papacostas and P D Prevedouros. Transportation Engineering and Planning. 2002.

5. B K Woods. Highway Engineering Handbook. McGraw Hill Company. 1960.


Transportation Systems Engineering 23. Multilane Highways

Chapter 23

Multilane Highways

23.1 Introduction

Increasing traffic flow has forced engineers to increase the number of lanes of highways in order

to provide good manoeuvring facilities to the users. The main objectives of this lecture is to

analyse LOS which is very important factor for a traffic engineer because it describes the traffic

operational conditions within a traffic stream. Also we are going to study the characteristics

and capacity for multilane highways. Free-flow speed is an important parameter that is being

used extensively for capacity and level-of- service analysis of various types of highway facilities.

23.2 Multilane Highways

A highway is a public road especially a major road connecting two or more destinations. A

highway with at least two lanes for the exclusive use of traffic in each direction, with no control

or partial control of access, but that may have periodic interruptions to flow at signalized

intersections not closer than 3.0 km is called as multilane highway. They are typically located

in suburban areas leading to central cities or along high-volume rural corridors that connect

two cities or important activity centres that generate a considerable number of daily trips.

23.2.1 Highway Classification

There are various ways of classification of highways; we will see classification of highways

according to number of lanes.

• Two lane highways.

• Multilane highways



��

��

Figure 23:1: Divided multilane highway in a rural/suburban environment

Figure 23:2: UnDivided multilane highway in a rural/suburban environment

23.2.2 Highway Characteristics

Multilane highways generally have posted speed limits between 60 km/h and 90 km/h. They

usually have four or six lanes, often with physical medians or two-way right turn lanes (TWRTL),

although they may also be undivided. The traffic volumes generally varies from 15,000 - 40,000

vehicles per day. It may also go up to 100,000 vehicles per day with grade separations and no

cross-median access. Traffic signals at major intersections are possible for multilane highways

which facilitate partial control of access. Typical illustrations of multilane highway configura-

tions are provided in Fig. 23:1 and 23:2

23.3 Highway Capacity

An important operation characteristic of any transport facility including the multi lane highways

is the concept of capacity. Capacity may be defined as the maximum sustainable flow rate at

which vehicles or persons reasonably can be expected to traverse a point or uniform segment of



Table 23:1: Free flow speed and capacity for Multilane highway

Types of facility Free flow Capacity

speed(kmph) (pcphpl)

Multilane 100 2200

90 2100

80 2000

70 1900

a lane or roadway during a specified time period under given roadway, traffic, environmental,

and control conditions; usually expressed as vehicles per hour, passenger cars per hour, or

persons per hour. There are two types of capacity, possible capacity and practical capacity.

Possible capacity is defined as the maximum number of vehicles that can pass a point in one

hour under prevailing roadway and traffic condition. Practical capacity on the other hand is

the maximum number that can pass the point without unreasonable delay restriction to the

average driver’s freedom to pass other vehicles. Procedure for computing practical capacity for

the uninterrupted flow condition is as follows:

1. Select an operating speed which is acceptable for the class of highways the terrain and

the driver.

2. Determine the appropriate capacity for ideal conditions from table 1.

3. Determine the reduction factor for conditions which reduce capacity (such as width of

road, alignment, sight distance, heavy vehicle adjustment factor).

4. Multiply these factors by ideal capacity value obtained from step 2.

23.4 Level of Service

Level of service (LOS) is a qualitative term describing the operational performance of any

transportation facility. The qualitative performance measure can be defined using various

quantitative terms like:

1. Volume to capacity ratio,

2. Mean passenger car speed,( in km/h)



Figure 23:3: LOS A

3. Density, (in p/kmln).

Basically any two of the following three performance characteristics can describe the LOS for a

multilane highway. Each of these measures can indicate how well the highway accommodates

the traffic demand since speed does not vary over a wide range of flows, it is not a good indicator

of service quality. Density which is a measure of proximity of other vehicles in the traffic stream

and is directly perceived by drivers and does not vary with all flow levels and therefore density

is the most important performance measure for estimating LOS. Based on the quantitative

parameter, the LOS of a facility can be divided into six qualitative categories, designated as

LOS A,B,C,D,E,F The definition of each level of service, is given below:

23.4.1 Level of Service A

Travel conditions are completely free flow. The only constraint on the operation of vehicles

lies in the geometric features of the roadway and individual driver preferences. Lane changing,

merging and diverging manoeuvre within the traffic stream is good, and minor disruptions to

traffic are easily absorbed without an effect on travel speed. Average spacing between vehicles

is a minimum of 150 m or 24 car lengths. Fig. 23:3 shows LOS A.

23.4.2 Level of Service B

Travel conditions are at free flow. The presence of other vehicles is noticed but it is not a con-

straint on the operation of vehicles as are the geometric features of the roadway and individual

driver preferences. Minor disruptions are easily absorbed, although localized reduction in LOS

are noted. Average spacing between vehicles is a minimum of 150 m or 24 car lengths. Fig. 23:4

below shows LOS B.



Figure 23:4: LOS B

Figure 23:5: LOS C

23.4.3 Level of Service C

Traffic density begins to influence operations. The ability tomanoeuvre within the traffic stream

is affected by other vehicles. Travel speeds show some reduction when free-flow speeds exceed

80 km/h. Minor disruptions may be expected to cause serious local deterioration in service,

and queues may begin toform. Average spacing between vehicles is a minimum of 150 m or 24

car length. Fig. 23:5 shows LOS C.

23.4.4 Level of Service D

The ability to manoeuvre is severely restricted due to congestion. Travel speeds are reduced

as volumes increase. Minor disruptions maybe expected to cause serious local deterioration in

service, and queues may begin to form. Average spacing between vehicles is a minimum of 150

m or 24 car length. Fig. 23:6 shows LOS D.

Figure 23:6: LOS D



Figure 23:7: LOS E

Figure 23:8: LOS F

23.4.5 Level of Service E

Operations are unstable at or near capacity. Densities vary, depending on the free-flow speed.

Vehicles operate at the minimum spacing for which uniform flow can be maintained. Disruptions

cannot be easily dissipated and usually result in the formation of queues and the deterioration

of service to LOS F. For the majority of multilane highways with free-flow speed between 70

and 100km/h, passenger-car mean speeds at capacity range from 68 to 88 km/h but are highly

variable and unpredictable. Average spacing between vehicles is a minimum of 150 m or 24 car

length. Fig. 23:7 shows LOS E.

23.4.6 Level of Service F

A forced breakdown of flow occurs at the point where the numbers of vehicles that arrive at

a point exceed the number of vehicles discharged or when forecast demand exceeds capacity.

Queues form at the breakdown point, while at sections downstream they may appear to be at

capacity. Operations are highly unstable, with vehicles experiencing brief periods of movement

followed by stoppages. Travel speeds within queues are generally less than 48 km/h. Note that

theterm LOS F may be used to characterize both the point of the breakdown and the operating

condition within the queue. Fig. 23:8 shows LOS F.



23.5 Determination of Level of Service

The determination of level of service for a multilane highway involves three steps:

1. Determination of free-flow speed

2. Determination of flow rate

3. Determination of level of service

23.5.1 Free-flow speed

Free-flow speed is the theoretical speed of traffic density, when density approaches zero. It is

the speed at which drivers feel comfortable travelling under the physical, environmental and

traffic conditions existing on an uncongested section of multilanehighway. In practice, free-flow

speed is determined by performing travel-timestudies during periods of low-to-moderate flow

conditions. The upper limit for low to moderate flow conditions is considered 1400 passenger

cars per hour per lane(pc/h/ln) for the analyses. Speed-flow and density flow relationships are

shown in Fig. 23:9 and Fig. 23:10. These relationships hold for a typical uninterrupted-flow

segment on a multilane highway under either base or no base conditions in which free-flow

speed is known. Fig. 23:9 indicates that the speed of traffic volume up to a flow rate of 1400

pc/h/ln. It also shows that the capacity of a multilane highway under base conditions is 2200

pc/h/ln for highways with a 90 km/h free-flow speed. At flow rates between 1400 and 2200

pc/h/ln, the speed on a multilane highway drops; for example, by 8 km/h for a highways with

a free-flow speed of 90 km/h. Fig. 23:10 shows that density varies continuously throughout the

full range of flow rates. The capacity value of 2200 pc/h/ln is representative of the maximum

15-min flow rate that can be accommodated under base conditions for highways with 90 km/h

free-flow speed. From various studies of the flow characteristics, base conditions for multilane

highways are defined as follows:

1. Lane widths are 3.6 m.

2. Lateral clearance is 1.8 m.

3. A minimum of 3.6 m of total lateral clearance in the direction of travel. Clearances

are measured from the edge of the outer travelled lanes (shoulders included) and lateral

clearance of 1.8 m or greater are considered to be equal to 1.8 m.

4. No direct access points along the highway.



110

100

90

80

70

60

50

40

30

20

10

0400 800 1200 1600 2000 24000

(pc/h/ln)Flow

Spe

ed(k

m/h

r)

Figure 23:9: Speed-flow relationship on multilane highways

1

Flow (pc/h/ln)

Den

sity

(pc/

h/ln

)

Free flow speed = 100 km/hr

Free flow speed = 70 km/hrFree flow speed = 80 km/hrFree flow speed = 90 km/hr

0

5

10

15

20

25

30

35

40

45

50

400 800 1200 1600 2000 24000

Figure 23:10: Density-flow relationships on multilane highways

1600400 800 1200 2000 2400

10

20

100

110

90

80

70

60

40

50

30

0

Ave

rage

Pas

seng

er−C

ar S

peed

(km

/h)

Flow Rate (pc/h/ln)

EDLOS A B C

70 km/h

80 km/h

90 km/h

Free−Flow Speed, FFS = 100 km/h

Den

sity

= 7

pc/k

m/ln

11pc

/km

/ln

16pc

/km

/ln22

pc/k

m/ln

28 pc

/km/ln

Figure 23:11: Speed-flow curves with LOS criteria for multilane highways



110

100

90

80

70

60

50

40

30

20

10

0

(pc/h/ln)Flow

Density = 25 pc/km/lnDensity = 22 pc/km/ln

Density = 7 pc/km/lnDensity = 11 pc/km/lnDensity = 16 pc/km/ln

(km

/hr)

Spe

ed

400 800 1200 1600 2000 24000

Figure 23:12: Flowchart showing step by step procedure to find density and LOS

5. A divided highway.

6. Only passenger cars in the traffic stream.

7. A free-flow speed of 90 km/h or more.

The average of all passenger-car speeds measured in the field under low volume conditions can

be used directly as the free-flow speed if such measurements were taken at flow rates at or below

1400 pc/h/ln. No adjustments are necessary as this speed reflects the net effect of all conditions

at the site that influence speed, including lane width, lateral clearance, type of median, access

points, posted speedlimits, and horizontal and vertical alignment. Free-flow speed also can be

estimated from 85th-percentile speed or posted speed limits, research suggests that free-flow

speed under base conditions is 11 km/h higher than the speed limit for 65 km/h to 70 km/h

speed limits and 8 km/h higher for 80 km/h to 90 km/h speed limits. Fig. 23:12 shows speed-

flow curves with LOS criteria for multilane highways, here LOS is easily determined for any

value of speed simply by plotting the point which is a intersection of flow and corresponding

speed. Note that density is the primary determinant of LOS. LOS F is characterized by highly

unstable andvariable traffic flow. Prediction of accurate flow rate, density, and speed at LOS

F is difficult.

23.5.2 Determination of free-flow speed

When field data are not available, the free-flow speed can be estimated indirectly as follows:

FFS = BFFS − fLW − fLC − fM − fA (23.1)

where, FFS is the estimated FFS (km/h), BFFS= base FFS (km/h), fLW= adjustment for

lane width, from Table 3 (km/h), fLC= adjustment for lateral clearance, from Table 4 (km/h),



Table 23:2: Level of Service criteria for a typical free flow speed of 100 kmph proposed in HCM

2000

Free-Flow Criteria (LOS) (LOS) (LOS) (LOS) (LOS)

Speed A B C D E

100 km/h Max. density 7 11 16 22 25

(pc/km/ln)

Average speed 100 100 98.4 91.5 88

(kmph)

Max. volume 0.32 0.50 0.72 0.92 1.00

capacity ratio

Max. service 700 1100 1575 2015 2200

flow rate

(pc/h/ln)

fM= adjustment for median type, from Table 5 (km/h), and fA= adjustment for access points,

from Table 6 (km/h). FFS on multilane highways under base conditions is approximately 11

km/h higher than the speed limit for 65 and 70 km/h speed limits, and it is 8 km/h higher for

80 and 90 km/h speed limits. BFFS is approximately equal to 62.4 km/h ( i.e decrease in 1.6

km/h) when the 85 th percentile speed is 64 km/h, and it is 91.2 km/h ( i.e decrease in 4.8

km/h) when the 85 th percentile speed is 96 km/h and the in between speed values is found

out by interpolation. According to Table 3, the adjustment in km/h increase as the lane width

decreases from a base lane width of 3.6 m. No data exist for lane widths less than 3.0m.

The adjustment for lateral clearance (TLC) is given as:

TLC = LCL + LCR (23.2)

where, TLC = Total lateral clearance (m), LCL = Lateral clearance (m), from the right edge of

the travel lanes to roadside obstructions (if greater than 1.8 m, use 1.8 m), and LCR= Lateral

clearance (m), from the left edge of the travel lanes to obstructions in the roadway median

(if the lateral clearance is greater than 1.8 m, use 1.8 m). Once the total lateral clearance is

computed, the adjustment factor is obtained from Table 4. For undivided highways, there is

no adjustment for the right-side lateral clearance as this is already accounted for in the median

type. Therefore, in order to use Table 5 for undivided highways, the lateral clearance on the

left edge is always 1.8 m, as it for roadways with TWRTLs. The access-point density, which

is use in Table 6, for a divided roadway is found by dividing the total number of access points



Table 23:3: Adjustment for lane width (Source: HCM, 2000)

Lane Width (m) Reduction in FFS(km/h)

3.6 0.0

3.5 1.0

3.4 2.1

3.3 3.1

3.2 5.6

3.1 8.1

3.0 10.6

Table 23:4: Adjustment for lateral clearance(Source: HCM, 2000)

Four-Lane Highways Six-Lane Highways

Total Lateral Reduction in FFS Total Lateral Reduction in FFS

Clearance a (m) (km/h) Clearance a (m) (km/h)

3.6 0.0 3.6 0.0

3.0 0.6 3.0 0.6

2.4 1.5 2.4 1.5

1.8 2.1 1.8 2.1

1.2 3.0 1.2 2.7

0.6 5.8 0.6 4.5

0.0 8.7 0.0 6.3

Table 23:5: Adjustment to free flow speed for median type(Source: HCM, 2000)

Median Type Reduction in FFS (km/h)

Undivided highways 2.6

Divided highways 0.0



Table 23:6: Adjustment to free flow speed for Access-point density(Source: HCM, 2000)

Access Points/Kilometre Reduction in FFS (km/h)

0 0.0

6 4.0

12 8.0

18 12.0

≥ 24 16.0

(intersections and driveways) on the right side of the roadway in the direction of travel being

studied by the length of the segment in kilometres. The adjustment factor for access-point

density is given in Table 6. Thus the free flow speed can be computed using equation 1 and

applying all the adjustment factors.

23.5.3 Determination of Flow Rate

The next step in the determination of the LOS is the computation of the peak hour factor. The

fifteen minute passenger-car equivalent flow rate (pc/h/ln), is determined by using following

formula:

vp =V

(PHF × N × fHV × fp)(23.3)

where, vp is the 15-min passenger-car equivalent flow rate (pc/h/ln), V is the hourly volume

(veh/h), PHF is the peak-hour factor, N is the number of lanes, fHV is the heavy-vehicle

adjustment factor, and fp is the driver population factor. PHF represents the variation in

traffic flow within an hour. Observations of traffic flow consistently indicate that the flow rates

found in the peak 15-min period within an hour are not sustained throughout the entire hour.

The PHFs for multilane highways have been observed to be in the range of 0.75 to 0.95. Lower

values are typical of rural or off-peak conditions, whereas higher factors are typical of urban

and suburban peak-hour conditions. Where local data are not available, 0.88 is a reasonable

estimate of the PHF for rural multilane highways and 0.92 for suburban facilities. Besides that,

the presence of heavy vehicles in the traffic stream decreases the FFS because base conditions

allow a traffic stream of passenger cars only. Therefore, traffic volumes must be adjusted to

reflect an equivalent flow rate expressed in passenger cars per hour per lane (pc/h/ln). This

is accomplished by applying the heavy-vehicle factor (fHV ). Once values for ET and ER have



Table 23:7: Passenger-car equivalent on extended general highway segments(Source: HCM,

2000)

Factor Type of Terrain

Level Rolling Mountainous

ET (Trucks and Buses) 1.5 2.5 4.5

ER (RVs) 1.2 2.0 4.0

been determined, the adjustment factors for heavy vehicles are applied as follows:

fHV =1

(1 + PT (ET − 1) + PR(ER − 1)(23.4)

where, ET and ER are the equivalents for trucks and buses and for recreational vehicles (RVs),

respectively, PT and PR are the proportion of trucks and buses, and RVs, respectively, in the

traffic stream (expressed as a decimal fraction), fHV is the adjustment factor for heavy vehicles.

Adjustment for the presence of heavy vehicles in traffic stream applies for three types of vehicles:

trucks, buses and recreational vehicles (RVs). Trucks cover a wide range of vehicles, from lightly

loaded vans and panel trucks to the most heavily loaded coal, timber, and gravel haulers. An

individual truck’s operational characteristics vary based on the weight of its load and its engine

performance. RVs also include a broad range: campers, self-propelled and towed; motor homes;

and passenger cars or small trucks towing a variety of recreational equipment, such as boats,

snowmobiles, and motorcycle trailers. There is no evidence to indicate any distinct differences

between buses and trucks on multilane highways, and thus the total population is combined.

23.5.4 Determination of Level of Service

The level of service on a multilane highway can be determined directly from Fig. 23:12 or Table-

2 based on the free-flow speed (FFS) and the service flow rate (vp) in pc/h/ln. The procedure

as follows:

1. Define a segment on the highway as appropriate. The following conditions help to define

the segmenting of the highway,

• Change in median treatment

• Change in grade of 2% or more or a constant upgrade over 1220 m

• Change in the number of travel lanes



• The presence of a traffic signal

• A significant change in the density of access points

• Different speed limits

• The presence of bottleneck condition

In general, the minimum length of study section should be 760 m, and the limits should

be no closer than 0.4 km from a signalized intersection.

2. On the basis of the measured or estimated free-flow speed on a highway segment, an

appropriate speed-flow curve of the same as the typical curves is drawn.

3. Locate the point on the horizontal axis corresponding to the appropriate flow rate (vp)

in pc/hr/ln and draw a vertical line.

4. Read up the FFS curve identified in step 2 and determine the average travel speed at the

point of intersection.

5. Determine the level of service on the basis of density region in which this point is located.

Density of flow can be computed as

D =vp

S(23.5)

where, D is the density (pc/km/ln), vp is the flow rate (pc/h/ln), and S is the aver-

age passenger-car travel speed (km/h). The level of service can also be determined by

comparing the computed density with the density ranges shown in table given by HCM.

To use the procedures for a design, a forecast of future traffic volumes has to be made

and the general geometric and traffic control conditions, such as speed limits, must be

estimated. With these data and a threshold level of service, an estimate of the number

of lanes required for each direction of travel can be determined.

Numerical example 1

A segment of undivided four-lane highway on level terrain has field-measured FFS 74.0-km/h,

lane width 3.4-m, peak-hour volume 1,900-veh/h, 13 percent trucks and buses, 2 percent RVs,

and 0.90 PHF. What is the peak-hour LOS, speed, and density for the level terrain portion of

the highway?

Solution The solution steps are given below:



1. Data given: Level terrain, field measured FFS = 74 km/h, lane width is 3.4 m, peak-

hour volume = 1900 veh/h, percent trucks and buses pt = 0.13, percent RVs PR = 0.02,

and PHF=0.90.

2. Determination of flow rate(Vp): LOS can be calculated by knowing flow rate and

free flow speed. Flow rate (Vp) is calculated from the equation

V p =V

(PHF × N × fHV × fp)

Since fHV is unknown it is calculated from the equation

fHV =1

(1 + PT (ET − 1) + PR(ER − 1)

where, ET and ER are passenger-car equivalents for trucks and buses and for recreational

vehicles (RVs) respectively PT and PR are proportion of trucks and buses, and RVs,

respectively, in the traffic stream (expressed as a decimal fraction)

fHV =1

1 + 0.13(1.5 − 1) + 0.02(1.2 − 1)= 0.935.

Assume no RVs, since none is indicated.

V p =1900

(0.90 × 2 × 0.935 × 1)

= 1129 pc/h/ln.

3. Determination of free flow speed(S): In this example the free flow speed (FFS)

measured at the field is given and hence no need to compute free flow speed by indirect

method. Therefore, FFS = S = 74.0km/h.

4. Determination of density(D): The density of flow is computed from the equation

D = V p/S = 15.3

5. Determination of LOS: LOS determined from the speed-flow diagram. LOS = C.

Numerical example 2

A segment of an east-west five-lane highway with two travel lanes in each direction separated

by a two-way left-turn lane (TWLTL) on a level terrain has- 83.0-km/h 85th-percentile speed

,3.6-m lane width, 1,500-veh/h peak-hour volume, 6 % trucks and buses, 8 access points/km

(WB), 6 access points/km (EB), 0.90 PHF, 3.6-m and greater lateral clearance for westbound

and eastbound. What is the LOS of the highway on level terrain during the peak hour?



Solution The solution steps are enumeratd below:

1. Data given: Level terrain, 85th-percentile speed is 83.0 km/h , lane width is 3.6 m, peak-

hour volume, v=1500 veh/h percent of trucks and buses PT=0.06, 8 access points/km

in WB, 6 access points/km in EB, PHF = 0.90, and lateral clearance for westbound and

eastbound is more than 3.6 m.

2. Determination of flow rate(VP): LOS can be calculated by knowing flow rate and

free flow speed. Flow rate (Vp) is calculated from the equation

V p =V


where, Vp = 15-min passenger-car equivalent flow rate (pc/h/ln), V = hourly volume

(veh/h), PHF = peak-hour factor, N = number of lanes, fHV = heavy-vehicle adjustment

factor, and fp = driver population factor Since fHV is unknown it is calculated from the

equation

fHV =1

(1 + PT (ET − 1) + PR(ER − 1)

where, ET and ER = passenger-car equivalents for trucks and buses and for recreational

vehicles (RVs), respectively PT and PR = proportion of trucks and buses, and RVs,

respectively, in the traffic stream (expressed as a decimal fraction) Assume no RVs, since

none is indicated.

fHV =1

1 + 0.06(1.5 − 1) + 0= 0.970.

V p =1500

(0.90 × 2 × 0.970 × 1)

= 858 pc/h/lane

3. Determination of free flow speed(S): BFFS is approximately equal to 62.4 km/h

when the 85 th percentile speed is 64 km/h, and it is 91.2 km/h when the 85 th percentile

speed is 96 km/h and the in between speed values is found out by interpolation. Hence,

BFFS = 80 km/h. Now, compute east bound and west bound free-flow speeds

FFS = BFFS − fLW − fLC − fA − fM

= 80 − 0 − 0 − 4 − 0

= 76 kmph (WB)

= 80 − 0 − 0 − 5.3 − 0

= 74.7 kmph (EB)



4. Determination of LOS: LOS determined from the speed-flow diagram. LOS = C (for

EB) LOS = C (for WB)

Numerical example 3

A 10 km long 4 lane undivided multilane highway in a suburban area has a segment 1 km

long with a 3% upgrade and a segment 1 km long with a 3% downgrade. The section has a

volume of 1900 vehicles/hr in each direction with 13% trucks and buses and 2% recreational

vehicles. The 85 th percentile speed of passenger car is 80 km/hr on upgrade and 86km/hr on

downgrade. There are total of 12 access points on both sides of the roadway. The lane width

is 3.6 m, PHF is 0.90 and having a 3m lateral clearance. Determine the LOS of the highway

section (upgrade and downgrade) during the peak hour? From HCM, For a 3% upgrade and 1

km length( ET=1.5 , ER=3) For a 3% downgrade and 1 km length( ET=1.5 , ER=1.2 )

Solution

1. Data given: 3%upgrade and 3%downgrade No of lanes = 4, N = 4, 80.0 km/h 85th-

percentile speed for upgrade, 86 km/h 85t h-percentile speed for downgrade, 3.6-m lane

width, 1,900-veh/h peak-hour volume, (V =1900 veh/h) 13 % trucks and buses, (PT

=0.13) 2 % Recreational vehicles, ( Pr=0.02 ) 12 access points/km, PHF = 0.90 lateral

clearance = 3 m

2. Determination of flow rate(VP): LOS can be calculated by knowing flow rate and

free flow speed.

For upgrade: Flow rate is calculated from the equation

V p =V


where, Vp = 15-min passenger-car equivalent flow rate (pc/h/ln), V = hourly volume

(veh/h), PHF = peak-hour factor, N = number of lanes, fHV = heavy-vehicle adjustment

factor, and fp = driver population factor Since fHV is unknown it is calculated from the

equation

fHV =1

(1 + PT (ET − 1) + PR(ER − 1)

where, ET and ER = passenger-car equivalents for trucks and buses and for recreational

vehicles (RVs), respectively PT and PR = proportion of trucks and buses, and RVs,



respectively, in the traffic stream (expressed as a decimal fraction) Assume no RVs, since

none is indicated.

fHV =1

1 + 0.13(1.5 − 1) + 0.02(3 − 1)= 0.905.

V p =1900

(0.90 × 2 × 0.905 ∗ 1)

= 1166 pc/h/ln

For downgrade:

fHV =1

1 + 0.13(1.5 − 1) + 0.02(1.2 − 1)= 0.935

V p =1900

(0.90 × 2 × 0.935 × 1)

= 1128 pc/h/ln

3. Determination of free flow speed(S): For upgrade: BFFS is approximately equal

to 62.4 km/h when the 85 th percentile speed is 64 km/h, and it is 91.2 km/h when

the 85 th percentile speed is 96 km/h and the in between speed values is found out by

interpolation. Hence for 86 km/hr 85th percentile speed from interpolation we get, BFFS

= 77.0 km/h Now, Compute east bound and west bound free-flow speeds


= 77 − 0 − 0.6 − 8.0 − 2.6

= 65.8 km/h

For downgrade: BFFS is approximately equal to 62.4 km/h when the 85 th percentile

speed is 64 km/h, and it is 91.2 km/h when the 85 th percentile speed is 96 km/h and the

in between speed values is found out by interpolation. Hence for 86 km/hr 85th percentile

speed from interpolation we get, BFFS= 82.0 km/h Now, Compute the free-flow speed


= 82 − 0 − 0.6 − 8.0 − 2.6

= 71 km/h

4. Determination of LOS LOS determined from the speed-flow diagram. LOS = D (for

upgrade) LOS = D (for downgrade)



23.6 Conclusion

This chapter helps to determine the level of service and capacity for a given road segment. In

the first part we studied highways in general there classification and characteristics which gives

the overall idea of multilane highways. Then we studied determination of capacity for multilane

highway which is again a very important parameter used to determine the level of service, then

we studied the concept of level of service and procedure to determine level of service. Also by

using its applications, number of lanes required (N), and flow rate achievable (vp), Performance

measures related to density (D) and speed (S) can also be determined.

23.7 References

1. R Asworth. Highway Engineering. Heinemann Education books limited, London, 1966.

2. Nicholas J Garber and Lester A Hoel. Traffic and Highway Engineering. Cengage

Learning, 2009.



4. R W McShane and R P Roess. Highway Engineering. McGraw Hill Company, 1984.

5. P Y TSENG and F B LIN. Journal of the eastern asia society for transportation studies,

2005.

6. B K Woods. Highway Engineering Handbook. McGraw Hill Company. 1960.

7. H R Wright. Highway Engineering. Library Of Congress Catlaloging-in-Publication

Data, 1996.


Transportation Systems Engineering 24. Freeway Operations

Chapter 24

Freeway Operations

24.1 Introduction

A freeway is defined as a divided highway with full control of access and two lanes for the

exclusive use of traffic in each direction. Freeways were originally intended to serve longer trips

of generally regional and interurban character. Traffic on freeways differs from that on city

streets and rural roads in that it moves at higher speeds (depending on traffic conditions, design

standards, etc.), more smoothly, and at much larger rates of flow. Speed limits are generally

higher on freeways, and are occasionally non-existent. Because higher speeds reduce decision

time, freeways are usually equipped with a larger number of guide signs than other roads, and

the signs themselves are physically larger. Guide signs are often mounted on overpasses or

overhead gantries so that drivers can see where each lane goes. Access to freeways is typically

provided only at grade-separated interchanges, though lower-standard right-in/right-out access

can be used for direct connections to side roads. This chapter basically describes the capacity

and level of service. Later weaving phenomenon in has been described.

24.2 Basic features of freeway

Freeway provides uninterrupted traffic flow on a freeway. Traffic on freeway is free-flowing. All

cross-traffic (and left-turning traffic) is relegated to overpasses or underpasses, so that there are

no traffic conflicts on the main line of the highway which must be regulated by traffic lights,

stop signs, or other traffic control devices. Spefic features are:

1. There are no signalized or stop-controlled at-grade intersections.

2. Direct access to and from adjacent property is not permitted.

3. Acess to and from the freeway is limited to ramp locations.



Not to scale

Basic Freeway Segment Basic Freeway Segment

Figure 24:1: Basic freeway segment

4. Opposing directions of flow are continuously separated by a raised barrier, an at-grade

median, or a continuous raised median.

5. The advantage of grade-separated interchanges is that freeway drivers can almost always

maintain their speed at junctions since they do not need to yield to vehicles crossing

perpendicular to mainline traffic.

A freeway is composed of following three components

1. Basic freeway segment

2. Ramp junction

3. Weaving areas

24.2.1 Basic freeway segment

Basic freeway are that part of segment of freeway which are outside of the influence area of

ramps or weaving areas of freeway. We can see in Fig.24:1 that a basic freeway segment is

independent of the ramps and weaving areas and the flow in such section occurs smoothly at

the much larger rates. Merging and diverging of traffic occurs where on-or-off ramps join the

basic freeway segment. Weaving occurs when vehicles cross each other’s path while travelling

on freeway lanes. The exact point at which basic freeway segment begins or ends- that is, where

the influence of weaving areas and ramp junctions has dissipated- depends on local conditions,

particularly the level of service operating at the time. If traffic flow is light, the influence may

be negligible, whereas under congested conditions, queues may be extensive.



Base condition of basic freeway segment

The base conditions under which the full capacity of a basic freeway segment is achieved are

good weather, good visibility, and no incidents or accidents. For the analysis procedures in this

chapter, these base conditions are assumed to exist. A set of base conditions for basic freeway

segments has been established. These conditions serve as a starting point for the

1. Lane widths of 3.6 m,

2. Clearance of 1.8 m between the edge of the travel lanes and the nearest obstructions or

objects at the roadside and in the median,

3. Free-flow speed of 120 km/h for freeways,

4. Only passenger cars in the traffic stream (no heavy vehicles),

5. Level terrain,

6. No no-passing zones on two-lane highways, and

7. No impediments to through traffic due to traffic control or turning vehicles.

Base conditions for intersection approaches include the following:

1. Lane widths of 3.6 m,

2. Level grade,

3. No curb parking on the approaches,

4. Only passenger cars in the traffic stream,

5. No local transit buses stopping in the travel lanes,

6. Intersection located in a noncentral business district area, and

7. No pedestrians

24.3 Capacity of a freeway segment

Freeway capacity is defined as:



the maximum sustained 15-min flow rate, expressed in passenger cars per hour per

lane, that can be accommodated by a uniform freeway segment under prevailing

traffic and roadway conditions in one direction of flow.

Capacity analysis is based on freeway segments with uniform traffic and roadway conditions.

If any of the prevailing conditions change significantly, the capacity of the segment and its

operating conditions change as well. Therefore, each uniform segment should be analysed

separately.

24.3.1 Factors affecting Capacity

Roadway conditions

Roadway conditions include geometric and other elements. In some cases, these influence the

capacity of a road; in others, they can affect a performance measure such as speed, but not the

capacity or maximum flow rate of the facility. Roadway factors include the following:

1. Number of lanes, Number of lanes decided for basic freeway is five or more than five but

if number of lanes is less than five then capacity of freeway is reduced.

2. Lane widths, If the lanewidth is less than the specified lane width for basic freeway

segment, i.e 3.6m then capacity is reduced because traffic flow tends to be restricted.

3. Shoulder widths and lateral clearances, shoulder width and lateral clearance influences

the capacity of freeway. When lane widths are less than 3.65 m, drivers are forced

to travel closer to one anotherlaterally than they would normally desire. Drivers tend

to compensate for this by reducing their travel speed. The effect of restricted lateral

clearance is similar. When objects are located too close to the edge of the median and

roadside lanes, drivers in these lanes will shy away from them, positioning themselves

further from the lane edge hence capacity is reduced.

4. Design speed, freeway is designed for free flow speed around 120 km per hour ,if some

vehicle is moving less than the design speed then capacity of freeway.

5. Grades: Effect of grade depends on both the length and slope of the grade.Traffic opera-

tions significantly affected when grades of 3% or more are longer than one quarter miles

and when grades are less than 3% and longer than mile.The effect of heavy vehicles on

such grades is much greater.



Traffic conditions

Traffic conditions that influence capacities and service levels include vehicle type and lane or

directional distribution.

Vehicle type The entry of heavy vehicles - that is, vehicles other than passenger cars (a

category that includes small trucks and vans) - into the traffic stream affects the number of

vehicles that can be served. Heavy vehicles are vehicles that have more than four tires touching

the pavement. Trucks, buses, and recreational vehicles (RVs) are the three groups of heavy

vehicles.

1. They are larger than passenger cars and occupy more roadway space; and

2. They have poorer operating capabilities than passenger cars, particularly with respect to

acceleration, deceleration, and the ability to maintain speed on upgrades.

Directional and Lane Distribution In addition to the distribution of vehicle types, two

other traffic characteristics affect capacity and level of service: directional distribution and lane

distribution. Each direction of the facility usually is designed to accommodate the peak flow

rate in the peak direction. Typically, morning peak traffic occurs in one direction and evening

peak traffic occurs in the opposite direction. Lane distribution also is a factor on multilane

facilities. Typically, the shoulder lane carries less traffic than other lanes.

Control conditions

For interrupted-flow facilities, the control of the time for movement of specific traffic flows

is critical to capacity and level of service. The most critical type of control is the traffic

signal. The type of control in use, signal phasing, allocation of green time, cycle length,

and the relationship with adjacent control measures affect operations. Stop signs and yield

signs also affect capacity, but in a less deterministic way. A Impact of control conditions

traffic signal designates times when each movement is permitted; however, a stop sign at a

two-way stop-controlled intersection only designates the right-of-way to the major street. The

capacity of minor approaches depends on traffic conditions on the major street. An all-way stop

control forces drivers to stop and enter the intersection in rotation. Capacity and operational

characteristics can vary widely, depending on the traffic demands on the various approaches.



24.4 Level of service (LOS) of a basic freeway segment

Level of service is defined as:

qualitatively measures both the operating conditions within a traffic system and

how these conditions are perceived by drivers and passengers.

These operational conditions within a traffic stream are generally described in terms of service

measures as speed and travel time, freedom to manoeuver, traffic interruptions, and comfort

and convenience. The three measures of speed, density and flow are interrelated. If values

of two are known, the third can be computed. Six LOS are defined for each type of facility

that has analysis procedures available. Letters designate each level, from A to F, with LOS A

representing the best operating conditions and LOS F the worst. Each level of service represents

a range of operating conditions and the driver’s perception of those conditions. Safety is not

included in the measures that establish service levels.

1. LOS A describes free-flow operations. Free-flow speeds prevail. Vehicles are almost

completely unimpeded in their ability to manoeuver within the traffic stream. The effects

of incidents or point breakdowns are easily absorbed at this level.

2. LOS B represents reasonably free flow, and free-flow speeds are maintained. The ability

to manoeuver within the traffic stream is only slightly restricted, and the general level of

physical and psychological comfort provided to drivers is still high. The effects of minor

incidents and point breakdowns are still easily absorbed.

3. LOS C provides for flow with speeds at or near the FFS of the freeway. Freedom to

manoeuver within the traffic stream is noticeably restricted, and lane changes require

more care and vigilance on the part of the driver. Minor incidents may still be absorbed,

but the local deterioration in service will be substantial. Queues may be expected to form

behind any significant blockage.

4. LOS D is the level at which speeds begin to decline slightly with increasing flows and

density begins to increase somewhat more quickly. Freedom to manoeuver within the

traffic stream is more noticeably limited, and the driver experiences reduced physical and

psychological comfort levels. Even minor incidents can be expected to create queuing,

because the traffic stream has little space to absorb disruptions.

5. LOS E describes operation at capacity. Operations at this level are volatile, because there

are virtually no usable gaps in the traffic stream. Vehicles are closely spaced leaving



Figure 24:2: LOS A

little room to manoeuver within the traffic stream at speeds that still exceed 80 km/h.

Any disruption of the traffic stream, such as vehicles entering from a ramp or a vehicle

changing lanes, can establish a disruption wave that propagates throughout the upstream

traffic flow. At capacity, the traffic stream has no ability to dissipate even the most

minor disruption, and any incident can be expected to produce a serious breakdown with

extensive queuing. Manoeuverability within the traffic stream is extremely limited, and

the level of physical and psychological comfort afforded the driver is poor.

6. LOS F describes breakdowns in vehicular flow. Such conditions generally exist within

queues forming behind breakdown points. Breakdowns occur for a number of reasons:

(a) Traffic incidents can cause a temporary reduction in the capacity of a short segment,

so that the number of vehicles arriving at the point is greater than the number of

vehicles that can move through it.

(b) Points of recurring congestion, such as merge or weaving segments and lane drops,

experience very high demand in which the number of vehicles arriving is greater than

the number of vehicles discharged.

In all cases, breakdown occurs when the ratio of existing demand to actual capacity

forecast demand to estimated capacity exceeds 1.00. The figures 24:2-24:7 given below

gives a better idea of the LOS classification done on the basis of density of the traffic

stream.

24.5 Determination of LOS

A basic freeway segment can be characterized by three performance measures: density in terms

of passenger cars per kilometre per lane, speed in terms of mean passenger-car speed, and

volume-to-capacity (v/c) ratio. Each of these measures is an indication of how well traffic flow

is being accommodated by the freeway. The measure used to provide an estimate of level of



Figure 24:3: LOS B

Figure 24:4: LOS C

Figure 24:5: LOS D

Figure 24:6: LOS E

Figure 24:7: LOS F



service is density. The three measures of speed, density, and flow or volume are interrelated. If

values for two of these measures are known, the third can be computed.

24.5.1 Methodology

Level of service of an existing freeway is determined considering it as a stretch of basic freeway

segment. It means that we have to take all the base conditions decided for basic freeway

segment as a standard or intial input. The following steps are followed to determine the level

of service of a freeway.

1. The very first step of methodology is to collect all the input data like geometric data,

measured FFS or BFFS, volume.

2. volume adjustment: The hourly volume is converted into flow rate of passenger cars i.e

pc/hr/ln.

3. Computation of FFS: If BFFS is the input, then for getting the value of FFS ,we have

to adjust the BFFS for the lane width,number of lanes,interchange density and lateral

clearance.

4. computation of S(average passenger car speed): S is calculated from the FFS. If FFS is

measured directly in field, then FFS can be taken as S.

5. Speed-flow curve is designed and speed is determined using this curve.

6. Density is determined from the flow rate and speed taken from the speed-flow curve.

7. Based on the density, the corresponding level of service(LOS) can be determined .

The steps involved in calculation of LOS are-

1. Calculation of flow rate (Vp)

2. Calculation of average passenger car (S)

3. Calculation of density (D) and determining LOS



24.5.2 Calculating Flow rate (Vp)

The hourly flow rate must reflect the influence of heavy vehicles, the temporal variation of traffic

flow over an hour, and the characteristics of the driver population. These effects are reflected

by adjusting hourly volumes or estimates, typically reported in vehicles per hour (veh/h), to

arrive at an equivalent passenger-car flow rate in passenger cars per hour (pc/h). The equivalent

passenger-car flow rate is calculated using the heavy-vehicle and peak-hour adjustment factors

and is reported on a per lane basis (pc/h/ln). The flow rate can be given as-

Vp =V

PHF × N × fHV × fP

(24.1)

where, V = hourly volume, PHF = peak hour factor (0.80-0.95), N = no. of lanes, fHV =

heavy vehicle adjustment factor, fP = driver population factor

Peak hour factor (PHF) The peak-hour factor (PHF) represents the variation in traffic

flow within an hour. Observations of traffic flow consistently indicate that the flow rates found

in the peak 15-min period within an hour are not sustained throughout the entire hour.

PHF =V

V15×4

(24.2)

Where, V = hourly volume in veh/hr for hour of analysis, V15 = Maximum 15-min flow rate

within peak hour, 4 = number of 15-min period per hour.

On freeways, typical PHFs range from 0.80 to 0.95. Lower PHFs are characteristic of rural

freeways or off-peak conditions. Higher factors are typical of urban and suburban peak-hour

conditions. Field data should be used, if possible, to develop PHFs representative of local

conditions.

Heavy vehicle adjustment factor (fHV ) Freeway traffic volumes that include a mix of

vehicle types must be adjusted to an equivalent flow rate expressed in passenger cars per hour

per lane. This adjustment is made using the factor fHV . Once the values of ET and ER are

found, the adjustment factor, fHV , is determined by using equation given below -

fHV = 11 + PT (ET − 1) + PR(ER − 1) (24.3)

where, ET , ER = passenger car equivalents for truck buses and recreational vehicles (RV’s)

in traffic stream respectively, PT , PR = proportion of truck/buses and recreational vehicles in

traffic stream. Adjustments for heavy vehicles in the traffic stream apply for three vehicle types:

trucks, buses, and RVs. There is no evidence to indicate distinct differences in performance



between trucks and buses on freeways, and therefore trucks and buses are treated identically.

The factor fHV is found using a two-step process. First, the passenger-car equivalent for

each truck/bus and RV is found for the traffic and roadway conditions under study. These

equivalency values, ET and ER, represent the number of passenger cars that would use the same

amount of freeway capacity as one truck/bus or RV, respectively, under prevailing roadway and

traffic conditions. Second, using the values of ET and ER and the proportion of each type of

vehicle in the traffic stream (PT and PR), the adjustment factor fHV is computed.

Driver population factor: Under base conditions, the traffic stream is assumed to consist of

regular weekday drivers and commuters.Such drivers have a high familiarity with the roadway

and generally manoeuver and respond to the maneuvers of other drivers in a safe and predictable

fashion. But weekend drivers or recreational drivers are a problem. Such drivers can cause a

significant reduction in roadway capacity relative to the base condition of having only familiar

drivers. To account for the composition of the driver population, the fp adjustment factor is

used and its recommended range is 0.85 1.00.

24.5.3 Calculating average passenger car speed (S)

The average passenger car speed depends on the free flow speed (FFS) and flow rate as calcu-

lated earlier and can be given as - For, 90 ≤ FFS ≤ 120 and Vp ≤ (3100 − 15FFS),

S = FFS (24.4)

For, 90 ≤ FFS ≤ 120 and (3100 − 15FFS) ≤ vP ≤ (1800 + 5FFS)

S = FFS −

[

1/28(23FFS − 1800

(

Vp + 15FFS − 3100

20FFS − 1300

)

26

]

(24.5)

The average of all passenger-car speeds measured in the field under low- to moderate- volume

conditions can be used directly as the FFS of the freeway segment.

Concept of free flow speed (FFS) Free flow speed can be defined as:

the mean speed of passenger cars that can be accommodated under low to moder-

ate flow rates on a uniform freeway segment under prevailing roadway and traffic

conditions.

FFS is the mean speed of passenger cars measured during low to moderate flows (up to

1,300 pc/h/ln). For a specific segment of freeway, speeds are virtually constant in this range of



Table 24:1: Adjustment for Lane Width (reduction in free-flow speed for various widths of lane

Lane Width (m) fLW (km/h)

3.6 0.0

3.5 1.0

3.4 2.1

3.3 3.1

3.2 5.6

3.1 8.1

3.0 10.6

flow rates. Two methods can be used to determine the FFS of a basic freeway segment: field

measurement and estimation with guidelines provided in this section. The field-measurement

procedure is provided for users who prefer to gather these data directly. If field measurement of

FFS is not possible, FFS can be estimated indirectly on the measurement is not possible basis of

the physical characteristics of the freeway segment being studied. The physical characteristics

include lane width, number of lanes, right-shoulder lateral clearance, and interchange density.

Equation given below is used to estimate the free-flow speed of a basic freeway segment:

FFS = BFFS − fLW − fLC − fN − fID (24.6)

where, FFS = free flow speed (km/h), BFFS = base free flow speed (km/h), fLW = adjustment

for lane width (km/h), fLC = adjustment for right shoulder clearance (km/h),fN = adjustment

for no. of lanes (km/h), fID = adjustment for interchange density (km/h) Estimation of FFS

for an existing or future freeway segment is accomplished adjusting a base free-flow speed

downward to reflect the influence of four factors: lane width, lateral clearance, number of

lanes, and interchange density. Thus, the analyst is required to select an appropriate BFFS as

a starting point.

Adjustment for Lane Width The base condition for lane width is 3.6 m or greater. When

the average lane width across all lanes is less than 3.6 m, the base free-flow speed (e.g., 120

km/h) is reduced. Adjustments to reflect the effect of narrower average lane width are given

in Table 24:1.

Adjustment for Lateral Clearance Base lateral clearance is 1.8 m or greater on the right

side and 0.6 m or greater on the median or left side, measured from the edge of the paved

shoulder to the nearest edge of the travelled lane. When the right-shoulder lateral clearance



Table 24:2: Adjustment for Lateral Clearance (reduction in free-flow speed for various values

of lateral clearence)

Right Shoulder fLC (km/h)

Lateral Lanes in One Direction

Clearance (m) 2 3 4 ≥5

≥1.8 0.0 0.0 0.0 0.0

1.5 1.0 0.7 0.3 0.2

1.2 1.9 1.3 0.7 0.4

0.9 2.9 1.9 1.0 0.6

0.6 3.9 2.6 1.3 0.8

0.3 4.8 3.2 1.6 1.1

0.0 5.8 3.9 1.9 1.3

Table 24:3: Adjustment for number of lanes (reduction in free-flow speed for number of lanes

in one direction)

Number of Lanes fN (km/h)

≥ 5 0.0

4 2.4

3 4.8

2 7.3

is less than 1.8 m, the BFFS is reduced. Adjustments to reflect the effect of narrower right-

shoulder lateral clearance are given in Table 24:2.

Adjustment for Number of Lanes Freeway segments with five or more lanes (in one

direction) are considered as having base conditions with respect to number of lanes. When

fewer lanes are present, the BFFS is reduced. Table 24:3 provides adjustments to reflect the

effect of number of lanes on BFFS. In determining number of lanes, only mainline lanes, both

basic and auxiliary, should be considered.

Adjustment for Interchange Density The base interchange density is 0.3 interchanges

per kilometer, or 3.3-km interchange spacing. Base free-flow speed is reduced when interchange

density becomes greater. Adjustments to reflect the effect of interchange density are provided in

Table 24:4. Interchange density is determined over a 10-km segment of freeway (5 km upstream



Table 24:4: Adjustment for Interchange Density (Reduction in Free-Flow Speed for various

values of interchange density)

Interchanges per km fID (km/h)

≤ 0.3 0.0

0.4 1.1

0.5 2.1

0.6 3.9

0.7 5.0

0.8 6.0

0.9 8.1

1.0 9.2

1.1 10.2

1.2 12.1

and 5 km downstream) in which the freeway segment is located. An interchange is defined as

having at least one on-ramp. Therefore, interchanges that have only off-ramps would not be

considered in determining interchange density. Interchanges considered should include typical

interchanges with arterials or highways and major freeway-to-freeway interchanges.

24.5.4 Calculation of Density and determining LOS

Level of service on the basis of density can be calculated using the equation 24.7

D =Vp

S(24.7)

Where, D = density (pc/km/ln), Vp= flow rate (pc/h/ln), S = average passenger car speed

(km/h). The density of the traffic stream can be used to determine the level of service of a

freeway segment. Level-of-service thresholds based on density for a basic freeway segment are

summarized in the Table 24:5 shown below.

Numerical example 1

Consider an existing four lane freeway in rural area, having very restricted geometry with

rolling terrain. Peak hour volume is 2000 veh/h with 5% trucks. The traffic is commuter type

with peak hour factor 0.92 and interchange density as 0.6 interchanges per kilometer. Freeway

consists of two lanes in each direction of 3.3 m width with lateral clearance of 0.6 m. Find the

LOS of freeway during peak hour.



Table 24:5: LOS for a freeway segment

LOS Density Range (pc/km/ln)

A 0 - 7

B >7 - 11

C >11 - 16

D >16 - 22

E >22 - 28

F >28

Solution Assumptions: Assume 0 percent buses and RVs since none are indicated. Assume

BFFS of 120 km/h for rural areas. Since the freeway is in a rural area assume that the number

of lanes does not affect free-flow speed. Assume fp = 1.00 for commuter traffic. We can get the

corresponding values of adjustment factors from the tables as - fLW =3.1, fLC=3.9, fID=3.9

and fN=0.

Step 1 Find fHV using equation 24.3 as given below -

fHV =1

1 + PT (ET − 1) + PR(ER − 1)

=1

1 + 0.05(2.5 − 1) + 0= 0.930

Step 2 Convert volume (veh/h) to flow rate (pc/h/ln) using equation as given below

Vp =V


=2000

0.92 × 2 × 0.930 × 1.00= 1, 169 pc/h/ln

Step 3 Compute free-flow speed from equation 24.6 as given below and putting the respective

values of adjustment factors we get FFS as

FFS = BFFS − fLW − fLC − fN − fID

= 120 − 3.1 − 3.9 − 0.0 − 3.9

= 109.1 kmph.



Step 4 Determine the density using the equation 24.7 as -

D =Vp

S

Since, 90 ≤ FFS ≤ 120 and Vp ≤ (3100−15FFS) we can take S = FFS (from equation 24.4).

Keeping values of Vp and S we can get the value of density as -

D =1169

109.1= 10.7 pc/km/ln

Step 5 Find Level of service, for the calculated value of density we can get the level of service

from the LOS table. i.e for D = 10.7 pc/km/ln we get LOS = B

Numerical example 2

A new suburban freeway is designed in the level terrain. Peak hour volume is 4,000 veh/h and

the flow consists of 15% trucks and 3% recreational vehicles (RV’s). The traffic is commuter

type with peak hour factor 0.85 and interchange density as 0.9 interchanges per kilometer. Lane

width is proposed to be 3.6 m with lateral clearance of 1.8 m. How many lanes are needed to

provide LOS C during the peak hour?

Solution Assumptions: Assume BFFS of 120 km/h. Since the freeway is being designed in

a suburban area assume that the number of lanes affects free-flow speed. For commuter traffic

we can take fp = 1.00. We can get the corresponding values of adjustment factors from the

tables as - fLW = 0, fLC = 0, fID = 8.1 and fN = 4.8.

Step 1 Find fHV using equation 24.3 as given below:

fHV =1

1 + PT (ET − 1) + PR(ER − 1)

=1

1 + 0.15(1.5 − 1) + 0.03(1.2 − 1)= 0.925

Step 2 Convert volume (veh/h) to flow rate (pc/h/ln) using equation 24.2. Consider a four

lane option, for four lane N = 2, keeping value of fHV and N in equation 24.2 we get Vp as:

Vp =V


=4000

0.85 × 2 × 0.925 × 1.00= 2, 544 pc/h/ln.



Four lane option is not acceptable as 2544 pc/h/ln exceeds capacity of 2400 pc/h/ln. Here

2400 pc/h/ln is the capacity of a single lane under standard conditions.

Step 4 Consider a six lane option

Vp =4000

(.85 × 3 × 0.925 × 1.00

= 1, 696 pc/h/ln.

Step 5 Compute FFS for a six-lane freeway from equation 24.6 and putting the respective

values of adjustment factors we get FFS as:

FFS = BFFS − fLW − fLC − fN − fID

= 120 − 0 − 0 − 4.8 − 8.1

= 107.1. km/h.

Step 6 Determine density from equation 24.7

D =Vp

S

Since, 90 ≤ FFS ≤ 120 and v−p ≤ (3100−15FFS) we can take S = FFS (from equation 24.4)

Putting values of Vp and S we get density as

D =1696

107.1= 15.8 pc/km/ln

Step 7 Check the LOS, for the calculated value of density we can get the level of service

from the LOS table; i.e for D = 15.8 pc/km/ln we get LOS = C. Hence number of lanes to be

provided to satisfy LOS C during peak hour = 6.

24.6 Weaving in freeways

Weaving is defined as the crossing of two or more traffic streams travelling in the same general

direction along a significant length of highway without the aid of traffic control devices (with the

exception of guide signs). Weaving segments are formed when a merge area is closely followed

by a diverge area, or when an on-ramp is closely followed by an off-ramp and the two are joined

by an auxiliary lane.

Weaving segments require intense lane-changing manoeuvers as drivers must access lanes

appropriate to their desired exit points. Thus, traffic in a weaving segment is subject to



D

A

B

C

Figure 24:8: Simple weaving segment

turbulence in excess of that normally present on basic freeway segments. The turbulence

presents special operational problems and design requirements. Fig. 24:8 shows the simple

weaving segment formed by a single merge point followed by a single diverge point. Multiple

weaving segments may be formed where one merge is followed by two diverge points or where

two merge points are followed by one diverge point.

24.6.1 Weaving configurations

The most critical aspect of operations within a weaving segment is lane changing. Weaving

vehicles, which must cross a roadway to enter on the right and leave on the left, or vice versa,

accomplish these manoeuvers by making the appropriate lane changes. The configuration of the

weaving segment (i.e., the relative placement of entry and exit lanes) has a major effect on the

number of lane changes required of weaving vehicles to successfully complete their manoeuver.

There is also a distinction between lane changes that must be made to weave successfully and

additional lane changes that are discretionary (i.e., are not necessary to complete the weaving

manoeuver). The former must take place within the confined length of the weaving segment,

whereas the latter are not restricted to the weaving segment itself. There are three major

categories of weaving configurations: Type A, Type B, and Type C.

Type A weaving configuration

The identifying characteristic of a Type A weaving segment is that all weaving vehicles must

make one lane change to complete their manoeuver successfully. All of these lane changes occur

across a lane line that connects from the entrance gore area directly to the exit gore area. Such

a line is referred to as a crown line. Type A weaving segments are the only such segments to

have a crown line.

The most common form of Type A weaving segment is shown in Fig. 24:9. The segment is

formed by a one-lane on-ramp followed by a one-lane off-ramp, with the two connected by a

continuous auxiliary lane. The lane line between the auxiliary lane and the right-hand freeway

lane is the crown line for the weaving segment. All on-ramp vehicles entering the freeway must



B

C

D

A

Figure 24:9: Ramp Weave

C

DB

A

Figure 24:10: Major Weave

make a lane change from the auxiliary lane to the shoulder lane of the freeway. All freeway

vehicles exiting at the off-ramp must make a lane change from the shoulder lane of the freeway

to the auxiliary lane. This type of configuration is also referred to as a ramp-weave. Fig. 24:10

illustrates a major weaving segment that also has a crown line. A major weaving segment is

formed when three or four of the entry and exit legs have multiple lanes. As in the case of a

ramp-weave, all weaving vehicles, regardless of the direction of the weave, must execute one

lane change across the crown line of the segment.

Type B weaving configuration

Type B weaving segments are shown in Figs. 24:11 to 24:13. All Type B weaving segments

fall into the general category of major weaving segments in that such segments always have

at least three entry and exit legs with multiple lanes (except for some collector distributor

configurations). It is the lane changing required of weaving vehicles that characterizes for the

Type B configuration:

1. One weaving movement can be made without making any lane changes, and

2. The other weaving movement requires at most one lane change.

Figs. 24:11 to 24:13 show two Type B weaving segments. In both cases, Lane balance defined

Movement B-C (entry on the right, departure on the left) may be made without executing any

lane changes, whereas Movement A-D (entry on the left, departure on the right) requires only

one lane change. Essentially, there is a continuous lane that allows for entry on the right and

departure on the left.



A

C

DB

Figure 24:11: Major Weave with Lane Balance at Exit Gore

A

B

C

D

Figure 24:12: Major Weave with Merge at Entry Gore

In Fig. 24:11 this is accomplished by providing a diverging lane at the exit gore. From this

lane, a vehicle may proceed down either exit leg without executing a lane change. This type

of design is also referred to as lane balanced, that is, the number of lanes leaving the diverge

is one more than the number of lanes approaching it. In Fig. 24:12 the same lane-changing

scenario is provided by having a lane from Leg A merge with a lane from Leg B at the entrance

gore. This is slightly less efficient than providing lane balance at the exit gore but produces

similar numbers of lane changes by weaving vehicles. The configuration shown in Fig. 24:13

is unique, havingboth a merge of two lanes at the entrance gore and lane balance at the exit

gore. In this case, both weaving movements can take place without making a lane change. Such

configurations are most often found on collector-distributor roadways as part of an interchange.

B

A C

D

Figure 24:13: Major Weave with Merge at Entry Gore and Lane Balance at Exit Gore



A

B

C

D

Figure 24:14: Major Weave without Lane Balance or Merging

A

B

D

Figure 24:15: Two-Sided Weave

Type C weaving configuration

Type C weaving segments are similar to those of Type B in that one or more through lanes

are provided for one of the weaving movements. The distinguishing characteristic of a Type C

weaving segment is that the other weaving movement requires a minimum of two lane changes

for successful completion of a weaving maneuver. Thus, a Type C weaving segment is charac-

terized by the following:

1. One weaving movement may be made without making a lane change, and

2. The other weaving movement requires two or more lane changes.

Figs. 24:14 to 24:15 shows two types of Type C weaving segments. In Fig. 24:14 Movement

B-C does not require a lane change, whereas Movement A-D requires two lane changes. This

type of segment is formed when there is neither merging of lanes at the entrance gore nor lane

balance at the exit gore, and no crown line exists. Although such a segment is relatively efficient

for weaving movements in the direction of the freeway flow, it cannot efficiently handle large

weaving flows in the other direction.

Fig. 24:15 shows a two-sided weaving segment. It is formed when a right-hand on-ramp is

followed by a left-hand off-ramp, or vice versa. In such cases, the through freeway flow operates

functionally as a weaving flow. Ramp-to-ramp vehicles must cross all lanes of the freeway to

execute their desired manoeuver. Freeway lanes are, in effect, through weaving lanes, and

ramp-to-ramp vehicles must make multiple lane changes as they cross from one side of the

freeway to the other.



24.6.2 Effect of weaving configuration

The configuration of the weaving segment has a marked effect on operations because of its in-

fluence on lane-changing behavior. A weaving segment with 1,000 veh/h weaving across 1,000

veh/h in the other direction requires at least 2,000 lane changes per hour in a Type A segment,

since each vehicle makes one lane change. In a Type B segment, only one movement must

change lanes, reducing the number of required lane changes per hour to 1,000. In a Type C

segment, one weaving flow would not have to change lanes, while the other would have to make

at least two lane changes, for a total of 2,000 lane changes per hour.

Configuration has a further effect on the proportional use of lanes by weaving and lanes non-

weaving vehicles. Since weaving vehicles must occupy specific lanes to efficiently complete their

manoeuvers, the configuration can limit the ability of weaving vehicles to use outer lanes of

the segment. This effect is most pronounced for Type A segments, because weaving vehicles

must primarily occupy the two lanes adjacent to the crown line. It is least severe for Type

B segments, since these segments require the fewest lane changes for weaving vehicles, thus

allowing more flexibility in lane use.

24.7 Conclusion

Freeways are most efficient type of highway. Level of service (LOS) is a quality measure

describing operational conditions within a traffic stream of freeways. Prevailing roadway, traffic

and control conditions define capacity; these conditions should be reasonably uniform for any

section of freeway analysed. Freeway management system works for smooth operations of

freeway.

24.8 References

1. Traffic operations, traffic signal systems and freeway operations, 1995.

2. Freeway operations, 2019. Highway Research Board, bulletin 324; 1962 ; pageno. 46-73.




5. C S Papacostas. Transportation engineering and planning by Papacostas. C. S, 3rd

edition, Prentice-Hall of India in 2001. Prentice-Hall of India, 2001.



6. Roess P Roger and Jose M Ulerio. Level of Service Analysis of Freeway Weaving Segments.

Transportation Research Record:2130, 2009.

7. S Wolfgang, Homburger, and James H Kell. Fundamentals of Traffic Engineering 12th

Edition. San Francisco, 1997.


Transportation Systems Engineering 25. Ramp Metering

Chapter 25

Ramp Metering

25.1 Introduction

Ramp metering can be defined as a method by which traffic seeking to gain access to a busy

highway is controlled at the access point via traffic signals. This control aims at maximize the

capacity of the highway and prevent traffic flow breakdown and the onset of congestion. Ramp

metering is the use of traffic signals to control the flow of traffic entering a freeway facility.

Ramp metering, when properly applied, is a valuable tool for efficient traffic management on

freeways and freeway networks.

25.1.1 Objectives

The objectives of ramp metering includes:

1. Controling the number of vehicles that are allowed to enter the freeway,

2. Reducing freeway demand, and

3. Breaking up of the platoon of vehicles released from an upstream traffic signal.

Figure 25:1 given below is a typical example of ramp metering. The signal placed at the ramp,

controls the traffic flow which can enter the freeway through merge lane. Vehicle detectors are

also shown at the downstream end of the freeway.

25.1.2 Benefits

Ramp metering has many positive benefits in freeway management with in measurable param-

eters such as reduced delay, reduced travel time, reduced accident risk and increased operating

speed. The typical advantages are:



Direction of travel

Traffic signalon mergeramp

Merge laneVehicle detectors monitoringtraffic density through lane occupancy

Figure 25:1: Schematic diagram of ramp metering

1. Improved System Operation: Ramp metering essentially aims to control the access to a

freeway to reduce congestion, freewaydelay and ultimately overalldelay. Although sev-

eral ramp metering strategies are available with individual pros and cons, overall, ramp

metering helps to break up plantoons of vehicles from entering a freeway and causing

turbulence, reduces delay due to random access and defers if not eliminates the onset of

congestion.

2. Improved Safety: Ramp areas are accident prone areas due to unmanaged merging and

diverging. Ramp metering makes merging and diverging operation to a freeway smooth

and controlled, reducing the risk of accidents arising out of sudden driver decisions. Ran-

dom entry of platoons is also prevented which decreases the risk of accidents at merge or

diverge areas.

3. Reduced vehicle operating expense and emission: Ramp metering essentially reduces the

number of stops and delays for the freeway as well as the ramps. This in turn reduces

the fuel consumption and emission for a vehicle.

25.2 Metering strategies

Metering strategies can be defined as the approach used to control the traffic the flow on the

ramps. Three Ramp metering strategies are available to control the flow on the ramps which

can enter the busy freeway. Capacity of an uncontrolled single-lane freeway entrance ramp

is 1800 to 2200 vehicles per hour (VPH). Since Ramp metering is a traffic flow controlling

approach it decreases the capacity of the ramps. Three ramp-metering strategies are as follows:

25.2.1 Single-lane one car per green

Single-lane one car per green ramp metering strategy allows only one car to enter the freeway

during each singal cycle. The salient features of this strategy are:



1. The length of green plus yellow indications is set to ensure sufficient time for one vehicle

to cross the stop line. The length of red interval should be sufficient to ensure that the

following vehicle completely stops before proceeding.

2. A typical cycle length is taken as, the smallest possible cycle is 4 seconds with 1 second

green, 1 second yellow, and 2 seconds red. This produces a meter capacity of 900 VPH.

3. A more reasonable cycle is around 4.5 seconds, obtained by increasing the red time to 2.5

seconds. This increase in red would result in a lower meter capacity of 800 VPH.

25.2.2 Single-lane multiple cars per Green

Single-Lane Multiple Cars per Green is also known as Platoon metering, or bulk metering. This

approach allows two or more vehicles to enter the freeway during each green indication. The

most common form of this strategy is to allow two cars per green. The salient features of this

type of ramp metering are:

1. Three or more cars can be allowed; however, this will sacrifice the third objective(breaking

up large platoons).

2. Furthermore, contrary to what one might think, bulk metering does not produce a drastic

increase in capacity over a single-lane one car per green operation. This is because this

strategy requires longer green and yellow times as ramp speed increases, resulting in a

longer cycle length. Consequently, there are fewer cycles in one hour.

3. Two cars per green strategy requires cycle lengths between 6 and 6.5 seconds and results

in metering capacity of 1100 to 1200 VPH. This analysis illustrates that bulk metering

does not double capacity and this finding should be noted.

25.2.3 Dual-lane metering

In dual lane metering two lanes are required to be provided on the ramp in the vicinity of the

meter which necks down to one lane at the merge. The salient features of this type of ramp

metering are:

1. In this strategy, the controller displays the green-yellow-red cycle for each lane.

2. Synchronized cycles are used such that the green indications never occur simultaneously

in both lanes.



100

90

80

70

60

50

40

30

20

10

01200 1300 1400 1500 1600 1700 180011001000900800

Ramp demand volume (vph)

Metering quality

Fai

rF

ail

Dual lane, single entry

3 cars/green

2 cars/green

1 car/green

Goo

d

Figure 25:2: Comparison of metering quality of different approaches with Ramp demand volume

3. The green indications are timed to allow a constant headway between vehicles from both

lanes. Dual-lane metering can provide metering capacity of 1600 to 1700 VPH.

4. In addition, dual-lane ramps provide more storage space for queued vehicles.

25.2.4 Quality of metering

The quality of ramp metering essentially implies the efficiency of handling the flow and reducing

unnecessary delays through metering strategies. For a ramp meter to produce the desired

benefits, the engineer should select a metering strategy appropriate for the current or projected

ramp demand. The ramp width will depend on this selection. The following fig. 25:2 shows the

metering availability (percent of time the signal is metering) of the three metering strategies

for a range of ramp demand volumes. In Figure 25:2, if the flow on a single lane ramp which

has Single-Lane One Car per Green approach is 1000 vph, then the metering availability is

only 80 percent since the metering approach installed has the capacity of 800 vph. Therefore

metering availability decreases as the traffic flow increases. If the flow is around 1600 vph then

Dual-Lane Metering gives 100 percent metering availability. Thus it is imperative to select the

metering strategy based on the flow and accordingly select the required ramp width.

25.3 Design of ramp metering

There are some considerations to be taken into account before designing and installing a ramp

meter. Installation of a ramp meter to achieve the desired objectives requires sufficient room



at the entrance ramp. The determination of minimum ramp length to provide safe, efficient,

and desirable operation requires careful consideration of several elements described below:

1. Sufficient room must be provided for a stopped vehicle at the meter to accelarate and

attain safe merge speeds.

2. Sufficient space must be provided to store the resulting cyclic queue of vehicles without

blocking an upstream signalized intersection.

3. Sufficient room must be provided for vehicles discharged from the upstrem signal to safely

stop behind the queue of vehicles being metered.

Provision for the distances mentioned is an integral part of ramp design. Figure 25:3 illstrates

the requirements for the different types of distances explained above.

25.3.1 Minimum stopping distance to the back of queue

Sufficient stopping distance is required to be provided prior to entry to the ramp. Motorists

leaving an upstream signalized interchange will likely encounter the rear end of a queue as they

proceed toward the meter. Adequate maneuvering and stopping distances should be provided

for both turning and frontage road traffic. This stopping distance calculated simmilar to the

stopping sight distance which is a combination of the brake distance and lag distance travelled

by a vehicle before stopping. The equation to calculate the minimum stopping distance is given

below:

X = vt +v2

2gf(25.1)

where, X is the stopping distance in meters, v is the velocity of the vehicle in m/sec, t is the time

in seconds, g is the gravity coefficient in m/sec2, f is the friction coefficient. This is the minimum

distance to be provided from the back of the queue for safe stopping of vehicles approaching

the ramp. Figure 25:3 shows Safe stopping distance, storage distance and acceleration distance

which are respective three criteria for ramp design.

25.3.2 Storage distance

The storage distance is required to store the vehicles in queue to a ramp meter. The queue

detector controls the maximum queue length in real-time. Thus, the distance between the meter

and the queue detector defines the storage space. The following generalized spacing model can

be used to determine the single-lane storage distance:

L = aV − bV 2 ∀ V ≤ 1600 vph (25.2)



Safe stopping distance

Single lanemeter

QueueDetector

Storage space

Acceleration distanceRamp length

Figure 25:3: Components of Ramp design criteria

Dual lane

Single laneBulk metering

Ramp demand volume (vph)

Dis

tanc

e to

met

er (

met

res)

300 600 900 1200 15000

50

0

200

150

100

Figure 25:4: Variation of distance to meter with Ramp demand volume for different strategies

of Ramp metering

In this equation, L (in meters) is the required single-lane storage distance on the ramp when

the expected peak-hour ramp demand volume is V vph and a, b are constants. This figure

shows the requirements for three metering strategies:

1. Single-lane with single vehicle release per cycle.

2. Single-lane with bulk metering (three vehicles per green).

3. Dual-lane metering assuming single-line storage.

In the Figure 25:4 the curve is shown for the variation of storage distance i.e. distance to meter

with ramp demand volume for different strategy used for Ramp metering.

25.3.3 Distance from meter to merge

The distance from meter to merge is provided so that vehicles can attain a suitable merging

speed after being discharged from the ramp meter. AASHTO provides speed-distance profiles



3%

0%

−3%

0

700

600

500

400

300

200

100

70 80 90 10060

Freeway merge speed (km/hr)

Dis

tanc

e to

mer

ge (

met

res)

Figure 25:5: Acceleration length v/s merge speed for different strategies of Ramp metering

Table 25:1: Acceleration length of ramps

Merge speed Ramp Grade (%)

(kmph) -3 0 +3

60 90 112 150

70 127 158 208

80 180 228 313

90 248 323 466

100 331 442 665

for various classes of vehicles as they accelerate from a stop to speed for various ramp grades.

Figure 25:5, given below provides similar acceleration distances needed to attain various freeway

merging speeds based on AASHTO design criteria. Table 25:1 provides the acceleration length

for different merge speed and with ramps of different grade. The desired distances to merge

increases with increasing freeway merge speed and the same ramp grade.

25.4 Ramp design methodology

To model the ramp influence area, a length of 450 m just upstream (for off ramp) and down-

stream (for on ramp) is considered to be affected. The input data required is the geometric

data of the freeway and the ramp and the demand flow. The three steps of design are:



{{ }}V

RVR

VF V12

12

D SR

450 m

FO

Figure 25:6: Schematic view of a typical merging area

1. The flow enetering lanes 1 and 2 of the freeway upstream of merge area or diverge area

is first determined.

2. The capacity of the freeway, ramp and merge and diverge areas are determined and

checked with limiting values to determine the chance of occurenece of congestion.

3. The density in the ramp influence area is then found out and depnedinf on the value f

this variable, the level of service is determined.

From design point of view analysis of merge area and diverge area are treated separately but

follows the same basic principle already explained.

25.5 Merging influence area

The Merging influence area is the area where increase in local density, congestion, and reduced

speeds is generally observed due to merging traffic from ramps. The ramp contributing traffic

to the freeway is called an ON ramp. The analysis of the merging influence area is done to find

out the level of service of the ON ramp (Figure 25:6). The analysis of merge area is done in

following three primary steps:

25.5.1 Predicting entering flow

The first step of the merge area analysis is to predict the flow enetering lanes 1and 2 of the

freeway (V12). The terms used in above figure are explained below. V12 is influenced by the

following factors:

1. Total freeway flow approaching merge area (VF ) (pc/h): The total approach flow is the

most important influencing factor for the flow remaining in lanes 1 and 2 of the freeway.

2. Total Ramp Flow (VR): This is the total flow on the ramp which ultimately enters the

freeway to merge with exinting flow.



3. Total length of acceleration lane: A longer acceleration lane reduces the turbulence and

hence the density in the influence area of the ramp. The flow in the lanes 1 and 2 thus

are higher.

4. Free- flow speed of ramp at point of merge area: Higher the free flow speed of ramp

vehicles, vehicles on freeway tend to move away from merging flow to avoid high speed

turbulence.

HCM 2000 provides model for predicting V12 at on-ramps as given below:

V12 = VF × PFM (25.3)

where V12 is the flow rate in lane 1 and 2 of freeway entering ramp influence area (pc/h), VF

is the total freeway flow approaching merge area, and PFM is the Proportion of approaching

freeway flow remaining in lanes 1 and 2 immediately upstream of merge. For four lanes freeway

(2 lanes in each direction) PFM = 1.00

25.5.2 Determining capacity

Determining the capacity of the merge area is the second step of the analysis. The capacity

of a merge area is determined by the capacity of the downstream freeway segment. Thus, the

total flow arriving on the upstream freeway and the on-ramp cannot exceed the basic freeway

capacity of the departing downstream freeway segment.

vR12 = v12 + vR (25.4)

Two conditions may occur in a given analysis:

1. The total departing freeway flow, given as V = vF + vR, is greater than the capacity of

the down steam freeway segment, and hence the LOS is F and queuing is expected on

the freeway.

2. Flow entering the ramp influence area exceeds its capacity but total departing freeway

flow is within capacity. This may result in in local high densities and queuing is not

expected on the freeway.

25.5.3 Determining LOS

Determining the level of service (LOS) of the merge area is the third step in merge area analysis.

LOS depends on the density in the influencing area. HCM 2000 provides the equation to



Table 25:2: LOS criteria for merge and diverge areas

LOS Density (pc/km/lane)

A ≥ 6

B 6 - 12

C 12 - 17

D 17 - 22

E > 22

F Demands exceeds capacity

estimate the density in the merge influence area.

DR = a + b VR + c V12 + d LA (25.5)

where, DR is the density of merge influence area (pc/km/ln), VR is the on-ramp peak 15-min

flow rate (pc/h), LA is the length of acceleration lane (m), V12 is the flow rate entering ramp

influence area (pc/h), and a, b, c, and d are constants.

Numerical example

Consider a single lane on-ramp to a six-lane freeway. The length of the acceleration lane is 150

m. What is the LOS during the peak hour for the first on-ramp? Given that the peak hour

factor is 0.95, the heavy vehicle adjustment factor is 0.976, the driver adjustment factor is 1.0

and proportion of approaching freeway flow remaining is 55.5%? The freeway volume is 3000

veh/hr and the on-ramp volume is 1800 veh/hr.

Solution

1. Convert volume to flow rate: Convert volume in (veh/hr) to flow rate (pc/hr) using

vi =Vi

PHF × Fhv × Fp

where, vi is the flow rate in pc/hr for direction i, Vi is the hourly volume in veh/hr for

direction i, PHF is the peak hour factor, and Fhv is the adjustment factor for heavy

vehicles, and Fp is the adjustment factor for driver population.

VF = 3236 pc/hr (Fhv = 0.976, Fp = 1.000)

VR = 1941 pc/hr (Fhv = 0.976, Fp = 1.000)



2. Compute V12 as:

V12 = VF × PFM

= 3236 × 0.555 = 1796 pc/hr.

3. Compute density at ramp influence area using equation:

DR = a + b VR + c V12 + d LA

= 3.402 + 0.00456 VR + 0.0048 V12 − 0.01278 LA

= 3.402 + 0.00456 × 1941 + 0.0048 × 1796 − 0.01278 × 150

= 18.96 pc/km/ln.

4. Compute LOS For DR=18.96 pc/km/ln, the LOS = D from the LOS table above.

25.6 Diverge influence area

The Diverging influence area is the area where increase in local density, congestion, and reduced

speeds is generally observed due to diverging traffic to ramps. The ramp which diverge traffic

to the ramp is called an OFF ramp. The analysis of the diverging influence area is done to

find out the level of service of the OFF ramp. The analysis of diverge area is done in following

three primary steps:

25.6.1 Predicting entering flow

The first step is same as that of merge area analysis. The flow in lanes 1 and 2 of the freeway

is first predicted. However, there are two major differences in the analysis of diverge area.

1. First, approaching flow V12 is measured for a point immediately upstream of the deceler-

ation lane.

2. Second, V12 includes VR at the diverge area. V12 is the flow rate entering ramp influence

area (pc/h), and vR is the Off-ramp demand flow rate (pc/h).

The general model given by HCM 2000 treats V12 as the sum of the off-ramp flow plus a

proportion of the through freeway flow.

V12 = VR + (VF − VR) × PFD (25.6)



{{ }}V

R12

VF V12

VRD RS

450 m VR

FO

Figure 25:7: Typical diverging area diagram

where, V12 is the flow rate in lanes 1 and 2 of freeway upstream of diverge area in (pc/hr),

VF is the freeway demand flow rate immediately upstream of diverge in (pc/h), and PFD is

the proportion of through freeway flow remaining in lanes 1 and 2 immediately upstream of

diverge. For four lanes freeway (2 lanes in each direction) PFD is 1.00.

25.6.2 Determining capacity

As in the merge area analysis, determining the capacity is the second step of the diverge area

analysis. Three limiting values should be checked:

1. Total flow that can depart from the diverge: this is limited by the capacity of the lanes

in the freeway prior to approach of the diverge.

2. The capacities of the departing freeway leg or legs or ramp or both. This is the most

important of the three as generally diverge areas fail due to failure of one or more exit

legs..

3. V12 (approaching flow) prior to deceleration lane: this flow also includes the off-ramp flow

and must be checked against capacity.

25.6.3 Determining LOS

Determing the level of service (LOS) of the diverge area is the third step of the diverge area

analysis. LOS criteria for diverge area are based on density in the diverge influence area. HCM

2000 provides the equation to estimate the density in the merge influence area.

DR = a + b V12 + cLD (25.7)

where, DR is the density of diverge influence area (pc/km/ln), V12 is the flow rate entering ramp

influence area (pc/h), LD is the length of deceleration lane(m), and a, b & c are constants.

This equation is applicable only for undersaturated conditions of flow. The density calculation



150 m 225 m 90 m

RDR S


is not done when either of the three capacities mentioned earlier are exceeded. In such cases,

the LOS is assigned as F.

Numerical example

Consider an off-ramp (Single-lane) pair, 225 meters apart, from a six lane freeway. The length

of the first deceleration lane is 150m and that of the second deceleration lane is 90 m. What is

the LOS during the peak hour for the first off-ramp given that the peak hour factor is 0.95, the

heavy vehicle adjustment factor is 0.93, the driver adjustment factor is 1.0 and the proportion

of through freeway flow remaining is 61.7%? The freeway volume is 4500 veh/hr and the first

off-ramp volume is 300 veh/hr.

Solution

1. Convert volume to flow rate: Convert volume in veh/hr to flow rate in pc/hr as

follows:

vi =Vi

(PHF × Fhv × Fp)

VF = 5093 pc/hr (Fhv = 0.930, Fp = 1.0)

VR = 340 pc/hr (Fhv = 0.930, Fp = 1.0)

2. Compute V12 as below:

V12 = VR + (VF − VR) × PFD

= 340 + (5093 − 340) × (0.617)

= 3273 pc/hr



3. Compute density at ramp influence area as below:

DR = 2.642 + 0.0053 V12 − 0.0183 LD

DR = 2.642 + 0.0053 × 3273 − 0.0183 × 150

DR = 17.2 pc/km/ln.

4. Determine LOS: For DR=17.2 pc/km/ln the LOS is D.

25.7 Fixed, reactive and predictive systems

There are two different metering approaches available. First is Pre-timed metering, which use

fixed signal cycles. Second is Traffic responsive, which uses real time traffic data to calculate

signal cycle lengths. Traffic responsive systems can be local or system-wide.

25.7.1 Pre-timed (fixed) systems

In the pre-timed ramp metering systems, the ramp signal operates with a constant cycle in ac-

cordance with a metering rate prescribed for the particular control period.. the salient features

of this type of ramp metering are:

1. It is the simplest and least expensive form of ramp metering for construction and instal-

lation.

2. It is also the most rigid approach because it cannot make adjustments for real-time

conditions including non-recurring congestion (i.e., congestion that occurs as a result of

weather, collisions, etc.).

3. Th system being pre-timed, it is best used to address conditions that are predictable from

day-today.

4. If there is no mainline or ramp detection, agencies must regularly collect data by al-

ternative means in order to analyze traffic conditions on the freeway and determine the

appropriate metering rates.

5. The metering operation will require frequent observation so that rates can be adjusted to

meet traffic conditions which is a drawback.



25.7.2 Traffic responsive systems

In contrast to the pre-timed metering control, traffic-responsive metering is directly influenced

by the mainline and ramp traffic conditions during the metering period. Metering rates are

selected on the basis of real-time measurements of traffic variables indicating the current relation

between upstream and downstream capacity. The salient features of this type of ramp metering

system are:

1. This system uses freeway loop detectors or other surveillance systems to calculate or select

ramp metering rates based on current freeway conditions.

2. It is generally considered to be five to ten percent better than those of pre-timed metering.

3. A traffic responsive approach can be used either locally or system-wide.

Local traffic responsive

Local ramp metering is employed when only the conditions local to the ramp (as compared

with other ramps) are used to provide the metering rates. The salient features are:

1. Local traffic responsive metering approaches base metering rates on freeway conditions

near the metered ramp.

2. This is used where the traffic congestion at a location can be reduced by the metering of

a single ramp.

3. They are used as backups when system-wide algorithms fail.

4. Unlike pre-timed systems, local systems require surveillance of the freeway using traffic

detectors.

5. Although, more capital costs are required to implement traffic responsive systems, they

more easily adapt to changing conditions and can provide better results than their pre-

timed counterparts.

System-wide traffic responsive

In most cases, it is preferable to meter a series of ramps in a freeway section in a coordinated

fashion based on criteria that consider the entire freeway section. The strategy may also consider

the freeway corridor consisting of the freeway section as well as the surface streets that will be

affected by metered traffic. The salient features are:



1. This is used when there are multiple bottlenecks or locations of recurring congestion along

a freeway.

2. This type of ramp metering is used to optimize traffic flow along a metered stretch of

roadway, rather than at a specific point on the freeway (as is the case of local traffic

responsive systems).

3. Like local traffic responsive systems, system-wide traffic responsive systems require data

from ramp detectors and local freeway detectors.

4. In addition to these components, system-wide traffic responsive systems are unique in the

fact that data is also needed from downstream detectors and/or upstream detectors at

multiple locations, potentially from cross-street signal controllers, and from the central

computer.

5. System-wide traffic responsive systems have the most complex hardware configuration

compared to the other metering approaches discussed so far (i.e., pre-timed and local

traffic responsive).

25.8 Summary

In this chapter we discussed ramp metering, different strategies of ramp metering, procedure

to find out the level of service of on and off ramps, different kind of metering systems. From

the analysis that we have done in this chapter we can say that the Ramp metering can result

into increased freeway speed, decreased travel time, increase in freeway capacity, reduction in

accidents and congestion, improved fuel economy and efficient use of capacity.

25.9 References

1. Ismail Chabini and Amedeo R Odoni. Transportation Flow Systems. MIT, 2019.

2. A Chaudhary and J Messer. Report on design criteria for ramp metering. Texas

Transportation Institute, Texas, 2000.



4. P Stewart. Ramp metering study. SIAS Limited, Dundee, UK, 2003.


Transportation Systems Engineering 27. Principles of Traffic Control

Chapter 27

Principles of Traffic Control

27.1 Overview

Intersection is an area shared by two or more roads. This area is designated for the vehicles

to turn to different directions to reach their desired destinations. Its main function is to

guide vehicles to their respective directions. Traffic intersections are complex locations on any

highway. This is because vehicles moving in different direction wan to occupy same space at the

same time. In addition, the pedestrians also seek same space for crossing. Drivers have to make

split second decision at an intersection by considering his route, intersection geometry, speed

and direction of other vehicles etc. A small error in judgment can cause severe accidents. It also

causes delay and it depends on type, geometry, and type of control. Overall traffic flow depends

on the performance of the intersections. It also affects the capacity of the road. Therefore,

both from the accident perspective and the capacity perspective, the study of intersections very

important for the traffic engineers especially in the case of urban scenario.

27.2 Conflicts at an intersection

Conflicts at an intersection are different for different types of intersection. Consider a typical

four-legged intersection as shown in figure. The number of conflicts for competing through

movements are 4, while competing right turn and through movements are 8. The conflicts

between right turn traffics are 4, and between left turn and merging traffic is 4. The conflicts

created by pedestrians will be 8 taking into account all the four approaches. Diverging traffic

also produces about 4 conflicts. Therefore, a typical four legged intersection has about 32

different types of conflicts. This is shown in figure 27:1.

The essence of the intersection control is to resolve these conflicts at the intersection for

the safe and efficient movement of both vehicular traffic and pedestrians. Two methods of

intersection controls are there: time sharing and space sharing. The type of intersection control



P

P

P P

P

P

PP

P 8 Pedestrian

Conflicts in a traffic signal

8 Right turn−Through

Total = 32 Conflicts

4 Merging

4 Right turn

4 Through traffic

4 Diverging

Figure 27:1: Conflicts at an intersection

that has to be adopted depends on the traffic volume, road geometry, cost involved, importance

of the road etc.

27.3 Levels of intersection control

The control of an intersection can be exercised at different levels. They can be either passive

control, semi control, or active control. In passive control, there is no explicit control on the

driver . In semi control, some amount of control on the driver is there from the traffic agency.

Active control means the movement of the traffic is fully controlled by the traffic agency and

the drivers cannot simply maneuver the intersection according to his choice.

27.3.1 Passive control

When the volume of traffic is less, no explicit control is required. Here the road users are

required to obey the basic rules of the road. Passive control like traffic signs, road markings

etc. are used to complement the intersection control. Some of the intersection control that are

classified under passive control are as follows:

1. No control If the traffic coming to an intersection is low, then by applying the basic

rules of the road like driver on the left side of the road must yield and that through

movements will have priority than turning movements. The driver is expected to obey

these basic rules of the road.

2. Traffic signs: With the help of warning signs, guide signs etc. it is able to provide

some level of control at an intersection. Give way control, two-way stop control, and



all-way stop control are some examples. The GIVE WAY control requires the driver in

the minor road to slow down to a minimum speed and allow the vehicle on the major

road to proceed. Two way stop control requires the vehicle drivers on the minor streets

should see that the conflicts are avoided. Finally an all-way stop control is usually used

when it is difficult to differentiate between the major and minor roads in an intersection.

In such a case, STOP sign is placed on all the approaches to the intersection and the

driver on all the approaches are required to stop the vehicle. The vehicle at the right

side will get priority over the left approach. The traffic control at ’at-grade’ intersection

may be uncontrolled in cases of low traffic. Here the road users are required to obey the

basic rules of the road. Passive control like traffic signs, road markings etc. are used to

complement the intersection control.

3. Traffic signs plus marking: In addition to the traffic signs, road markings also comple-

ment the traffic control at intersections. Some of the examples include stop line marking,

yield lines, arrow marking etc.

27.3.2 Semi control

In semi control or partial control, the drivers are gently guided to avoid conflicts. Channelization

and traffic rotaries are two examples of this.

1. Channelization: The traffic is separated to flow through definite paths by raising a

portion of the road in the middle usually called as islands distinguished by road markings.

The conflicts in traffic movements are reduced to a great extent in such a case. In

channelized intersections, as the name suggests, the traffic is directed to flow through

different channels and this physical separation is made possible with the help of some

barriers in the road like traffic islands, road markings etc.

2. Traffic rotaries: It is a form of intersection control in which the traffic is made to flow

along one direction around a traffic island. The essential principle of this control is to

convert all the severe conflicts like through and right turn conflicts into milder conflicts

like merging, weaving and diverging. It is a form of ‘at-grade’ intersection laid out for the

movement of traffic such that no through conflicts are there. Free-left turn is permitted

where as through traffic and right-turn traffic is forced to move around the central island

in a clock-wise direction in an orderly manner. Merging, weaving and diverging operations

reduces the conflicting movements at the rotary.



27.3.3 Active control

Active control implies that the road user will be forced to follow the path suggested by the

traffic control agencies. He cannot maneuver according to his wish. Traffic signals and grade

separated intersections come under this classification.

1. Traffic signals: Control using traffic signal is based on time sharing approach. At a

given time, with the help of appropriate signals, certain traffic movements are restricted

where as certain other movements are permitted to pass through the intersection. Two or

more phases may be provided depending upon the traffic conditions of the intersection.

When the vehicles traversing the intersection is very large, then the control is done with

the help of signals. The phases provided for the signal may be two or more. If more than

two phases are provided, then it is called multiphase signal.

The signals can operate in several modes. Most common are fixed time signals and vehicle

actuated signals. In fixed time signals, the cycle time, phases and interval of each signal

is fixed. Each cycle of the signal will be exactly like another. But they cannot cater

to the needs of the fluctuating traffic. On the other hand, vehicle actuated signals can

respond to dynamic traffic situations. Vehicle detectors will be placed on the streets

approaching the intersection and the detector will sense the presence of the vehicle and

pass the information to a controller. The controller then sets the cycle time and adjusts

the phase lengths according to the prevailing traffic conditions.

2. Grade separated intersections: The intersections are of two types. They are at-grade

intersections and grade-separated intersections. In at-grade intersections, all roadways

join or cross at the same vertical level. Grade separated intersections allows the traffic to

cross at different vertical levels. Sometimes the topography itself may be helpful in con-

structing such intersections. Otherwise, the initial construction cost required will be very

high. Therefore, they are usually constructed on high speed facilities like expressways,

freeways etc. These type of intersection increases the road capacity because vehicles can

flow with high speed and accident potential is also reduced due to vertical separation of

traffic.

27.4 Channelized intersection

Vehicles approaching an intersection are directed to definite paths by islands, marking etc. and

this method of control is called channelization. Channelized intersection provides more safety

and efficiency. It reduces the number of possible conflicts by reducing the area of conflicts



��

��

��

��

��

��

��

��

Figure 27:2: Channelization of traffic through a three-legged intersection

��

��

��

��

��

��

��

��

��

��

Figure 27:3: Channelization of traffic through a four-legged intersection

available in the carriageway. If no channelizing is provided the driver will have less tendency to

reduce the speed while entering the intersection from the carriageway. The presence of traffic

islands, markings etc. forces the driver to reduce the speed and becomes more cautious while

maneuvering the intersection. A channelizing island also serves as a refuge for pedestrians and

makes pedestrian crossing safer. Channelization of traffic through a three-legged intersection

(refer figure 27:2) and a four-legged intersection (refer figure 27:3) is shown in the figure.

27.5 Summary

Traffic intersections are problem spots on any highway, which contribute to a large share of

accidents. For safe operation, these locations should be kept under some level of control de-

pending upon the traffic quantity and behavior. Based on this, intersections and interchanges

are constructed, the different types of which were discussed in the chapter.



27.6 References


New Delhi, 1987.


Transportation Systems Engineering 26. Corridor Analysis

Chapter 26

Corridor Analysis

26.1 Introduction

Transport problems are very critical one to be solved frequently, sequentially and economically

for all sectors of one nation. Even though these solutions are mandatory, they are continuous

and expensive so needs to be planned systematically. These all requirements will lead us to

Transportation System Planning. Transportation System Planning is a tool that attempts to

provide feasible and systematic method for solving transport problems of the society. Trans-

portation system planning starts from the problem of the society which is the difference of users

desire to the existing condition of the system. Afterwards following its stages it will attempt

to meet its goals and objectives. While in the process so many analyses are required to be

done from them the one is done to know the performance of the existing system. This can be

expressed as either individual component performance or the whole system performance. Doing

this is dependent on the type of transportation system. Among them multimodal multi facility

system is the one which requires aggregate performance measurement for all components which

constitutes. According to our study area we can choose from the two methods of performance

measurement alternatives which are Corridor analysis and Area wide analysis.

26.2 Terminologies

The terminologies used in the corridor analysis is provided below.

26.2.1 Corridor system

1. Corridor: A corridor is a set of essentially parallel and competing facilities and modes

with cross-connectors that serve trips between two designated points. A corridor may

contain several subsystems of facilities freeway, rural highway, urban street, transit, pedes-

trian, and bicycle Figure. 26:1.



Segment

PointFreeway

Arterials

Figure 26:1: Showing the Point Segment and Corridor Model

2. Segment: Segments are stretches of a facility in which the traffic demand and capacity

conditions are relatively constant.

3. Point: Points are locations at the beginning and end of each segment, at which traffic

enters, leaves, or crosses the facility.

4. Facility: is a structure built or road design modification to increase the efficiency of the

two main road way services (accessibility and Mobility).

26.2.2 Highway sub systems

1. Freeway: A freeway is defined as a divided highway with full control of access and having

two uninterrupted flow or more lanes for the exclusive use of traffic in each direction. All

the access is through a ramp a separate entrance or exit way to or from the Freeway.

2. Rural highway: A road with only one lane in each direction and traffic signals spaced

no closer than 3.0 km. mostly recognized by its low flow condition.

3. Urban Street: With traffic signals spaced no farther than 3.0 km apart. Since in

Urban areas most activities are fond of Transportation, are characterized by its high

flow condition and high traffic movements due the complex interaction between vehicles

accidents are also high in urban areas. To avoid this and other conflicts Traffic control is

required especially in urban areas.



26.2.3 Transit

Transits are a means of transporting massive either passenger or freight on a separated route.

These modes of transportations are a key to every city especially in urban areas. The most

common types of Transits include:

1. Bus transit is a term applied to a variety of public transportation systems using buses

to provide faster, more efficient service than an ordinary bus line. Often this is achieved

by making improvements to existing infrastructure, vehicles and scheduling. Bus rapid

transit also called Bus way and/or Quality bus.

2. Street car is a means of public transport which requires their own rail to flow through the

system these rails can be built embedded in roadways. Streetcar (also called Tram) is a

passenger rail vehicle which runs on tracks along public urban streets and also sometimes

on separate rights of way.

3. Rail transit is a form of urban rail public transportation that generally has a lower

capacity and lower speed than heavy rail and metro systems, but higher capacity and

higher speed than traditional street-running tram systems.

26.3 Segment capacity

Capacity is the maximum hourly flow rate, at which persons or vehicles reasonably can be

expected to traverse a point or a uniform section, of a lane or roadway during a given time

period, under prevailing roadway, traffic and control conditions. But sometimes the demand

may exceed the capacity during peak hours, which will bring queue delay. Thus demand

adjustment is required and is done as follows. Adjusting for excess demand from the capacity

is necessary only if working with forecasted or estimated demands rather than counted traffic.

If the demand exceeds the capacity at any point in time or space, then the excess demand must

be stored on the segment and carried over to the following hour. The downstream demands

are reduced by the amount of excess demand stored on the segment. The algorithm starts with

the entry gate segments on the periphery of the corridor and works inward until all segment

demands have been checked against their capacity.

26.3.1 Demand adjustment algorithm

The following steps are used to adjust demand when excess demand occurs in a time period.

Step 1. Select the entry gate segment with the highest priority and the highest v/c ratio.



Step 2. Select the first time period.

Step 3. If demand ≤ capacity or the initial queue = 0, go to Step 7.

Step 4. If demand > capacity or queue > 0, then calculate new queue by using eqn. 26.1.

queuei = queuei−1+ demand − capacity (26.1)

where, i is the current analysis period, i − 1 is the previous analysis period, queuei−1 is

the queue remaining from the preceding analysis period.

Step 5. Reduce downstream segment demand by the amount that the demand exceeds

the capacity. Propagate this reduction to all connecting downstream segments in pro-

portion to the ratio of each downstream segment demand to all segments exiting from

the subject segment. Continue the process downstream until the reduction is less than 5

percent of capacity.

Step 6. Add the excess demand - the amount by which the demand exceeds the capacity

- to the next time period demand for the subject segment.

Step 7. Apply the increment to the next time period. Repeat Steps 3 through 6 until

the processes for all the time periods are finished.

Step 8. Go to next gate tree with unanalyzed segments in current rank. Repeat Steps 2

through 7 until all segments of current rank have been analyzed.

Step 9. Apply the increment to current Rank (the new one). Go to the segment with

the highest v/c ratio among those of the new rank. Repeat Steps 2 through 8 until all

segments are analyzed.

26.3.2 Free flow Travel time

The segment free-flow traversal times are obtained by dividing the length of the segment by

the estimated free-flow speed (FFS), as shown in equation 26.2

Rf =L

Sf

(26.2)

where, Rf is the Segment free-flow travel time for given Direction of Segment and Time Period,

(hr), L is the length of segment (km), and Sf is the Segment free-flow speed computed (km/hr).

The FFS is computed according to the Part III methods using the adjusted demands determined

in the previous step. The computation is repeated for each direction of each segment for each

time subperiods.



26.3.3 Queue delay

The queuing delay only the amount due to demand exceeding capacity is computed for all

segments. The queuing delay is computed for each direction of each segment and time period

only when demand is greater than Capacity by eqn. 26.3.

Di =T

2× Di−1 + [V − c] ×

T 2

2(26.3)

where, Di is the total delay due to excess demand (veh-hr) for direction, segment, and time

period; T is the duration of time subperiod (hr); Di−1 is the queue left over at end of previous

time period (veh); V is the demand rate for current time period (veh/hr); and c is the capacity

of segment in subject direction (veh/hr). These the above steps are repeated for any additional

time periods to be analyzed. For example, if the peak period lasts for 4 hours, it might

be divided into four 1hr periods (or 16 quarter hr periods), with each time period analyzed

in sequence. The first and the last analysis periods must be uncongested for all delay to

be included in the performance measures. Once all time periods have been analyzed, the

performance measures are computed.

26.4 Determining performance measures

This step describes how to compute performance measures of congestion intensity, duration,

extent, variability, and accessibility for the corridor.

26.4.1 Intensity

The possible performance measures for the intensity of congestion on the highway subsystems

(freeway, two-lane highway, and arterial) in the corridor are computed from one or more of the

following: person-hours of travel, person-hours of delay, mean trip speed, and mean trip delay.

If average vehicle occupancy (AVO) data are not available, then the performance measures are

computed in terms of vehicle-hours rather than person-hours.

1. The eqn. 26.4 given below is used to determine PHT.

PHT = AV O × Σd,l,h[V × R + DQ] (26.4)

where, PHT is the person-hours of travel in corridor, AV O is the average vehicle occu-

pancy, V is the vehicle demand in Direction on Link during Time Period (veh), R is the

segment traversal time (h/km), and DQ is the queuing delay (veh-h).



2. The mean trip time is computed by dividing the total person hours of travel by the

number of person trips.

t = 60 × PHT/P (26.5)

where, t is the mean trip time (min/person), PHT is the person-hours of travel, and P

is the total number of person trips.

3. The mean trip speed is computed by dividing the total number of person-kilometres by

the total person-hours of travel as in eqn. 26.6 below:

S =PkmT

PHT= AV O ×

Σd,l,h[V × L]

PHT(26.6)

where, S is the mean corridor trip speed (km/h), PkmT is the person-kilometres of travel,

PHT is the person-hours of travel, AV O is the average vehicle occupancy, V is the vehicle

demand in the given Direction on a Segment and Period (veh), and L is the length of

segment (km).

4. The mean trip delay is computed by subtracting the PHT under free-flow conditions from

the PHT under congested conditions and dividing the result by the number of person-

trips. The person-hours of travel under free-flow conditions is computed like PHT for

congested conditions, but using free-flow traversal times and zero queuing delay. It can

be determined using eqn. 26.7 given below:

d = 3600 ×(PHT − PHTf)

P(26.7)

where, d is the mean trip delay (s/person), PHT is the person-hours of travel, PHTf is

the person-hours of travel under free-flow conditions, and P is the total number of person

trips.

26.4.2 Duration

Performance measurements of duration can be computed from the number of hours of conges-

tion observed on any segment. The duration of congestion is the sum of the length of each

analysis subperiods for which the demand exceeds capacity. The duration of congestion (i.e.,

oversaturation) for any link is computed using Eqn. 26.8 as:-

Hi = Ni × T (26.8)

where, Hi is the duration of congestion for Link i(h), Ni is the number of analysis subperiods

for which v/c > 1.00 on Link i, and T is the duration of analysis subperiods (h). The maximum

duration on any link indicates the amount of time before congestion is completely cleared from

the corridor.



Table 26:1: Queue density defaults given by HCM 2000

Sub system Storage Density Vehicle Spacing

(veh/Km/ln) (m)

Freeway 75 13.3

Two lane highway 130 7.5

Urban Street 130 7.5

26.4.3 Extent

Performance measures of the extent of congestion can be computed from the sum of the length

of queuing on each segment. One can also identify segments in which the queue overflows the

storage capacity; this is particularly useful for ramp metering analyses. To compute the queue

length, an assumption must be made about the average density of vehicles in a queue. Default

values are suggested in Table. 26:1 To compute queue length, Eqn. 26.9 is used.

QL =T × [v − c]

N × ds

(26.9)

where, QL is the queue length (km) for the given Direction, of Segment, for Time Subperiod;

v is the segment demand (veh/h); c is the segment capacity (veh/h); N is the number of lanes;

ds is the storage density (veh/km/ln); and T is the duration of analysis period (h). Note that if

v < c, then QL = 0, and if QL > L, then the queue overflows the storage capacity. The queue

lengths for all segments then can be added up to obtain the length of queuing in kilometres in

the subsystem during the analysis period. The number of segments in which the queue exceeds

the storage capacity also might be reported. This statistics is particularly useful for identifying

queue overflows that result from ramp metering.

26.4.4 Variability

Variability is a sensitivity measure. The variability or sensitivity of the results can be deter-

mined by substituting higher and lower demand estimates. For example assuming 110 percent

of the original demand estimates for all segments and repeating the calculations.

26.4.5 Accessibility

Accessibility can be measured in terms of the number of trip destinations reachable within a

selected travel time for a designated set of origin locations such as a residential zone. The



1

8 7

6

4

5

2

3

Arterials

Figure 26:2: Two way Arterials Highway system

Table 26:2: Peak hour input demand rate 1

control North bound South bound East bound West bound

point Lt Th Rt Lt Th Rt Lt Th Rt Lt Th Rt

2 53 268 34 378 536 176 163 963 55 110 779 110

4 43 684 109 144 810 153 113 1065 81 126 945 145

results for each origin zone are tabulated and reported as X percent of the homes in the study

area can reach Y percent of the jobs within Z minutes.

Numerical example

For the given Urban street system geometry and Data inputs determine the performance mea-

surement using Corridor analysis. Given that:

1. Average vehicle vccupancy (AVO) is 1.2.

2. Peak Hour Demand data all Volumes are in (veh/hr) is given in Table. 26:2.

3. Capacities, Lengths, Free flow speeds and average flow speeds for each link input data is

also given in Table. 26:3.

Solution:

1. Step 1. Because we have Traffic count data we should convert it as link data. This can

be done by allocating the flow and adding the volume as per its logical direction (Table

4 col (3)). The flow allocation overview is as shown below. In Fig. 26:3



Table 26:3: Capacity, length and Speeds input

link length Capacity FFS Actual

(km) (veh/hr) (km/hr) speed(km/hr)

1 2 1.06 1400 56 40

2 1 1.06 3400 56 56

2 4 1.67 1400 56 41

4 2 1.67 1400 56 46

2 8 1.21 1400 56 43

8 2 1.21 1700 56 26

2 3 0.09 3400 56 40

3 2 0.09 1400 56 12

4 7 1.21 1400 56 43

7 4 1.21 1200 56 43

4 6 0.76 3400 56 56

6 4 0.76 1400 56 33

4 5 0.09 3400 56 40

5 4 0.09 1400 56 11

1

8

2

3 5

4

7

6

During Variation use the smaller

Use 999

366 701

Lt WBTh SBRt EBNB

RtLtTh

SB

LtRt

Th

1090541

Rt WBTh NBLt EB

836 1017

NB

Lt Rt

Th

Lt WB

Rt EBTh SB

Th

LtRt

SBRt WBTh NBLt EB

942 1107

1216

1318

Lt

SB

Th

EB

Rt

NB

Th

Lt

Rt

WB

Th

Lt

Rt

WB

999

1375

Lt

SB

Th

EB

Rt

NB

Th

Lt

Rt

EB

12591141

Lt N

BT

h W

BR

t SB

11011008

Th

Lt

Rt

Lt N

BT

h W

BR

t SB

22

22

22 22

Figure 26:3: Showing how the flow allocation is done



Table 26:4: Demand by Capacity

link Demand(V) Capacity(C) V/c

(1) (2) (3) (4) (5)

1 2 1181 1400 0.843571

2 1 1008 3400 0.296471

2 4 1375 1400 0.899286

4 2 1141 1400 0.713571

2 8 541 1400 0.386429

8 2 1090 1700 0.641176

2 3 701 3400 0.206176

3 2 355 1400 0.253571

4 7 942 1400 0.672857

7 4 1107 1200 0.9225

4 6 1318 3400 0.387647

6 4 1216 1400 0.868571

4 5 1017 3400 0.299118

5 4 836 1400 0.597143

2. Step 2. Calculate V/C ratio demand by capacity for each link which is as shown below

in Table. 5 col (5).

3. Step 3. For V/C > 1 find the Queued vehicles simply the difference of demand to

capacity.

4. Step 4. Adjust the demand downstream till it reaches 10% of the volume before doing

further check up. Until all V/C ratios are below 1.

5. Step 5. Determination of person hour delay (PHD), person hours travel (PHT), person

kilometre hour travel (PkmT).

Note that in Table. 5

(a) None of them(V/C) is greater of unity.

(b) No Adjustment is required.

(c) Indicates No Queue delay Determination

6. Step 6. Free VHT (col(7))= (col (3) × col (4))/col (5)



Table 26:5: PHD and PHT calculationLink Len. Dem- FFS Actual free actual Free Actual Delay

and speed speed VHT VHT PHT PHT PHT Total

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)

1 2 1.06 1181 56 40 22.35 31.30 26.83 37.56 10.73 1251.86

2 1 1.06 1008 56 56 19.08 19.08 22.90 22.90 0.00 1068.48

2 4 1.67 1375 56 41 41.00 56.01 49.21 67.21 18.00 2296.25

4 2 1.67 1141 56 46 34.03 41.42 40.83 49.71 8.88 1905.47

2 8 1.21 541 56 43 11.69 15.22 14.03 18.27 4.24 654.61

8 2 1.21 1090 56 26 23.55 50.73 28.26 60.87 32.61 1318.9

2 3 0.09 701 56 40 1.13 1.58 1.35 1.89 0.54 63.09

3 2 0.09 355 56 12 0.57 2.66 0.68 3.20 2.51 31.95

4 7 1.21 942 56 43 20.35 26.51 24.42 31.81 7.38 1139.82

7 4 1.21 1107 56 43 23.92 31.15 28.70 37.38 8.68 1339.47

4 6 0.76 1318 56 56 17.89 17.89 21.46 21.46 0.00 1001.68

6 4 0.76 1216 56 33 16.50 28.00 19.80 33.61 13.80 924.16

4 5 0.09 1017 56 40 1.63 2.29 1.96 2.75 0.78 91.53

5 4 0.09 836 56 11 1.34 6.84 1.61 8.21 6.60 75.24

12.18 13828 Sum 282.05 396.81 114.76 13162.51



Table 26:6: Performance measurementFacility type Length PkmT PHT PHD Speed(S)

(Km) Pers. Km Pers. Hr Pers. Hr km/hr

Arterial sub. system 12.8 15795 396.8 114.75 39.6

7. Step 7. Actual VHT (col(8))= Qd +(col (3) × col (4))/col (6), where, Qd is the queue

delay in our case zero.

8. Step 8. Free PHT (col(9))= AVO × col (7)

9. Step 9. Actual PHT (col(10))= AVO × col (7)

10. Step 10. Travel Delay (PHD) (col(11))= Actual PHT (col(10)) - Free PHT (col(9))

11. Step 11. Calculation of PkmT

PkmT = AV O × ΣV × L

where, V is adjusted volume, L is length of the Link, and ΣV L is col(12) last cell in

Table. 26:5.

12. Step 12. Intensity measures

PHT = ΣactualPHT

= 396.8pers.hr

t =60 × PHT

AV O × ΣV= 1.43min/pers

S =PkmT

PHT= AV O × (Σd,l,h[V × L])/PHT

= 39.6km/hr

d = 3600 ×(PHT − PHTf)

P= 24.9sec/pers.

26.5 Summary

Corridor Analysis is the method of combining Point, Segment and Facility analysis to estimate

the overall performance of multimodal corridor. Mostly the performance measures of any

corridor are determined by calculating its capacity, the travel time and queue delay in the



given section. Since this tool is required for multi facility and multimodal transportation

system mostly it covers Highway subsystems (Freeways, Rural highways and urban streets)

and Transit.

26.6 References

1. Urban transportation planning model update - phase ii, 1981. Task F- Development of

Corridor Analysis Procedures.

2. Highway Capacity manual part V Draft Working Paper 385-9. University of Florida

Transportation Research Center and T-Concepts Corp, Proposed 2010 Highway Capacity

manual part V Draft Working Paper 385-9, 2007., 2010.




Transportation Systems Engineering 28. Traffic Signs

Chapter 28

Traffic Signs

28.1 Overview

Traffic control device is the medium used for communicating between traffic engineer and road

users. Unlike other modes of transportation, there is no control on the drivers using the road.

Here traffic control devices comes to the help of the traffic engineer. The major types of

traffic control devices used are- traffic signs, road markings , traffic signals and parking control.

This chapter discusses traffic control signs. Different types of traffic signs are regulatory signs,

warning signs and informatory signs.

28.2 Requirements

The requirements of traffic control devices are listed below:

1. The control device should fulfill a need : Each device must have a specific purpose

for the safe and efficient operation of traffic flow. The superfluous devices should not be

used.

2. It should command attention from the road users: This affects the design of signs.

For commanding attention, proper visibility should be there. Also the sign should be

distinctive and clear. The sign should be placed in such a way that the driver requires no

extra effort to see the sign.

3. It should convey a clear, simple meaning: Clarity and simplicity of message is

essential for the driver to properly understand the meaning in short time. The use of

color, shape and legend as codes becomes important in this regard. The legend should be

kept short and simple so that even a less educated driver could understand the message

in less time.



4. Road users must respect the signs: Respect is commanded only when the drivers are

conditioned to expect that all devices carry meaningful and important messages. Overuse,

misuse and confusing messages of devices tends the drivers to ignore them.

5. The control device should provide adequate time for proper response from the

road users: This is again related to the design aspect of traffic control devices. The sign

boards should be placed at a distance such that the driver could see it and gets sufficient

time to respond to the situation. For example, the STOP sign which is always placed

at the stop line of the intersection should be visible for atleast one safe stopping sight

distance away from the stop line.

28.3 Communication tools

A number of mechanisms are used by the traffic engineer to communicate with the road user.

These mechanisms recognize certain human limitations, particularly eyesight. Messages are

conveyed through the following elements.

1. Color: It is the first and most easily noticed characteristics of a device. Usage of different

colors for different signs are important. The most commonly used colors are red, green,

yellow, black, blue, and brown . These are used to code certain devices and to reinforce

specific messages. Consistent use of colors helps the drivers to identify the presence of

sign board ahead.

2. Shape : It is the second element discerned by the driver next to the color of the device.

The categories of shapes normally used are circular, triangular, rectangular, and diamond

shape. Two exceptional shapes used in traffic signs are octagonal shape for STOP sign

and use of inverted triangle for GIVE WAY (YIELD) sign. Diamond shape signs are not

generally used in India.

3. Legend : This is the last element of a device that the drive comprehends. This is an

important aspect in the case of traffic signs. For the easy understanding by the driver,

the legend should be short, simple and specific so that it does not divert the attention of

the driver. Symbols are normally used as legends so that even a person unable to read

the language will be able to understand that. There is no need of it in the case of traffic

signals and road markings.

4. Pattern: It is normally used in the application of road markings, complementing traffic

signs. Generally solid, double solid and dotted lines are used. Each pattern conveys dif-

ferent type of meaning. The frequent and consistent use of pattern to convey information



is recommended so that the drivers get accustomed to the different types of markings and

can instantly recognize them.

28.4 Types of traffic signs

There are several hundreds of traffic signs available covering wide variety of traffic situations.

They can be classified into three main categories.

1. Regulatory signs: These signs require the driver to obey the signs for the safety of

other road users.

2. Warning signs:These signs are for the safety of oneself who is driving and advice the

drivers to obey these signs.

3. Informative signs: These signs provide information to the driver about the facilities

available ahead, and the route and distance to reach the specific destinations

In addition special type of traffic sign namely work zone signs are also available. These type

of signs are used to give warning to the road users when some construction work is going on

the road. They are placed only for short duration and will be removed soon after the work is

over and when the road is brought back to its normal condition. The first three signs will be

discussed in detail below.

28.4.1 Regulatory signs

These signs are also called mandatory signs because it is mandatory that the drivers must obey

these signs. If the driver fails to obey them, the control agency has the right to take legal action

against the driver. These signs are primarily meant for the safety of other road users. These

signs have generally black legend on a white background. They are circular in shape with red

borders. The regulatory signs can be further classified into :

1. Right of way series: These include two unique signs that assign the right of way to

the selected approaches of an intersection. They are the STOP sign and GIVE WAY sign

For example, when one minor road and major road meets at an intersection, preference

should be given to the vehicles passing through the major road. Hence the give way sign

board will be placed on the minor road to inform the driver on the minor road that he

should give way for the vehicles on the major road. In case two major roads are meeting,

then the traffic engineer decides based on the traffic on which approach the sign board



has to be placed. Stop sign is another example of regulatory signs that comes in right of

way series which requires the driver to stop the vehicle at the stop line.

2. Speed series: Number of speed signs may be used to limit the speed of the vehicle on

the road. They include typical speed limit signs, truck speed, minimum speed signs etc.

Speed limit signs are placed to limit the speed of the vehicle to a particular speed for

many reasons. Separate truck speed limits are applied on high speed roadways where

heavy commercial vehicles must be limited to slower speeds than passenger cars for safety

reasons. Minimum speed limits are applied on high speed roads like expressways, freeways

etc. where safety is again a predominant reason. Very slow vehicles may present hazard

to themselves and other vehicles also.

3. Movement series: They contain a number of signs that affect specific vehicle maneuvers.

These include turn signs, alignment signs, exclusion signs, one way signs etc. Turn signs

include turn prohibitions and lane use control signs. Lane use signs make use of arrows

to specify the movements which all vehicles in the lane must take. Turn signs are used to

safely accommodate turns in unsignalized intersections.

4. Parking series: They include parking signs which indicate not only parking prohibitions

or restrictions, but also indicate places where parking is permitted, the type of vehicle to

be parked, duration for parking etc.

5. Pedestrian series: They include both legend and symbol signs. These signs are meant

for the safety of pedestrians and include signs indicating pedestrian only roads, pedestrian

crossing sites etc.

6. Miscellaneous: Wide variety of signs that are included in this category are: a ”KEEP

OF MEDIAN” sign, signs indicating road closures, signs restricting vehicles carrying

hazardous cargo or substances, signs indicating vehicle weight limitations etc.

Some examples of the regulatory signs are shown in figure 28:1. They include a stop sign, give

way sign, signs for no entry, sign indicating prohibition for right turn, vehicle width limit sign,

speed limit sign etc.

28.4.2 Warning signs

Warning signs or cautionary signs give information to the driver about the impending road

condition. They advice the driver to obey the rules. These signs are meant for the own safety

of drivers. They call for extra vigilance from the part of drivers. The color convention used for



2 M��

��

��

�� 50

��

��

STOPGIVEWAY

Figure 28:1: Examples of regulatory signs ( stop sign, give way sign, signs for no entry, sign

indicating prohibition for right turn, vehicle width limit sign, speed limit sign)

��

��

Figure 28:2: Examples of cautionary signs ( right hand curve sign board, signs for narrow road,

sign indicating railway track ahead)

this type of signs is that the legend will be black in color with a white background. The shape

used is upward triangular or diamond shape with red borders. Some of the examples for this

type of signs are given in fig 28:2 and includes right hand curve sign board, signs for narrow

road, sign indicating railway track ahead etc.

28.4.3 Informative signs

Informative signs also called guide signs, are provided to assist the drivers to reach their desired

destinations. These are predominantly meant for the drivers who are unfamiliar to the place.

The guide signs are redundant for the users who are accustomed to the location.

Some of the examples for these type of signs are route markers, destination signs, mile posts,

service information, recreational and cultural interest area signing etc. Route markers are used

to identify numbered highways. They have designs that are distinctive and unique. They are

written black letters on yellow background. Destination signs are used to indicate the direction

to the critical destination points, and to mark important intersections. Distance in kilometers



��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

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TOLL BOOTH

AHEAD

��

��

NH

��

��

8

Figure 28:3: Examples of informative signs (route markers, destination signs, mile posts, service

centre information etc)

are sometimes marked to the right side of the destination. They are, in general, rectangular

with the long dimension in the horizontal direction. They are color coded as white letters with

green background.

Mile posts are provided to inform the driver about the progress along a route to reach his

destination. Service guide signs give information to the driver regarding various services such

as food, fuel, medical assistance etc. They are written with white letters on blue background.

Information on historic, recreational and other cultural area is given on white letters with brown

background. In the figure 28:3 we can see some examples for informative signs which include

route markers, destination signs, mile posts, service centre information etc..

28.5 Summary

Traffic signs are means for exercising control on or passing information to the road users. They

may be regulatory, warning, or informative. Among the design aspects of the signs, the size,

shape, color and location matters. Some of the signs along with examples were discussed in this

chapter. A few web sites discussing on traffic signs are giben below: www.aptransport.org/html/signs.htm,

www.indiacar.com/infobank/Traffic-signs.htm.

28.6 References


New Delhi, 1987.


Transportation Systems Engineering 29. Road Markings

Chapter 29

Road Markings

29.1 Overview

The essential purpose of road markings is to guide and control traffic on a highway. They

supplement the function of traffic signs. The markings serve as a psychological barrier and

signify the delineation of traffic path and its lateral clearance from traffic hazards for the safe

movement of traffic. Hence they are very important to ensure the safe, smooth and harmonious

flow of traffic. Various types of road markings like longitudinal markings, transverse markings,

object markings and special markings to warn the driver about the hazardous locations in the

road etc. will be discussed in detail in this chapter.

29.2 Classification

The road markings are defined as lines, patterns, words or other devices, except signs, set

into applied or attached to the carriageway or kerbs or to objects within or adjacent to the

carriageway, for controlling, warning, guiding and informing the users. The road markings

are classified as longitudinal markings, transverse markings, object markings, word messages,

marking for parkings, marking at hazardous locations etc.

29.3 Longitudinal markings

Longitudinal markings are placed along the direction of traffic on the roadway surface, for the

purpose of indicating to the driver, his proper position on the roadway. Some of the guiding

principles in longitudinal markings are also discussed below.

Longitudinal markings are provided for separating traffic flow in the same direction and the

predominant color used is white. Yellow color is used to separate the traffic flow in opposite

direction and also to separate the pavement edges. The lines can be either broken, solid or



150

3 m 4.5 m

Figure 29:1: Centre line marking for a two lane road

double solid. Broken lines are permissive in character and allows crossing with discretion, if

traffic situation permits. Solid lines are restrictive in character and does not allow crossing

except for entry or exit from a side road or premises or to avoid a stationary obstruction.

Double solid lines indicate severity in restrictions and should not be crossed except in case

of emergency. There can also be a combination of solid and broken lines. In such a case, a

solid line may be crossed with discretion, if the broken line of the combination is nearer to the

direction of travel. Vehicles from the opposite directions are not permitted to cross the line.

Different types of longitudinal markings are centre line, traffic lanes, no passing zone, warning

lines, border or edge lines, bus lane markings, cycle lane markings.

29.3.1 Centre line

Centre line separates the opposing streams of traffic and facilitates their movements. Usually

no centre line is provided for roads having width less than 5 m and for roads having more

than four lanes. The centre line may be marked with either single broken line, single solid line,

double broken line, or double solid line depending upon the road and traffic requirements. On

urban roads with less than four lanes, the centre line may be single broken line segments of 3 m

long and 150 mm wide. The broken lines are placed with 4.5 m gaps (figure 29:1). On curves

and near intersections, gap shall be reduced to 3 metres. On undivided urban roads with at

least two traffic lanes in each direction, the centre line marking may be a single solid line of

150 mm wide as in figure 29:2, or double solid line of 100 mm wide separated by a space of

100 mm as shown in figure 29:3. The centre barrier line marking for four lane road is shown

in figure 29:4.

29.3.2 Traffic lane lines

The subdivision of wide carriageways into separate lanes on either side of the carriage way helps

the driver to go straight and also curbs the meandering tendency of the driver. At intersections,

these traffic lane lines will eliminate confusion and facilitates turning movements. Thus traffic

lane markings help in increasing the capacity of the road in addition ensuring more safety. The



1.5m 3m

4.5 m3m

Figure 29:2: Centre line and lane marking for a four lane road

3m1.5m

100

100

Figure 29:3: Double solid line for a two lane road

100 mm

1.5m 3m150 mm

Figure 29:4: Centre barrier line marking for four lane road



150

100

1.5m 3.0 m

Figure 29:5: Lane marking for a four lane road with solid barrier line

4.5 m

100

150

3.0 m

1.5m 3.0 m

Figure 29:6: Traffic lane marking for a four lane road with broken centre line

traffic lane lines are normally single broken lines of 100 mm width. Some examples are shown

in figure 29:5 and figure 29:6.

29.3.3 No passing zones

No passing zones are established on summit curves, horizontal curves, and on two lane and

three lane highways where overtaking maneuvers are prohibited because of low sight distance.

It may be marked by a solid yellow line along the centre or a double yellow line. In the case of

a double yellow line, the left hand element may be a solid barrier line, the right hand may be a

either a broken line or a solid line . These solid lines are also called barrier lines. When a solid

line is to the right of the broken line, the passing restriction shall apply only to the opposing

traffic. Some typical examples are shown in figure 29:7 and figure 29:8. In the latter case, the

no passing zone is staggered for each direction.

29.3.4 Warning lines

Warning lines warn the drivers about the obstruction approaches. They are marked on hori-

zontal and vertical curves where the visibility is greater than prohibitory criteria specified for

no overtaking zones. They are broken lines with 6 m length and 3 m gap. A minimum of seven

line segments should be provided. A typical example is shown in figure 29:9



yellow single/double line

Figure 29:7: Barrier line marking for a four lane road

Barrier li

ne

Figure 29:8: No passing zone marking at horizontal curves

3m6m

Figure 29:9: Warning line marking for a two lane road



300200

STOP

150

Figure 29:10: Stop line marking near an intersection

29.3.5 Edge lines

Edge lines indicate edges of rural roads which have no kerbs to delineate the limits upto which

the driver can safely venture. They should be at least 150 mm from the actual edge of the

pavement. They are painted in yellow or white.

All the lines should be preferably light reflective, so that they will be visible during night

also. Improved night visibility may also be obtained by the use of minute glass beads embedded

in the pavement marking materials to produce a retroreflective surface.

29.4 Transverse markings

Transverse markings are marked across the direction of traffic. They are marked at intersections

etc. The site conditions play a very important role. The type of road marking for a particular

intersection depends on several variables such as speed characteristics of traffic, availability of

space etc. Stop line markings, markings for pedestrian crossing, direction arrows, etc. are some

of the markings on approaches to intersections.

29.4.1 Stop line

Stop line indicates the position beyond which the vehicles should not proceed when required to

stop by control devices like signals or by traffic police. They should be placed either parallel to

the intersecting roadway or at right angles to the direction of approaching vehicles. An example

for a stop line marking is shown in figure 29:10.



Figure 29:11: Pedestrian marking near an intersection

29.4.2 Pedestrian crossings

Pedestrian crossings are provided at places where the conflict between vehicular and pedestrian

traffic is severe. The site should be selected that there is less inconvenience to the pedestrians

and also the vehicles are not interrupted too much. At intersections, the pedestrian crossings

should be preceded by a stop line at a distance of 2 to 3m for unsignalized intersections and at a

distance of one metre for signalized intersections. Most commonly used pattern for pedestrian

crossing is Zebra crossing consisting of equally spaced white strips of 500 mm wide. A typical

example of an intersection illustrating pedestrian crossings is shown in figure 29:11.

29.4.3 Directional arrows

In addition to the warning lines on approaching lanes, directional arrows should be used to guide

the drivers in advance over the correct lane to be taken while approaching busy intersections.

Because of the low angle at which the markings are viewed by the drivers, the arrows should

be elongated in the direction of traffic for adequate visibility. The dimensions of these arrows

are also very important. A typical example of a directional arrow is shown in figure 29:12.

29.5 Object marking

Physical obstructions in a carriageway like traffic island or obstructions near carriageway like

signal posts, pier etc. cause serious hazard to the flow of traffic and should be adequately

marked. They may be marked on the objects adjacent to the carriageway.



0.2m

1.25m

0.4m0.55 m

0.4m

1.2

m

0.5m

3.5m

1.2

m

3.5m

0.3m 0.3m

Figure 29:12: Directional arrow marking

29.5.1 Objects within the carriageway

The obstructions within the carriageway such as traffic islands, raised medians, etc. may be

marked by not less than five alternate black and yellow stripes. The stripes should slope forward

at an angle of 45◦ with respect to the direction of traffic. These stripes shall be uniform and

should not be less than 100 m wide so as to provide sufficient visibility.

29.5.2 Objects adjacent to carriageway

Sometimes objects adjacent to the carriageway may pose some obstructions to the flow of traffic.

Objects such as subway piers and abutments, culvert head walls etc. are some examples for

such obstructions. They should be marked with alternate black and white stripes at a forward

angle of 45◦ with respect to the direction of traffic. Poles close to the carriageway should be

painted in alternate black and white up to a height of 1.25 m above the road level. Other

objects such as guard stones, drums, guard rails etc. where chances of vehicles hitting them are

only when vehicle runs off the carriageway should be painted in solid white. Kerbs of all islands

located in the line of traffic flow shall be painted with either alternating black and white stripes

of 500 mm wide or chequered black and white stripes of same width. The object marking for

central pier and side walls of an underpass is illustrated in figure 29:13.

29.6 Word messages

Information to guide, regulate, or warn the road user may also be conveyed by inscription

of word message on road surface. Characters for word messages are usually capital letters.



Figure 29:13: Marking for objects adjacent to the road way

The legends should be as brief as possible and shall not consist of more than three words for

any message. Word messages require more and important time to read and comprehend than

other road markings. Therefore, only few and important ones are usually adopted. Some of

the examples of word messages are STOP, SLOW, SCHOOL, RIGHT TUN ONLY etc. The

character of a road message is also elongated so that driver looking at the road surface at a low

angle can also read them easily. The dimensioning of a typical alphabet is shown in figure 29:14.

29.6.1 Parking

The marking of the parking space limits on urban roads promotes more efficient use of the

parking spaces and tends to prevent encroachment on places like bus stops, fire hydrant zones

etc. where parking is undesirable. Such parking space limitations should be indicated with

markings that are solid white lines 100 mm wide. Words TAXI, CARS, SCOOTERS etc. may

also be written if the parking area is specific for any particular type of vehicle. To indicate

parking restriction, kerb or carriage way marking of continuous yellow line 100 mm wide covering

the top of kerb or carriageway close to it may be used.

29.6.2 Hazardous location

Wherever there is a change in the width of the road, or any hazardous location in the road,

the driver should be warned about this situation with the help of suitable road markings.



1250

260

313

78

Figure 29:14: Typical dimension of the character T used in road marking

LLL

Figure 29:15: Approach marking for obstructions on the road way

Road markings showing the width transition in the carriageway should be of 100 mm width.

Converging lines shall be 150 mm wide and shall have a taper length of not less than twenty

times the off-set distance. Typical carriageway markings showing transition from wider to

narrower sections and vice-versa is shown in figure 29:15. In the figure, the driver is warned

about the position of the pier through proper road markings.

29.7 Summary

Road markings are aids to control traffic by exercising psychological control over the road

users. They are made use of in delineating the carriage way as well as marking obstructions, to

ensure safe driving. They also assist safe pedestrian crossing. Longitudinal markings which are

provided along the length of the road and its various classifications were discussed. Transverse

markings are provided along the width of the road. Road markings also contain word messages,



but since it is time consuming to understand compared to other markings there are only very few

of them. Markings are also used to warn the driver about the hazardous locations ahead. Thus

road markings ensure smooth flow of traffic providing safety also to the road users. The following

web link give further insight in to the road markings: mutcd.fhwa.dot.gov/pdfs/200311/pdf-

index.htm.

29.8 References


New Delhi, 1987.


Transportation Systems Engineering 30. Uncontrolled Intersection

Chapter 30

Uncontrolled Intersection

30.1 Introduction

Uncontrolled intersections are the traffic junctions where there is no explict traffic control mea-

sures are adopted. The important aspects that will be covered in this chapter are: the concept

of two-way stop controlled intersection, all-way stop controlled intersection, gap acceptance,

critical gap, follow-up time, potential capacity, and delay determination. These concepts are

primarily adopted from Highway Capacity Manual.

30.1.1 Categories of Intersection

An intersection is a road junction where two or more roads either meet or cross at grade.

This intersection includes the areas needed for all modes of travel: pedestrian, bicycle, motor

vehicle, and transit. Thus, the intersection includes not only the pavement area, but typically

the adjacent sidewalks and pedestrian curb cut ramps.

All the road junctions designated for the vehicles to turn to different directions to reach

their desired destinations. Traffic intersections are complex locations on any highway. This is

because vehicles moving in different direction want to occupy same space at the same time. In

addition, the pedestrians also seek same space for crossing. Drivers have to make split second

decision at an intersection by considering his route, intersection geometry, speed and direction

of other vehicles etc. A small error in judgment can cause severe accidents. It causes delay

and it depends on type, geometry, and type of control. Overall traffic flow depends on the

performance of the intersections. It also affects the capacity of the road. Therefore, both

from the accident perspective and the capacity perspective, the study of intersections are very

important by the traffic engineers. Intersection design can vary widely in terms of size, shape,

number of travel lanes, and number of turn lanes. Basically, there are four types of intersections,

determined by the number of road segments and priority usage.

1. Priority Intersection: Occur where one of the intersecting roads is given definite pri-



ority over the other. The minor road will usually be controlled by some form of sing

marking, such as stop or yield sign; thus ensuring that priority vehicles travailing on the

main street will incur virtually no delay.

2. Space sharing intersection: Are intended to permit fully equally priority and to permit

continuous movement for all intersecting vehicle flows; example would be rotaries and

other weaving areas.

3. Time Sharing Intersection: Are those at which alternative flows are given the right

of way at different point in time. This type of intersection is controlled by traffic signal

or by police officer.

4. Uncontrolled intersection: are the most common type of intersection usually occurs

where the intersecting roads are relatively equal importance and found in areas where

there is not much traffic shown in Fig. 30:1.

At uncontrolled intersection the arrival rate and individuals drivers generally determine the

manner of operation, while the resulting performance characteristics are derived from joint

consideration of flow conditions and driver judgment and behavior patterns. In simplest terms,

an intersection, one flow of traffic seeks gaps in the opposing flow of traffic.

At priority intersections, since one flow is given priority over the right of way it is clear

that the secondary or minor flow is usually the one seeking gaps. By contrast at uncontrolled

intersection, each flow must seek gaps in the other opposing flow. When flows are very light,

which is the case on most urban and rural roads large gaps exist in the flows and thus few

situation arise when vehicles arrive at uncontrolled intersection less than 10 second apart or at

interval close enough to cause conflicts. However when vehicles arrive at uncontrolled intersec-

tion only a few second apart potential conflicts exist and driver must judge their relative time

relationships and adjusts accordingly.

Generally one or both vehicles most adjust their speeds i.e. delayed somewhat with the

closer vehicle most often taking the right of way; in a sense, of course, the earlier arriving

vehicle has priority and in this instance when two vehicles arrive simultaneous, the rule of

the road usually indicate priority for the driver on the right. The possibility of judgmental in

these, informal priority situation for uncontrolled intersection is obvious. At an Uncontrolled

intersection: Service discipline is typically controlled by signs (stop or yield signs) using two

rules two way stop controlled intersection (TWSC) and all way stop controlled intersection

(AWSC).



Figure 30:1: Example showing uncontrolled intersection

STOP

STOP

STOP

STOPFigure 30:2: Two way stop controlled intersection

30.1.2 Two-way stop-controlled intersection

Researchers rely on many specific definitions to describe the performance of traffic operation

systems. The clear understanding of such terminology is an important element is studying

two-way stop-controlled (TWSC) traffic operation system characteristics; defined as: One of

the uncontrolled intersections with stop control on the minor street shown in Fig. 30:2.

Characteristics of TWSC Intersections

At TWSC intersections, the stop-controlled approaches are referred to as the minor street

approaches; the intersection approaches that are not controlled by stop signs are referred to as

the major street approaches. A three-leg intersection is considered to be a standard type of



STOP STOP

STOP

Four−leg intersection T−intersection

Rank Rank Traffic streamTraffic stream

4321

7, 108, 111, 4, 13, 14, 9, 122, 3, 5, 6, 15, 16

321

74, 13, 14, 92, 3, 5, 15

111012

2

78 9

6

4

2

54

7 9

16

13

15

1413 14

153

1

5

3

Figure 30:3: Traffic flow stream in two way stop controlled intersection

TWSC intersection if the single minor street approach is controlled by a stop sign. Three-leg

intersections where two of the three approaches are controlled by stop signs are a special form

of uncontrolled intersection control.

Flows at TWSC Intersections

TWSC intersections assign the right-of-way among conflicting traffic streams according to the

following hierarchy:

1. The major street through and right-turning movements are the highest-priority move-

ments at a TWSC intersection. This movements shown Fig. 30:3 are 2, 3, 5, 6, 15 and

16.

2. Vehicles turning left from the major street onto the minor street yield only to conflicting

major street through and right-turning vehicles. All other conflicting movements yield to

these major street left-turning movements. The movements on this rank are 1, 4, 13, 14,

9 and 12.

3. Minor Street through vehicles yield to all conflicting major street through, right-turning,

and left-turning movements. The movements on this rank are 8 and 11.

4. Minor Street left-turning vehicles yield to all conflicting major street through, right-

turning, and left-turning vehicles and to all conflicting minor street through and right-

turning vehicles. The movements on this rank are 7 and 10.



STOP

STOP STOP

STOP

A

B

Figure 30:4: All way stop controlled intersection

30.1.3 All-way-stop-controlled intersection

All-way-stop-controlled intersection (AWSC) are mostly used approaching from all directions

and is required to stop before proceeding through the intersection as shown in Fig. 30:4. An

all-way stop may have multiple approaches and may be marked with a supplemental plate

stating the number of approaches.

The analysis of AWSC intersection is easier because all users must stop. In this type of

intersection the critical entity of the capacity is the average intersection departure head way.

Secondary parameters are the number of cross lanes, turning percentages, and the distribution

volume on each approach. The first step for the analysis of capacity is select approach called

subject approach the approach opposite to subject approach is opposing approach, and the

approach on the side of the subject approach is are called conflicting approach.

Characteristics of AWSC intersections

AWSC intersections require every vehicle to stop at the intersection before proceeding. Since

each driver must stop, the judgment as to whether to proceed into the intersection is a function

of traffic conditions on the other approaches. If no traffic is present on the other approaches, a

driver can proceed immediately after the stop is made. If there is traffic on one or more of the

other approaches, a driver proceeds only after determining that there are no vehicles currently

in the intersection and that it is the drivers turn to proceed.



30.2 Gap acceptance and follow-up time

Gap acceptance is one of the most important components in microscopic traffic characteristic.

The gap acceptance theory commonly used in the analysis of uncontrolled intersections based

on the concept of defining the extent drivers will be able to utilize a gap of particular size

or duration. A driver entering into or going across a traffic stream must evaluate the space

between a potentially conflicting vehicle and decide whether to cross or enter or not. One of

the most important aspects of traffic operation is the interaction of vehicles with in a single

stream of traffic or the interaction of two separate traffic streams. This interaction takes place

when a driver changes lanes merging in to a traffic stream or crosses a traffic stream. Inherent

in the traffic interaction associated with these basic maneuvers is concept of gap acceptance.

30.2.1 Basic Terminologies

1. Gap means the time and space that a subject vehicle needs to merge adequately safely

between two vehicles. Gap acceptance is the minimum gap required to finish lane changing

safely. Therefore, a gap acceptance model can help describe how a driver judges whether

to accept or not.

2. Gap acceptance: The process by which a minor stream vehicle accepts an available gap

to maneuver.

3. Critical gap: The minimum major-stream headway during which a minor-street vehicle

can make a maneuver.

4. Lag: Time interval between the arrival of a yielding vehicle and the passage of the next

priority stream vehicle (Forward waiting time).

5. Headway: The time interval between the arrivals of two successive vehicles. Headway

differs from gap because it is measured from the front bumper of the front vehicle to the

front bumper of the next vehicle.

6. Minimum Headway: The minimum gap maintained by a vehicle in the major traffic

stream.

7. Follow-up time: Time between the departure of one vehicle from the minor street and

the departure of the next vehicle using the same gap under a condition of continuous

queuing.

8. Delay: The additional travel time experienced by a driver, passenger or pedestrian.



9. Conflicting movements: The traffic streams in conflict at an intersection.

10. Capacity: The maximum hourly rate at which persons or vehicles can reasonably be

expected to traverse a point or uniform section of a lane or a roadway during a given time

period under prevailing roadway, traffic, and control conditions.

30.2.2 Critical Gap

The critical gap tcx for movement x is defined as the minimum average acceptable gap that

allows intersection entry for one minor street or major street. The term average acceptable

means that the average driver would accept or choose to utilize a gap of this size. The gap is

measured as the clear time in the traffic stream defined by all conflicting movements. Thus, the

model assumes that all gaps shorter than tcx are rejected or unused, while all gaps equal to or

larger than tcx would be accepted or used. The adjusted critical gap tcx computed as follows.

tcx = tcb + tcHV PHV + tcGG − tc,T − t3,LT (30.1)

where, tcx is the critical gap for movement “x”, tcb is the base critical gap from Table. 30:1 tcHV

is the adjustment factor for heavy vehicles PHV is the proportion of heavy vehicles tcG is the

adjustment factor for grade G is the percent grade divided by 100, tcT is the adjustment factor

for each part of a two-stage gap acceptance process, and t3LT is the critical gap adjustment

factor for intersection geometry.

30.2.3 Follow-up time

The follow up time tfx for movement “x” is the minimum average acceptable time for a second

queued minor street vehicle to use a gap large enough admit two or more vehicles. Follow-

up times were measured directly by observing traffic flow. Resulting follow-up times were

analyzed to determine their dependence on different parameters such as intersection layout.

This measurement is similar to the saturation flow rate at signalized intersection. Table. 30:1

and 30:2 shows base or unadjusted values of the critical gap and follow up time for various

movements. Base critical gaps and follow up times can be adjusted to account for a number

of conditions, including heavy - vehicle presence grade, and the existence of two stage gap

acceptance. Adjusted Follow up Time computed as:

tfx = tfb + tfHV PHV (30.2)

where, tfx is the follow-up time for minor movement x tfb is the base follow-up time from table

1 tfHV is the adjustment factor for heavy vehicles, and PHV is the proportion of heavy vehicles

for minor movement.



Table 30:1: Base critical gap and follow up times

Base Critical Gap,tc,base (s) Base Follow-up

Vehicle Movement Two-Lane Four-Lane Time

MajorStreet Major Street tf,base (s)

Left turn from major 4.1 4.1 2.2

Right turn from minor 6.2 6.9 3.3

Through traffic on minor 6.5 6.5 4.0

Left turn from minor 7.1 7.5 3.5

Table 30:2: Adjustments to base critical gap and follow up times

Adjustment Values(s)

Factor

tcHV 1.0 Two-lane major streets

2.0 Four-lane major streets

tcG 0.1 Movements 9 and 12

0.2 Movements 7,8,10 and 11

1.0 Otherwise

tcT 1.0 First or second stage of two-stage process

0.0 For one-stage process

T3LT 0.7 Minor-street LT at T-intersection

0.0 Otherwise

tfHV 0.9 Two-lane major streets

1.0 Four-lane major streets



Vehicle/Pedestrian ConflictsVehicle/Vehicle Conflicts

Figure 30:5: Conflicts at four legged intersection

30.2.4 Conflicting volume

The traffic flow process at un-controlled intersection is complicated since there are many distinct

vehicular movements to be accounted for. Most of this movements conflict with opposing

vehicular volumes. These conflicts result in decreasing capacity, increasing delay, and increasing

potentials for traffic accidents. Consider a typical four-legged intersection as shown in Fig. 30:5

The numbers of conflicts for competing through movements are 4, while competing right turn

and through movements are 8. The conflicts between right turn traffics are 4, and between left

turn and merging traffic are 4. The conflicts created by pedestrians will be 8 taking into account

all the four approaches. Diverging traffic also produces about 4 conflicts. Therefore, a typical

four legged intersection has about 32 different types of conflicts. Conflicts at an intersection are

different for different types of intersection. The essence of the intersection control is to resolve

these conflicts at the intersection for the safe and efficient movement of both vehicular traffic

and pedestrians. The movements for determining conflict in four legged intersection are:

1. Major street left turns seek gaps through the opposing through movement, the op-

posing right turn movement and pedestrians crossing the far side of the minor street.

2. Minor street right turns seek to merge in to the right most lane of the major street,

which contains through and right turning vehicles. Each right turn from the minor street

must also cross the two pedestrians path shown.

3. Through movements from the minor street must cross all major street vehicular and

pedestrians flows.

4. Minor street left turns must deal not only with all major street traffic flow but with

two pedestrians flows and the opposing minor street through and right turn movements.



13 14

15

32

97

45

STOP

Figure 30:6: Three legged intersection conflicts volume determination for movement 7

Through this movements the conflict volume (Vcx) for the given movement x is can be computed.

As an example the formula of conflict volume for movement 7 for three legged intersection shown

in Fig. 30:6 computed as:

Vc7 = 2Vc4 + Vc5 + Vc2 + 0.5V3 + V13 + V15 (30.3)

30.3 Potential Capacity

Capacity is defined as the maximum number of vehicles, passengers, or the like, per unit

time, which can be accommodated under given conditions with a reasonable expectation of

occurrence. Potential capacity describes the capacity of a minor stream under ideal conditions

assuming that it is unimpeded by other movements and has exclusive use of a separate lane.

Once of the conflicting volume, critical gap and follow up time are known for a given

movement its potential capacity can be estimated using gap acceptance models. The concept

of potential capacity assumes that all available gaps are used by the subject movement i.e.;

there are no higher priority vehicular or pedestrian movements and waiting to use some of

the gaps it also assumes that each movement operates out of an exclusive lane. The potential

capacity of can be computed using the formula:

cpx = vcx ×e−vcxtcx/3600

1 − e−vcxtfx/3600(30.4)

where, cpx is the potential capacity of minor movement x (veh/h), vcx is the conflicting flow rate



for movement x (veh/h), tcx is the critical gap for minor movement x, and tfx is the follow-up

time movement x.

30.4 Movement capacity and impedance effects

Vehicles use gaps at a TWSC intersection in a prioritized manner. When traffic becomes

congested in a high-priority movement, it can impede lower-priority movements that are streams

of Ranks 3 and 4 as shown in Fig. 30:4 from using gaps in the traffic stream, reducing the

potential capacity of these movements. The ideal potential capacities must be adjusted to

reflect the impedance effects of higher priority movements that may utilize some of the gaps

sought by lower priority movements. This impedance may come due to both pedestrians and

vehicular sources called movement capacity.

The movement capacity is found by multiplying the potential capacity by an adjustment

factor. The adjustment factor is the product of the probability that each impeding movement

will be blocking a subject vehicle. That is

Cmx = Cpx ×

∑

i

Pvi × Ppi (30.5)

where, Cmx is the movement capacity in vph, Cpx is the potential capacity movement x in

vph, Pvi is the probability that impeding vehicular movement i is not blocking the subject

flow; (also referred to as the vehicular impedance factor for movement i, Ppi is the probability

that impeding pedestrian movement j is not blocking the subject flow; also referred to us the

pedestrian impedance factor for the movement j.

30.4.1 Vehicular movements

Priority 2 vehicular movements LTs from major street and RTs from minor street are not

impeded by any other vehicular flow, as they represent the highest priority movements seeking

gaps. They are impeded, however, by Rank 1 pedestrian movements. Priority 3 vehicular

movements are impeded by Priority 2 vehicular movements and Priority l and 2 pedestrian

movements seeking to use the same gaps. Priority 4 vehicular movements are impeded by

Priority 2 and 3 vehicular movements, and Priority 1 and 2 pedestrian movements using the

same gaps. Table. 30:3 lists the impeding flows for each subject movement in a four leg.

Generally the rule stated the probability that impeding vehicular movement i is not blocking

the subject movement is computed as

Pvi = 1 −

vi

Cmi(30.6)



Table 30:3: Relative pedestrian/vehicle hierarchy

Vehicle Stream Must Yield to Impedance Factor for

Pedestrian Stream Pedestrians, Pp,x

V1 V16 Pp,16

V4 V15 Pp,15

V7 V15, V13 (Pp,15)(Pp,13)

V8 V15, V16 (Pp,15)(Pp,16)

V9 V15, V14 (Pp,15)(Pp,14)

V10 V16, V14 (Pp,16)(Pp,14)

V11 V15, V16 (Pp,15)(Pp,16)

V12 V16, V13 (Pp,16)(Pp,13)

where, vi is the demand flow for impeding movement i, and Cmi is the movement capacity for

impeding movement i vph. Pedestrian impedance factors are computed as:

30.4.2 Pedestrian Movements

One of the impeding effects for all the movement is pedestrians movement. Both approaches of

Minor-street vehicle streams must yield to pedestrian streams. Table. 30:3 shows that relative

hierarchy between pedestrian and vehicular streams used. A factor accounting for pedestrian

blockage is computed by Eqn. 30.7 on the basis of pedestrian volume, the pedestrian walking

speed, and the lane width that is:

Ppj = 1 −

Vj(W/Sp)

3600(30.7)

where, ppj is the pedestrian impedance factor for impeding pedestrian movement j, vj is the

pedestrian flow rate, impeding movement j in peds/hr, w is the lane width in m, and Sp is the

pedestrian walking speed in m/s.

30.4.3 Determining Shared Lane Capacity

The capacities of individual streams (left turn, through and right turn) are calculated sepa-

rately. If the streams share a common traffic lane, the capacity of the shared lane is then

calculated according to the shared lane procedure. But movement capacities still represent an

assumption that each minor street movement operates out of an exclusive lane. Where two or



three movements share a lane its combined capacity computed as:

CSH = ΣΣyVy

Σy(Vy

Cmy)

(30.8)

where, CSH is the shared lane capacity in veh/hr, Vy is the flow rate, movement y sharing lane

with other minor street flow, and Cmy is the movement capacity of movement y sharing lane

with other minor street.

30.5 Determining control delay

Delay is a complex measure and depends on a number of variables it is a measure of driver

discomfort, frustration, fuel consumption, increased travel time etc. Total delay is the difference

between the travel time actually experienced and the reference travel time that would result

during base conditions, in the absence of incident, control, traffic, or geometric delay. Also,

Average control delay for any particular minor movement is a function of the Capacity of the

approach and The degree of saturation. The control delay per vehicle for a movement in a

separate lane is given by:

dx =3600

Cmx+ 900T

(

Vx

Cmx− 1

)

+

√

(Vx

Cmx− 1)2 +

3600Cmx

Vx

Cmx

450T

+ 5 (30.9)

where, dx is the average control delay per vehicle for movement x in s/veh, Cmx is the capacity

of movement or shared lane x in veh/hr, T is the analysis period h (15 min=0.25 h), and Vx is

the demand flow rate, movement or shared lane x in veh/hr.

30.5.1 Performance measures

Four measures are used to describe the performance of TWSC intersections: control delay,

delay to major street through vehicles, queue length, and v/c ratio. The primary measure

that is used to provide an estimate of LOS is control delay. This measure can be estimated

for any movement on the minor (i.e., the stop-controlled) street. By summing delay estimates

for individual movements, a delay estimate for each minor street movement and minor street

approach can be achieved.

For AWSC intersections, the average control delay (in seconds per vehicle) is used as the

primary measure of performance. Control delay is the increased time of travel for a vehicle

approaching and passing through an AWSC intersection, compared with a free flow vehicle if

it were not required to slow or stop at the intersection. According to the performance measure



Table 30:4: Level of service criteria for TWSC intersectionLevel of Service Control delays(s/veh)

A 0-10

B > 10-15

C > 15-25

D > 25-35

E > 35-50

F > 50

STOP

12

20(4)

400(5)75)7)

15(13)

30(15)

9

(9)30(3)

200(2)

7

4

Vehicle Movement

Pedestrians Movement

Figure 30:7: Three legged intersection

of the TWSC intersection, LOS of the minor-street left turn operates at level of service C

approaches to B.

Numerical example

For a three legged intersection given in figure 30:7 determine the control delay and level of

service for movement 7. The total volume of both pedestrian and vehicular traffic at each

movement is given in the figure itself. Following data is also given:

• The speed of the pedestrians is 1.2m/s

• All flows contains 10% trucks

• The percentage of the grade is 0.00

• Ignore moments coming from south bound

• The analysis period is 15 min. (T=0.25)



Solution:

1. Compute the critical gap and follow up time:

(a) Critical gap tcx = tcb + tcHV PHV + tcGGtcT tLT . From table. 30:1 and table. 30:2 we

have tcb = 7.1 s , tcG = 0.2, tcT = 0.0, tLT = 0.0. Then tcx at movement 7 computed

as: tc7 = 7.1 + 1.0 × 0.1+0.2 × 0.0 - 0.0 - 0.0 = 6.50 sec

(b) To compute the Follow up time: From table. 30:1 and table. 30:2 we have tfb = 3.5

s , tfHV = 0.9. Then tfx at movement 7 computed as: tfx = tfb + tfHV PHV tf7 =

3.5 + 0.9 × 0.1 = 3.59 sec.

2. Compute the conflicting flow rate:

Vc7 = 2V4 + V5 + V13 + V2 + 0.5V3 + V15

= 40 + 400 + 15 + 200 + 0.5 × 30 + 30

= 700 conflicts/hr

3. Determining potential capacity:

Cpx = vcxe−(vcxtcx/3600)

1 − e−(vcxtfx/3600)

= 700e−(700×6.5/3600)

1 − e−(700×3.59/3600)

Cp7 = 394 vph.

4. Determine the impudence effect of the movement capacity for movement 7: From the

given figure movement 7 is impeded by vehicular movement 4 and 1 and pedestrian 13

and 15.

(a) Pedestrian impedance probability computed as:

Ppi = 1 −vj ×

[

wSp

]

3600

Pp13 = 1 −15 ×

[

61.2

]

3600= 1 − 0.0417 = 0.958

Pp15 = 1 −30 ×

[

4.51.2

]

3600= 1 − 0.03125 = 0.969.

(b) Vehicular impedance probabilities are:

Pvi = 1 −

vi

Cmi

Pv4 = 1 − 20/394 = 0.949



(c) Once the pedestrian and vehicular impedence is determined, the moment capacity

is computed as:

Cmx = CpxPPvi × Ppj

Cm7 = 394 × (0.949)(0.969)(0.958) = 347 vph.

5. Delay computation: The delay is Calculated by using the formula

d7 =3600

Cmx

+ 900T

(

Vx

Cmx

− 1

)

+

√

(Vx

Cmx

− 1)2 +3600Cmx

Vx

Cmx

450T

+ 5

=3600

347+ 900 × 0.25

(

75

347− 1

)

+

√

(75

347− 1)2 +

3600347

75347

450 × 0.25

+ 5

= 18.213 sec/veh

The delay of movement 7 is 18.213 sec/veh.

6. Determine the level of service: From the computed delay (18.213 se) in step 5 the level

of service is LOS C obtained from HCM table.

30.6 Conclusion

This chapter focuses on theoretical analysis of capacity at uncontrolled intersections. First the

gap acceptance theory and follow time was described; including conflict volume determination

through the hierarchy of priorities for two ways stop controlled intersection. Second, after

determining the potential capacity using the computed value and then prepare an adjustment

for this capacity. Finally, computation of the delay to determine the level of service (LOS) of

the given intersection is alos described.

30.7 References



2. W S Homburger. Fundamentals of traffic engineering. 2019. 12th Edition, pp 5-1 to 5-5.




Transportation Systems Engineering 31. Channelization

Chapter 31

Channelization

31.1 Introduction

One of the most effective and efficient methods of controlling the traffic on a highway is the

adoption of high intersection geometric design standards. Channelization is an integral part

of at grade intersections and is used to separate turning movements from through movements

where this is considered advisable and hence helps reduce the intensity and frequency of loss

of life and property due to accidents to a large extent. Proper channelization increases capac-

ity, improves safety, provides maximum convenience, and instils driver confidence. Improper

channelization has the opposite effect and may be worse than none at all. Over channelization

should be avoided because it could create confusion and worsen operations.

31.2 Definitions and Important Terms

1. Channelization - It is the separation or regulation of conflicting traffic movements into

definite paths of travel by traffic islands or pavement marking to facilitate the safe and

orderly movements of both vehicles and pedestrians.

2. Conflict - It is defined as the demand for the same highway space by two or more users

of the highway. Conflicts are classified into mainly three types:

(a) Crossing conflicts

(b) Diverging conflicts

(c) Merging conflicts

3. Angle of Intersection - The angle of intersection is that formed by the centerlines

of the intersecting streets. Where the angle of intersection departs significantly (more

than approximately 20o) from right angles, the intersection is referred to as a skewed



Min

or

Angle of Intersection

Major Leg

Leg

Figure 31:1: Angle of Intersection

intersection. Fig. 31:1 shows the angle made between the centre lines of the major and

minor legs.

4. Refuge Areas - The area which is used to give refuge to the pedestrians crossing a

street (the open area between two medians) is known as a refuge area.

31.3 Objectives

The use of channelization is often creative and innovative, providing for vehicle path separation

and distinct and thus in general making traffic flow safer, smoother, simpler and efficient. The

main objectives of channelization can be summarized as follows:

1. Separation of maneuver areas: The drivers should be presented with only one decision

at a time to reduce confusion and the influence of operations caused due to the overlapping

of maneuver areas.

2. Reduce excessively large paved areas: The spread of the paved area can be consider-

ably reduced by the construction of raised islands and medians where these are considered

safe and necessary.

3. Control of maneuver angle:The intensity of accidents can be reduced to a large extent

by providing small angles for merging, diverging and weaving (at low relative speeds) and

approximately right angles for crossing (at high relative speeds). The maneuver angle

can be easily controlled by constructing islands of appropriate shapes and sizes.

4. Favor predominant turning movements: Channelization is also directed for giving

preference to turning movements at an intersection where the proportion of such traffic

is high.



6

1

52

43

Figure 31:2: Illustration of T-intersection channelization, (a)Intersection with no channelization

5. Control of speed: Channelization is also used for supporting stop or speed regulations

by removing differentials in speed for merging, diverging, weaving and crossing by using

the bending and funneling techniques.

6. Protection and storage of turning and crossing vehicles: To shadow slow or

stopped vehicles from other traffic flows.

7. Blockage of prohibited movements: Proper channelization also helps maintain traffic

regulations by making prohibited movements impossible or inconvenient.

8. Provide space for traffic control devices: To provide space for traffic control devices

when the ideal location for the same is within the intersection area.

9. Segregation of non-homogenous flows: Channelization provides separate channels

for turning and through, fast and slow, and opposite direction traffic.

10. Protection of pedestrians and reduction of crossing distances between refuses:

Non-traversable and wide medians provide a refuge for pedestrians crossing a street.

Consider for example the T-intersection shown in Figs. 31:2, 31:3, and 31:4. In Fig. 31:2,

the intersection has no special channelization for helping drivers in avoiding conflicts between

movements. In Fig. 31:3, a passing lane for through vehicles in the eastbound direction and a

westbound right-turn lane has been added, which helps in separating the turning traffic from

the through ones. In Fig. 31:4, the use of lanes is further clarified due to the addition of

channelizing islands.

31.4 Design Principles

Design of a channelized intersection usually involves the following significant controls: the type

of design vehicle, the cross sections on the crossroads, the projected traffic volumes in relation



5

2

4

3

6

1

Figure 31:3: Illustration of T-intersection channelization, (b)Intersection with right-turn and

passing lane

��

��

��

��

��

��

��

��

Figure 31:4: Illustration of T-intersection channelization, (c)Fully channelized intersection

to capacity, the number of pedestrians, the speed of vehicles, and the type and location of

traffic control devices. Furthermore, the physical controls such as right-of-way and terrain have

an effect on the extent of channelization that is economically feasible.

The degree to which each of these principles applies will depend upon the features mentioned

above. While a principle may be modified in its application to a particular site, disregard of

these may result in a hazardous design. The principles may be summarized as follows:

1. Reduction of the Area of Conflict: The impact area is decreased when channelization

is provided, and hence the probability of conflicts is also reduced. The figure below further

clarifies the statement. Fig. 31:5 shows the conflict area in a Y-intersection without

channelization and Fig. 31:6 shows the reduced conflict area in the same intersection

after providing medians.

2. Merging traffic streams at small angles: Merging at small angles permits the flow

of traffic streams with minimum speed differentials. Hence, the gap acceptance time is

also small in such cases. The merging of roadways should be done as shown below in

Fig. 31:7.

3. Reduction of the speed of incoming traffic by bending its path: The speed



Figure 31:5: Conflict area in all paved intersection

Figure 31:6: Conflict area in a channelized intersection

��

��

��

��

��

Figure 31:7: Merging of traffic streams



��

��

��

��

��

��

A

Figure 31:8: Bending path of incoming minor street

��

��

3.5m3.5m

4m6m

6m 4m

Figure 31:9: Reduction of speed by funneling

of vehicles entering into the intersection can be reduced by bending the path to the

intersection approach. However as far as possible the path of the major traffic stream

should not be bent. The above technique is shown below in Fig. 31:8.

4. Reduction of speed of traffic by funneling: The funneling technique can also be

used for reducing the speeds of the incoming vehicles. Due to the decrease in the width

of the lane at the approach, the drivers tend to reduce the speed of their vehicles near

the intersection. Fig. 31:9 shows the funneling technique used for reduction of speed.

5. Protection for turning vehicles/crossing conflicting traffic streams: Provision

of a refuge area between the two opposing streams allows the driver of a crossing vehicle

to select a safe gap in one stream at a time and also provides a safer crossing maneuver.

Fig. 31:10further clarifies the above statement.

6. Discourage prohibited turns by island placement and shape: Undesirable and

prohibited turns can be discouraged by the proper selection of shape and location of the



��

��

��

��

Figure 31:10: Refuge area for protecting crossing or turning traffic

��

��

ONE WAY

Figure 31:11: Properly placed islands discourage prohibited movements

islands. Fig. 31:11 shows how prohibited turns can be discouraged by proper shaping and

placement of islands.

7. Providing locations of traffic control devices: Channelization may provide locations

for the installation of essential traffic control devices, such as stop and directional signs,

signals etc. Fig. 31:12 shows how channelizing devices can also be used for locating traffic

control devices.

31.5 Channelizing devices

A channelizing device can be defined as any structure which helps in providing channelization.

These can be wide raised medians, non-traversable road islands, traversable raised curbs or

even flush channelizing devices. A brief description of the various devices which are used for

the purpose of channelization are given in the following sections.

1. Wide Raised Medians

In this form of channelizing device, a raised wide separator is constructed between the



��

��

��

��

��

Figure 31:12: Location of signal posts on medians at intersections

Figure 31:13: Wide raised median

two opposing lanes and the space on the separator (median) is used either for planting

some trees and/or for providing space for traffic signs etc. Fig. 31:13 shows a typical wide

raised median on a freeway. A median varying between 1.2 m and 30 m in width may

be employed. The higher values of width are adopted on freeways, where sufficient space

is available for the construction of these. In addition, a well-landscaped wide median

will also provide aesthetic benefits to the surrounding neighborhood. A wide median, if

attractively landscaped, is often the most aesthetically pleasing separation method.

2. Non- traversable Raised Islands

In this type of device, a narrower and a higher median than the traversable island is

constructed between the opposing lanes. This class of device has the advantage of a

narrower median, but its use should be restricted to approach roadways with vehicle

speeds of 60 kmph or below. These are generally 15 to 20 cm high and about 60 cm

in width. Due to the height, most of the vehicles are not able to cross the median,

and hence the name. Fig. 31:14 shows a non-traversable raised island constructed on a



Figure 31:14: Non-traversable Raised Island (source: [13])

roadway. These devices are substantial enough that each installation should be carefully

designed, as an inappropriately placed median can constitute a hazard if struck by an

errant vehicle and hence the severity and crash risk is highly increased on the roadways

having non-traversable raised islands.

3. Traversable Raised Curb Systems

In this device, a narrow and mountable type of raised curb is constructed to separate the

traffic moving in the opposing lanes. This class of channelizing device is the narrowest,

and therefore the easiest to fit in a wide range of roadway cross-section widths. The curb

is upto 10 cm in height and upto about 30 cm in width. Curbs are formed with a rounded

shape that will create minimal vehicle deflection upon impact. Generally, it is used with

reboundable, reflectorized vertical panels to provide a visual deterrent to the drivers to

cross over to opposite traffic lane. The main advantage of this type of device is that it can

be installed on existing roadway centerlines, without the need for widening the roadway

approaches to the crossing. Figs. 31:15 and 31:16 shows traversable raised curbs with

and without vertical panels.

4. Flush Channelization

In this type of channelization, a variety of treatments, including raising them above the

pavement just slightly (2 to 5 cm); the application of pavement markings and other types

of contrasting surfaces etc are possible. These may also be unpaved where they are

formed by the pavement edges of existing roadways. In areas where snow plowing may be

necessary, flush islands are the preferred design. Fig. 31:17 below shows how flush islands

can also be used for achieving channelizing objectives. The area seen flushed with the

road surface in Fig. 31:17 is the flush island.



Figure 31:15: Traversable Raised Curb System (without vertical panels)

Figure 31:16: Traversable Raised Curb System (with vertical panels)

Flash Median0

Travel lane11’

Bike lane

5’

Parking 8.5’

Figure 31:17: Flush island providing channelization objectives



��

��

��

��

Figure 31:18: Channelizing Islands

31.6 Traffic Islands

A principle concern in channelization is the design of the islands. An island is a defined area

between traffic lanes for control of vehicle movements. Within an intersection area, a median

or an outer separation is considered to be an island. It may range from an area delineated by

barrier curbs to a pavement area marked by paint.

31.6.1 Classification of Islands

Traffic islands usually serve more than one function, but may be generally classified in three

separate types:

1. Channelizing Islands - These are designed to control and direct traffic movement,

usually turning. Channelizing islands are are shown in Fig. 31:18.

2. Divisional Islands - These are designed to divide opposing or same direction traffic

streams, usually through movements. Fig. 31:19 shows the placing of divisional islands

in a roadway.

3. Refuge islands - Pedestrian islands are provided to serve as safety zones for the aid

and protection of persons on foot. If a divisional island is located in an urban area where

pedestrians are present, portions of each island can be considered a refuge island. Refuge

islands are shown below I Fig. 31:20. The design aspects of the traffic islands are dealt

in detail in the following sections.



��

��

��

��

��

��

Figure 31:19: Divisional Islands

Figure 31:20: Refuge Islands



31.6.2 Design Considerations for Traffic Islands

The necessity for an island should be determined only by careful study, since it is placed in

an area that would otherwise be available for vehicular traffic. The island design should be

carefully planned so that the shape of the island will conform to natural vehicular paths and so

that a raised island will not constitute a hazard in the roadway. A judiciously placed island at

an intersection on a wide street may eliminate the need for traffic signal control by channelizing

traffic into orderly movements. The total design of traffic islands can be studied in three steps:

1. Selection of appropriate island type (barrier, mountable, painted or flush):

The site and traffic conditions in each intersection are different and hence the island type

suitable for each requires separate attention. The traffic island selected may vary from

barrier type islands to flush islands marked on the roadway surface.

2. Determination of shape and size of islands: The shape of the island and its size

in an intersection depends on the geometry and space availability at the same. A proper

shape and size of the island (in case of raised islands) must be selected so that it is able

to both channelize the traffic and not pose any type of hazard.

3. Location relative to adjacent traffic lanes: The islands must be offset from the

roadway by some distance to remove the risk of a vehicle dashing against the same. The

width of offset is maximum at the entry of the island and decreases gradually as one

moves towards the end of it.

31.6.3 Guidelines for selection of island type

As mentioned earlier, each intersection has a unique geometry and flow values, and hence needs

special attention as far as the use of channelization devices are concerned. The main factors

affecting the selection of the island type are:

1. Traffic characteristics at the intersection

2. Cost considerations, and

3. Maintenance needs

The raised islands and flush channelization are dealt with in details in the following sections.



Flush Channelization

Flush Channelization is usually appropriate in the following conditions:

1. On high speed rural highways to separate turning lanes.

2. In constrained locations, i.e. the locations where vehicle path definition is desired but

space for raised islands not available.

3. For separating opposing traffic streams of low speed streets.

4. In areas where frequent removal of snowfall is required, i.e. in places of high snow fall.

5. It can also be used as a temporary channelization either during construction or to test

traffic operations prior to the actual installation of raised islands.

However, the main demerits of this type of channelization are :

1. It is not effective in prohibiting or preventing traffic movements.

2. It is also not appropriate for islands intended to serve as pedestrian refuge.

Raised Islands

The locations where the construction of raised islands assumes importance are:

1. The primary function of the channelizing device is shielding pedestrians or to provide

refuge to pedestrians crossing a street.

2. Also, the primary/secondary function is locating traffic signals or other fixed objects.

3. Intension is to prohibit or prevent certain traffic movements.

4. To separate high volume opposing traffic flows.

5. The raised islands are also particularly important at intersections with unusual geometry

i.e. skewed intersections.

A comparison between the usefulness and the operating conditions of the two types of chan-

nelization is presented in Table. 31:1.



Table 31:1: Flush Channelization vs Raised ChannelizationFLUSH CHANNELIZATION OPERATING CONDITIONS

1. For Right turns High Speeds

2. To provide temporary or trail channelization Rural highway

3. To shadow left turns Minor urban intersections

RAISED CHANNELIZATION OPERATING CONDITIONS

1. Post signs or signals Urban streets

2. Provide pedestrian refuse Low speeds

3. Prevent wrong way movements High volumes

31.6.4 Guidelines for design of Traffic Islands

The main design principles followed for the design of the shape and size and shape of the traffic

island are as follows:

1. Shape and size: Islands are generally either narrow and elongated or triangular in

shape, are normally situated in areas of the roadway outside the planned vehicle paths,

and are shaped and dimensioned as component parts of the street or intersection layout.

The actual size differs as governed by site conditions, but the following minimum size

requirements should be met to insure that the island will be large enough to command

attention.

2. Traffic lanes or turning roadways should appear natural and convenient to their intended

users.

3. Number of islands should be held to a practical minimum to avoid confusion.

4. The islands should be large enough to be effective. Small islands do not serve as chan-

nelizing devices and pose maintenance problems.

5. These should not be introduced at locations with restricted sight distance or middle of

sharp horizontal curves due to sight distance considerations.

Table. 31:2 gives the recommended minimum and desired area values of the traffic islands in

typical urban and rural intersections.



Table 31:2: Recommended Island SizesLocation of Intersection Size(Sq.metres)

Minimum Desired

Urban 4.65 7

Rural and High Speed urban/Suburban 7 9.3

Direction ofTraffic

Direction of Traffic

Direction ofTraffic

Oe

Od

R2

Oa

Ob

R1

Of

R3

Oe

Figure 31:21: Recommended Offset Dimensions for location of Traffic Islands

31.6.5 Guidelines for providing offset to the traffic islands from the

road edge

The orientation of islands near intersections is dictated by the alignment of the intersecting

roadways and their associated travel paths. Proper island design must minimize the potential

for vehicle impacts and reduce their severity. This is most often accomplished by offsetting the

approach ends of islands from the edge of travel lane them, tapering them inward. Another

technique that is the use of rounded approach noses that may also be sloped downward on

their approach ends. The general design dimensions of corner islands for roadways in shown

in Fig. 31:21. Another design consideration for islands is their surface finishing. Islands may

be paved or landscaped. Though paved islands are easier to maintain, yet they are typically

not as aesthetically pleasing. The use of colors that have contrast with the pavement surface is

desirable because they allow the island to be more clearly seen by drivers. Normally concrete

islands are paired with asphalt roadways and vice versa. Brick pavers are also used in areas

where aesthetics are important. Other concerns include the need to provide adequate slope to

the surface of the island to facilitate drainage and to keep the island free of sight obstructions

and collision. Thus, all landscaping features should be kept below the clear vision envelop and



SingleRadius

Figure 31:22: Various types of curves used for a turning roadway , (a)Simple Radius

should not incorporate other fixed hazards.

Curve/taper combinations for turning roadways and islands

The combination of a simple radius flanked by tapers can often fit the pavement edge more

closely to the design motor vehicle than a simple radius (with no tapers). Figs. 31:22, 31:23

and 31:24 shows the various types of curves that can be used for a roadway. The closer fit

can be important for large design motor vehicles where effective pavement width is small (due

either to narrow pavement or need to avoid any encroachment), or where turning speeds greater

than the design speed are desired. Table. 31:3 and Table. 31:4 summarizes design elements

for curve/taper combinations that permit various design motor vehicles to turn, without any

encroachment, from a single approach lane into a single departure lane (Note: W should be

determined using the turning path of the design vehicle) The width of the roadway can be

found out from Table. 31:5 given below.



Offset

Taper

SingleRadius

Taper

Figure 31:23: Various types of curves used for a turning roadway, (b)Radius and Taper

Island

LargerRadius

SmallerRadius

LargerRadius

Figure 31:24: Various types of curves used for a turning roadway, (c)Turning Roadway



Table 31:3: Curve and Taper Corner Design Elements

Angle of Turn Design Vehicle Radius Offset Taper Length

(Degrees) (metres) (OS metres) (T1 metres)

Passenger Car 7.5 0.6 6

75 Single Unit Truck 13.5 0.6 6

Sigle Trailor Unit 19.5 0.9 13.5

Passenger Car 6 0.75 7.5

90 Single Unit Truck 12 0.6 6

Sigle Trailor Unit 18 1.2 18

Passenger Car 6 0.6 -

120 Single Unit Truck 9 0.9 -

Sigle Trailor Unit 13.5 1.2 18

Table 31:4: Design elements for Turning Roadways

Angle of Turn Design Vehicle Radius(metre) Offset

(Degrees) R1-R2-R1 (OS metre)

Passenger Car (P) 30-22.5-30 0.6

75 Single Unit Truck (SU) 36-13.5-36 0.6

Semi-Trailor Unit (WB-50) 45-15-45 2

Passenger Car (P) 30-6-30 0.8

90 Single Unit Truck (SU) 36-12-36 0.6

Semi-Trailor Unit (WB-50) 54-18-54 2

Passenger Car (P) 30-6-30 0.6

120 Single Unit Truck (SU) 30-9-30 0.9

Semi-Trailor Unit (WB-50) 54-12-54 2.6



Table 31:5: Width of roadway required for negotiating the turn for different classes of vehicles

(W)

Radius on One-Lane One Way One-Lane One Way Two way operation

inner edge Operation (No Operation (Having Either One way or Two

of provision of passing a provision of passing a way (Same Type of vehicle

pavement stalled vehicle) in metre stalled vehicle) in metre in both lanes) in metre

in metre P SU WB-50 P SU WB-50 P SU WB-50

15 3.9 5.4 7.8 6 8.7 13.2 7.8 10.5 15

22.5 3.9 5.1 6.6 5.7 8.1 10.8 7.5 9.9 12.6

30 3.9 4.8 6.3 5.7 7.5 10.2 7.5 9.3 12

45 3.6 4.8 5.7 5.4 7.2 8.7 7.2 9 10.5

60 3.6 4.8 5.1 5.4 6.9 8.1 7.2 8.7 9.9

90 3.6 4.5 5.1 5.4 6.6 7.5 7.2 8.4 9.3

31.7 Guidelines for design of Median islands

The general guidelines to be followed in the design of median islands (separators of opposing

traffic flows) are:

1. The approach noses should be offset 0.6 to 1.8 m from through lanes to minimize accidental

impacts.

2. Shape should be based on design turning paths and island function. (Generally parabolic

or circular arcs are used)

3. The length of median before the intersection is related to approach speed (normally 3 sec

driving time to intersection). It is also affected by available widths, taper designs and

local constraints.

4. The width of the medians should serve its primary intended function.

5. The median should always be provided well past crest vertical curves.

Fig. 31:25 shows the general design elements of medians provided just at the approach to a

intersection. The required median widths for performing their intended functions are provided

by AASHTO and are shown in Table. 31:6 below. These widths are empirical and can be

applied at an intersection with reasonable efficiency.



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Barrier type median

Offset nosefrom

(0.6m min)

3 Sec. Travel time(min)

Mountable type medianRC at barrier nose or beyond

desirable

0.3m R

Traveltime

0.6m Stub

0.6m R

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W1 = Undivided approachwidth

W2 = Divided approachwidth

W3 = (W1/2) or 4.2mwhichever is larger

W4 = (W3 + W2/2 desirable

W3 = W2 + 0.3m

W1

112 Sec.

W2

W2

W4

W5W5

W3

Figure 31:25: Design Criteria for raised median approaches to intersections

Table 31:6: Basic median functions and their required width

Function Width in metre

Minimum Desirable

Separation of opposing traffic 1.2 3

Provision of pedestrian refuse 1.8 4.2

Provision of storage for left-turn vehicles 4.8 6

Provision for protection of vehicles crossing 7.5 9

through lanes

Provision for U turns, inside to outside lanes 4.8 6

Provision for U-turns, inside to inside lanes 7.8 9



Departure Taper

Approach TaperTaper

Bay

LengthDeceleration

StorageLength

Figure 31:26: Components of Auxiliary Lane

31.7.1 Auxiliary Lanes

Auxiliary lanes are used under conditions of relatively high traffic volumes in the intersections.

In these cases, traffic congestion problems can be significantly alleviated with auxiliary lanes

to handle turning movements. The median lane should be 12 feet (3.6m), but not less than 10

feet (3.0m) wide and should be clearly marked for this purpose.

Auxiliary lanes can also be introduced to provide for both left turns and right turns at inter-

sections. The need for such lanes is determined by capacity analysis and the acceptable level of

service designated for the facility. The lanes should be at least 2.7m wide for reconstruction and

resurfacing projects and at least 3.0m, preferably 3.6m for new construction projects. Auxiliary

lane shoulders can be reduced to 0.6 m wide on rural sections and 0 m wide on sections with

curb and gutter. The length of auxiliary lanes consists of five components:

1. Approach Taper

2. Deceleration Length

3. Bay Taper

4. Storage Length, and

5. Departure Taper.

A typical auxiliary lane with the components are shown in Fig. 31:26 below. These are discussed

in detail in the following section.

1. Approach Taper- The length of the approach taper varies with operating speeds. Guide-

lines for determining lengths are: (i) For speeds 70 kmph and over: L = 0.6WS, and (ii)

For speeds under 70 kmph: L = WS2/100 where, L is the length of entering taper in m,

W is the width to be tapered in m, and S is the operating Speed in kmph.



Table 31:7: Deceleration length vs Design Speed

Design Speed Deceleration Length

(kmph) (m)

40 35

55 45

65 55

70 65

80 95

2. Deceleration Length- The deceleration length is that required for a comfortable stop

of a vehicle from a speed that is typical of the average running speed on the facility.

The Bay Taper can be considered part of the deceleration length. AASHTO has again

given a table for calculating the decelerating length value from the design speed value

(Table. 31:7).

3. Bay Taper - This is a straight line taper with ratios varying from 5:1 to 10:1. Higher

speed facilities should generally have longer tapers. Empirically, the minimum and max-

imum values of bay taper are taken as 18m and 36m respectively.

4. Storage Length - The storage length should be sufficiently long to store the number of

vehicles likely to accumulate during the average daily peak period.

(a) At unsignalized intersections, length to be based on the number of vehicles likely to

arrive in an average 2-minute period within the peak hour.

(b) At signalized intersections, the required length depends on the signal cycle length,

the signal phasing arrangement and the rate of arrivals and departures of left turning

vehicles.

5. Departure Taper - The departure taper is normally taken equal in length to that of

the approach taper and should begin opposite the beginning of the Bay Taper.

31.7.2 Shape of Median Ends

Generally, two types of end shapes are used in practice:-semicircular shapes and bullet nose.

The shape adopted normally depends on the effective median width at the end of the median.

The dimensions of the various parameters for semi-circular and bullet nose ends area as: Semi-

circular- L = 2 × ControlR, R1 = M/2. Bullet-nose- L = ControlR, R1 = M/2, R2 = M/5



Table 31:8: Criteria for selection of median end shape

Effective Median Width Median End Shape

Less than 3m Semi-circular

3m - 20m Bullet Nose

Over 20m Treated as a separate intersection

L

Lane

Lane

(Nor

mal

) −M

Contro

lR

R1

Figure 31:27: Shapes of Median ends, (a)Semi-circular

The criteria for the selection of median end is as given below in Table. 31:8. The two shapes

are illustrated in Figs. 31:27 and 31:28. The designer should evaluate each intersection to

determine the best median opening shape that will accommodate the design vehicle.

31.7.3 Design of Median Openings

Median openings, sometimes called crossovers, provide for vehicular crossings of the median at

designated locations. The design of a median opening should be based on traffic volumes and

Lane

Lane

ControlR

M

b

L

R1

R1

R2

R1

R1

R2

Figure 31:28: Shapes of Median ends, (b)Bullet-nose



intersection L

Shoulder

Bay Taper

Bay Taper

Left turn Lane

ParabolicMMedianShoulder5.1

5.1

5.1

R=Var5.1

Left turn LaneParabolic

Flare Flare

Figure 31:29: Intersection Median Opening

types of turning vehicles. Cross and turning traffic must operate in conjunction with the through

traffic on the divided highway. This requirement makes it necessary to know the volume and

composition of all movements occurring simultaneously during the design hours. The design

of a median opening becomes a matter of considering what traffic is to be accommodated,

choosing the design vehicle to use for layout controls for each cross and turning movement,

investigating whether larger vehicles can turn without undue encroachment on adjacent lanes

and, finally, checking the intersection for capacity. If the capacity is exceeded by the traffic

load, the design must be expanded, possibly by widening or otherwise adjusting widths for

certain movements. Traffic control devices such as yield signs, stop signs or traffic signals

may be required to regulate the various movements effectively and to improve the efficiency of

operations. Median openings at close intervals on other types of highways create interference

with fast through traffic. Median openings should be spaced at intervals no closer than 500

m. However, if a median opening falls within 100 m of an access opening, it should be placed

opposite the access opening. Also, the length of median opening varies with width of median

and angle of intersecting roads. Fig. 31:29 shows the intersection median opening. The median

openings for the different classes of design vehicle are as given in the Table. 31:9.

31.8 Developing a Channelization Plan

1. Channelization is more of an art rather than science. Every intersection requires a spe-

cial study because of variations in physical dimensions, turning movements, traffic and

pedestrian volumes, type of traffic control etc.

2. In the next step several island configurations are considered and compared. Then a choice

is made between curbed, raised islands and flush channelization or pavement markings.

3. Next it must be checked that the design is compatible to handle turning movements of



Table 31:9: Median Openings

Width of Passenger Car Single Unit Truck Single Trailor Unit

Median(m) Semi - circular Bullet nose Semi - circular Bullet nose Semi - circular Bullet nose

1.2 22.8 22.8 28.8 28.8 43.8 36.6

1.8 22.2 18 28.2 22.8 43.2 34.5

2.4 21.6 15.9 27.6 20.4 42.6 33

3 21 14.1 27 18.6 42 31.5

3.6 20.4 12.9 26.4 17.4 41.4 30

4.2 19.2 12 25.8 15.9 40.8 28.8

4.8 18 12 25.2 15 40.2 27.6

6 16.8 12 24 13.2 39 25.5

large vehicles. Also, it should be such that the vehicles are guided in normal wheel paths,

so that the island does not create an obstruction in the roadway.

4. Signing and marking are redesigned to guide drivers and avoid confusion.

5. The final plan includes details of civil and electrical engineering features (like drainage

facilities, curbs, lightings, signals etc.) required for the project completion.

31.9 Typical Channelization Examples

Some typical channelization ways used in practice are as given below. Figs. 31:30 to 31:41

indicate both normal channelization and high type channelization techniques for various inter-

sections and situations.

31.10 Turning Vehicle Templates

In the design of intersections the turning paths of vehicles assumes utmost importance. The

turning paths of design vehicles are given in transparent templates such as the one shown in

Fig. 31:17 and Fig. 31:18. These templates are placed over the intersection plan to trace the

path of the turning vehicle. Once this is done, proper islands and other traffic control devices

can be designed. As per AASHTO, the turning templates are drawn at an approximate scale of

1”=50’. The radius of the template is measured to the outside front wheel path at the beginning



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Figure 31:30: Channelization for Y Intersections, (a)For low Flows

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Figure 31:31: Channelization for Y Intersections, (b)For High Flows

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Figure 31:32: Channelization for T Intersections, (a)For low Flows



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Figure 31:33: Channelization for T Intersections, (b)For High Flows

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Figure 31:34: Channelization for T or Y Intersections (Channelized-High Type)

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Figure 31:38: Channelization for 4-Leg Intersections (Channelized-High Type)



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Figure 31:39: Channelization for 4-Leg Intersections (Channelized-High Type)

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Figure 31:40: Channelization for Multi - leg Intersections

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Figure 31:41: Channelization for Multi - leg Intersections



Table 31:10: Dimensions of some common Design vehicles

Design Vehicle Type Symbol Overall Dimension

Height (m) Width (m) Length (m)

Passenger Car P 1.3 2.1 5.8

Single Unit Truck SU 4.1 2.6 9.1

Single Unit Bus BUS 4.1 2.6 12.1

Intermediate Semi-Trailer WB-15 4.1 2.6 16.7

U

F_A

R_1

wb_2 wb_1

LB A

WBWB

Single RearWheel for P Vehicle

Double Rear AxleSingle Rear Axle

Figure 31:42: Design vehicle Dimensions and Turning Properties

of the curve. The design vehicle for the purpose can be taken out of a list of 16 different types

of vehicles suggested by AASHTO. The dimensions of some of the design vehicles are given in

Table. 31:10 below. The templates are applied to the layout of intersections and other facilities

in accommodating vehicle maneuvers, including driveways, car parking, truck loading and bus

terminals. Here we shall take the cases of a passenger car (P) and a single unit truck (BUS) as

the design vehicles. The various design elements and their dimensions are shown in Fig. 31:42

and Table. 31:11 respectively. The templates were developed to include a variety of angles,

with specific configurations for every 30 degrees of turn (30, 60, 90, 120, 150 and 180). By

special manipulation of the template, any degree of turning can be produced within an overall

range of 20 to 200 degrees. The four variables-vehicle type, turning radius, angle of turn and

scale-provide full flexibility in the use of turning vehicle templates for layout and design. To

permit greater latitude in maneuvering of buses, single unit trucks and passenger cars, special

Table 31:11: Design vehicle Dimensions and Turning Properties for 90o turns

Vehicle WB MinimumTurn

Designation L(m) (m) A(m) B(m) W(m) U(m) U** (m) FA RT

(m) (m) (m)

BUS 12.1 7.5 2 2.5 2.6 2.6 4.98 1.25 13

Passenger Car (P) 5.8 3.4 0.9 15 2.1 1.8 2.61 0.6 7.5



Table 31:12: List of Templates

Vehicle Type Scales Turning Radius-m Average Size-cm

1:250 R= 13 & 18 20 × 25

BUS 1:500 R= 13 & 18 18 × 18

1:250 R=13 to 50 20 × 25

Bar Template

1:250 R=7.5 18 × 18

Passenger car 1:250 R=7.5 to 30 18 × 18

Bar template

bar tenders are included, consisting of turning radii in the range of 13 to 50 meters for the

first two and 5.5 to 30 meters for the last type of vehicles which are outside the scope of this

discussion. The list of templates for bus and passenger cars is shown in the Table. 31:12. The

templates for the Passenger Car (P) and Bus are as shown in Fig. 31:43, 31:44 below.



1.8’Passenger Car("P") 30

o

60o

90o

120 o

150 o180o

Figure 31:43: Design Template for Passenger Car (P)

Numerical example 1

Provide channelization for an intersection having EW as the major road. The major and minor

roads intersect at right angles. The design vehicle is WB-50 (R=25m) and design speed is 45

kmph. The intersection is unsignalised. EW road has 2 lanes in each direction and NS has

1 lane for each direction. Take lane width =3.6 m. Provide bullet nose median ends. Also

provide channelizing island for free right for WS bound traffic.

Solution : The approach taper for auxiliary lane is equal to 3.6 × 45× 45/100 = 73 m. The

deceleration Taper is taken as 40 m. Considering a 1:10 taper, the Bay Taper is found out

to be 18 m. Let the storage length = 30 m (say). Now from Table. 31:9, it is found that for

bullet nose median end, Median Opening = 30 m. The dimensions of all the components of

the auxiliary lane are shown in Fig. 31:45. The width required for the WB- 50 semi-trailor

unit is found to be about 6.5 m. Additional 0.5 m is provided on the outer side and 0.3 m is

provided on the inner side away from the edge of the island. For the turning roadway for the

W-S direction, the single offset method is used. At 0.3 + 0.5 + 6.5 = 7.3 m from the island

edge, a circle of radius 25 m is laid out. Then two tapers of slope 1:15 is laid out on either side

of the arc to join with the straight edge on either side. Thus the channelization is provided for

the W-S approach. Similar method can be used for designing the channelization schemes of the

other directions as well. The channelization for the W-S approach is shown in Fig. 31:46.



Bus 30o

60o

90o

120 o150 o180

o

Figure 31:44: Design Template for Bus

30 m

73 m

73 m40 m

18 m 30 m

Figure 31:45: Dimensions of components of the auxiliary lane for the intersection

1:15

1:15

R=25m

73 m

Figure 31:46: Channelization for the W-S direction with traffic island



WYE INTERSECTION

Figure 31:47: Wye Intersection

Numerical example 2

Following the principles of channelization suggest suitable island schemes for the following

intersections (considering both high relative speed and low relative speed) (Figs. 31:47, 31:48)

Solution

1. Y Intersection (Figs. 31:49, 31:50 and 31:51)

2. Skewed intersection (Figs. 31:52, 31:53 and 31:54)

31.11 Summary

This chapter presents one of the simple and cost effective way of intersection control, namely

the channelization. This is normally adopted for low and medium volume roads. The chapter

contains the design principles, traffic islands, and median.

31.12 References

1. Transportation research board channelization-the design of highway intersections at grade,

1962.

2. Mass highway, 2006- intersections, 2006.



SKEWED CROSS ROAD

Figure 31:48: Skewed Cross Road

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Figure 31:49: (a) Y - Intersection



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Figure 31:51: (c) Y - Intersection



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Figure 31:52: (a) Skewed Intersection

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3. 2011.

4. Channelization, 2011.

5. Highway design manual, 2000- pedestrian facility design, 2011.

6. Road design manual, 2011.

7. Roosevelt street - neighborhood traffic management plan, 2011.

8. Streetsblog, 2011.

9. Us department of transportation federal highway administration- guidance on the use of

traffic channelizing devices at highway-rail grade crossings, 2011.

10. Us department of transportation federal highway administration- innovative intersection

safety improvement strategies and management practices:a domestic scan, 2011.

11. Us department of transportation federal highway administration-safety benefits of raised

medians and pedestrian refuge areas, 2011.

12. S K Khanna C E G Justo. Highway Engineering. Nem Chand and Bros, Roorkee, 2001.

13. T R Neuman. Intersection channelization design guide. Transportation Research Board.

TRB NCHRP R 279, Washington, D.C., 1985.



14. R J Paquette, N Ashford, and P H Wright. Transportation Engineering : Planning and

Design. John Wiley, New York, 1972.






Transportation Systems Engineering 32. Traffic Rotaries

Chapter 32

Traffic Rotaries

32.1 Overview

Rotary intersections or round abouts are special form of at-grade intersections laid out for the

movement of traffic in one direction around a central traffic island. Essentially all the major

conflicts at an intersection namely the collision between through and right-turn movements are

converted into milder conflicts namely merging and diverging. The vehicles entering the rotary

are gently forced to move in a clockwise direction in orderly fashion. They then weave out of

the rotary to the desired direction. The benefits, design principles, capacity of rotary etc. will

be discussed in this chapter.

32.2 General

32.2.1 Advantages and disadvantages

The key advantages of a rotary intersection are listed below:

1. Traffic flow is regulated to only one direction of movement, thus eliminating severe con-

flicts between crossing movements.

2. All the vehicles entering the rotary are gently forced to reduce the speed and continue to

move at slower speed. Thus, none of the vehicles need to be stopped,unlike in a signalized

intersection.

3. Because of lower speed of negotiation and elimination of severe conflicts, accidents and

their severity are much less in rotaries.

4. Rotaries are self governing and do not need practically any control by police or traffic

signals.



5. They are ideally suited for moderate traffic, especially with irregular geometry, or inter-

sections with more than three or four approaches.

Although rotaries offer some distinct advantages, there are few specific limitations for rotaries

which are listed below.

1. All the vehicles are forced to slow down and negotiate the intersection. Therefore, the

cumulative delay will be much higher than channelized intersection.

2. Even when there is relatively low traffic, the vehicles are forced to reduce their speed.

3. Rotaries require large area of relatively flat land making them costly at urban areas.

4. The vehicles do not usually stop at a rotary. They accelerate and exit the rotary at

relatively high speed. Therefore, they are not suitable when there is high pedestrian

movements.

32.2.2 Guidelines for the selection

Because of the above limitation, rotaries are not suitable for every location. There are few

guidelines that help in deciding the suitability of a rotary. They are listed below.

1. Rotaries are suitable when the traffic entering from all the four approaches are relatively

equal.

2. A total volume of about 3000 vehicles per hour can be considered as the upper limiting

case and a volume of 500 vehicles per hour is the lower limit.

3. A rotary is very beneficial when the proportion of the right-turn traffic is very high;

typically if it is more than 30 percent.

4. Rotaries are suitable when there are more than four approaches or if there is no separate

lanes available for right-turn traffic. Rotaries are ideally suited if the intersection geometry

is complex.

32.3 Traffic operations in a rotary

As noted earlier, the traffic operations at a rotary are three; diverging, merging and weaving.

All the other conflicts are converted into these three less severe conflicts.



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Figure 32:1: Traffic operations in a rotary

1. Diverging: It is a traffic operation when the vehicles moving in one direction is separated

into different streams according to their destinations.

2. Merging: Merging is the opposite of diverging. Merging is referred to as the process of

joining the traffic coming from different approaches and going to a common destination

into a single stream.

3. Weaving: Weaving is the combined movement of both merging and diverging movements

in the same direction.

These movements are shown in figure 32:1. It can be observed that movements from each

direction split into three; left, straight, and right turn.

32.3.1 Design elements

The design elements include design speed, radius at entry, exit and the central island, weaving

length and width, entry and exit widths. In addition the capacity of the rotary can also

be determined by using some empirical formula. A typical rotary and the important design

elements are shown in figure 32:2

32.3.2 Design speed

All the vehicles are required to reduce their speed at a rotary. Therefore, the design speed

of a rotary will be much lower than the roads leading to it. Although it is possible to design

roundabout without much speed reduction, the geometry may lead to very large size incurring



splitterisland

lineGIVE WAY

width

radius of

circle

exit width

widthentry

entryradius

exit radius

weavin

g length

radius ofthe centralisland

widthweaving

circulation width

approach

the inscribed

speed = 30 − 40kmph

Rentry = 20 − 25m

Rexit = Rentry × 1.5to2

RCentralIsland = Rentry × 1.3

Figure 32:2: Design elements of a rotary

huge cost of construction. The normal practice is to keep the design speed as 30 and 40 kmph

for urban and rural areas respectively.

32.3.3 Entry, exit and island radius

The radius at the entry depends on various factors like design speed, super-elevation, and

coefficient of friction. The entry to the rotary is not straight, but a small curvature is introduced.

This will force the driver to reduce the speed. The entry radius of about 20 and 25 metres is

ideal for an urban and rural design respectively.

The exit radius should be higher than the entry radius and the radius of the rotary island so

that the vehicles will discharge from the rotary at a higher rate. A general practice is to keep

the exit radius as 1.5 to 2 times the entry radius. However, if pedestrian movement is higher

at the exit approach, then the exit radius could be set as same as that of the entry radius.

The radius of the central island is governed by the design speed, and the radius of the entry

curve. The radius of the central island, in practice, is given a slightly higher radius so that the

movement of the traffic already in the rotary will have priority. The radius of the central island

which is about 1.3 times that of the entry curve is adequate for all practical purposes.

32.3.4 Width of the rotary

The entry width and exit width of the rotary is governed by the traffic entering and leaving the

intersection and the width of the approaching road. The width of the carriageway at entry and

exit will be lower than the width of the carriageway at the approaches to enable reduction of

speed. IRC suggests that a two lane road of 7 m width should be kept as 7 m for urban roads

and 6.5 m for rural roads. Further, a three lane road of 10.5 m is to be reduced to 7 m and

7.5 m respectively for urban and rural roads.

The width of the weaving section should be higher than the width at entry and exit. Nor-

mally this will be one lane more than the average entry and exit width. Thus weaving width



d

b

c

d

c

b

aa

Figure 32:3: Weaving operation in a rotary

is given as,

wweaving =

(

e1 + e2

2

)

+ 3.5m (32.1)

where e1 is the width of the carriageway at the entry and e2 is the carriageway width at exit.

Weaving length determines how smoothly the traffic can merge and diverge. It is decided

based on many factors such as weaving width, proportion of weaving traffic to the non-weaving

traffic etc. This can be best achieved by making the ratio of weaving length to the weaving

width very high. A ratio of 4 is the minimum value suggested by IRC. Very large weaving

length is also dangerous, as it may encourage over-speeding.

32.4 Capacity

The capacity of rotary is determined by the capacity of each weaving section. Transportation

road research lab (TRL) proposed the following empirical formula to find the capacity of the

weaving section.

Qw =280w[1 + e

w][1 −

p

3]

1 + wl

(32.2)

where e is the average entry and exit width, i.e, (e1+e2)2

, w is the weaving width, l is the length

of weaving, and p is the proportion of weaving traffic to the non-weaving traffic. Figure 32:3

shows four types of movements at a weaving section, a and d are the non-weaving traffic and b

and c are the weaving traffic. Therefore,

p =b + c

a + b + c + d(32.3)

This capacity formula is valid only if the following conditions are satisfied.

1. Weaving width at the rotary is in between 6 and 18 metres.



1405

400

505

510

375 408650

500

600

250

1260

1140

420350

370

1433

N

EW

S

Figure 32:4: Traffic approaching the rotary

2. The ratio of average width of the carriage way at entry and exit to the weaving width is

in the range of 0.4 to 1.

3. The ratio of weaving width to weaving length of the roundabout is in between 0.12 and

0.4.

4. The proportion of weaving traffic to non-weaving traffic in the rotary is in the range of

0.4 and 1.

5. The weaving length available at the intersection is in between 18 and 90 m.

Numerical example

The width of a carriage way approaching an intersection is given as 15 m. The entry and exit

width at the rotary is 10 m. The traffic approaching the intersection from the four sides is

shown in the figure 32:4 below. Find the capacity of the rotary using the given data.

Solution

• The traffic from the four approaches negotiating through the roundabout is illustrated in

figure 32:5.

• Weaving width is calculated as, w = [e1+e2

2] + 3.5 = 13.5 m

• Weaving length, l is calculated as = 4×w = 54 m



S

370

350

650

510250

500

E375

510510

505

400 350

600

N

650

375505

+

408

+ +

+600+375

+

+

370

+

600

370

W

420

500

Figure 32:5: Traffic negotiating a rotary

• The proportion of weaving traffic to the non-weaving traffic in all the four approaches is

found out first.

• It is clear from equation,that the highest proportion of weaving traffic to non-weaving

traffic will give the minimum capacity. Let the proportion of weaving traffic to the non-

weaving traffic in West-North direction be denoted as pWN , in North-East direction as

pNE, in the East-South direction as pES, and finally in the South-West direction as pSW .

• The weaving traffic movements in the East-South direction is shown in figure 32:6. Then

using equation,

pES = 510+650+500+600510+650+500+600+250+375

=22602885

=0.783

pWN = 505+510+350+600505+510+350+600+400+370

=19652735

=0.718

pNE = 650+375+505+370650+375+505+370+510+408

=19002818

=0.674

pSW = 350+370+500+375350+370+500+375+420+600

=15952615

=0.6099

• Thus the proportion of weaving traffic to non-weaving traffic is highest in the East-South

direction.

• Therefore, the capacity of the rotary will be capacity of this weaving section. From

equation,

QES =280 × 13.5[1 + 10

13.5][1 −

0.7833

]

1 + 13.554

= 2161.164veh/hr. (32.4)



d

b

c

a

d

c

b

a

375

250

510+650

500+600

Figure 32:6: Traffic weaving in East-South direction

32.5 Summary

Traffic rotaries reduce the complexity of crossing traffic by forcing them into weaving operations.

The shape and size of the rotary are determined by the traffic volume and share of turning

movements. Capacity assessment of a rotary is done by analyzing the section having the greatest

proportion of weaving traffic. The analysis is done by using the formula given by TRL.

32.6 References


New Delhi, 1987.


Transportation Systems Engineering 33. Grade Separated Intersection

Chapter 33

Grade Separated Intersection

33.1 Overview

An intersection is the area shared by the joining or crossing of two or more roads. Since the

main function of an intersection is to enable the road user to make a route choice, it is a point

of decision. Hence the problems that are encountered by the motorist while passing through an

intersection must be recognized and the design should be in such a way that the driving task

is as simple as possible.

Intersection is also a point of large number of major conflicts, besides a point of decision.

These conflicts may be due to the crossing maneuvers of vehicles moving in different directions.

Good intersection design results from a minimization of the magnitude and characteristics of

the conflicts and a simplification of driver route selection process.

33.2 Classification of Intersection

Intersections are classified depending upon the treatment of crossing conflicts as follows (i) At

Grade Intersection and (ii) Grade Separated Intersection.

33.2.1 Grade Separated Intersection

It is a bridge that eliminates crossing conflicts at intersections by vertical separation of roadways

in space. Grade separated intersection are otherwise known as Interchanges. Grade separated

intersections cause less hazard and delay than grade intersections. Route transfer at grade

separations is accommodated by interchange facilities consisting of ramps. Interchange ramps

are classified as Direct, Semi-Direct and Indirect. Interchanges are described by the patterns

of the various turning roadways or ramps. The interchange configurations are designed in such

a way to accommodate economically the traffic requirements of flow, operation on the crossing



facilities, physical requirements of the topography, adjoining land use, type of controls, right-

of-way and direction of movements.

The ultimate objective of grade separated intersections is to eliminate all grade crossing

conflicts and to accommodate other intersecting maneuvers by merging, diverging and weaving

at low relative speed. The relative speed of the conflicting vehicle streams is an important

factor affecting the significance of a conflict. The benefit of providing for low relative speed is

twofold. First, events unfold more slowly allowing more judgement time and second, in case of

an impact the total relative energy to be absorbed are less and hence, the damage is less. In

addition, when relative speed is low, the average motorist will accept a smaller time gap space

between successive vehicles to complete his move. This condition increases roadway capacity.

33.2.2 Classification of Grade Separated Intersection

One of the distinctions made in type of interchange is between the directional and the non

directional interchange. Directional interchanges are those having ramps that tend to follow

the natural direction of movement. Nondirectional interchanges require a change in the natural

path of traffic flow. A comprehensive classification plan for grade separated intersection design

which includes all possible geometric patterns has not yet been developed. The design and

operational characteristics of each of the major interchange types are mentioned as follows and

are discussed in the following sections.

1. Underpass

2. Overpass

3. Trumpet Interchange

4. Diamond Interchange

5. Cloverleaf Interchange

6. Partial Cloverleaf Interchange

7. Directional Interchange

8. Bridged Rotary



Underpass

An underpass or a tunnel is an underground passageway, completely enclosed except for open-

ings for ingress and egress, commonly at each end. A tunnel may be for foot or vehicular road

traffic, for rail traffic. If an underpass is constructed for pedestrians and/or cyclists beneath

a road or railway, allowing them to reach the other side in safety, then such a construction

is termed as a Subway. These are constructed when it is necessary for pedestrians to cross a

railroad or a limited-access highway. Subways may also be constructed for the benefit of wildlife

Overpass

An overpass also known as a flyover, is a bridge, road, railway or similar structure that crosses

over another road or railway. A pedestrian overpass allows pedestrians safe crossing over busy

roads without impacting traffic. And Railway overpasses are used to replace at-grade crossing

as a safer alternative. Overpasses allows for unobstructed rail traffic flow from mixing with

vehicular and pedestrian traffic. Stack interchanges are made up of many overpasses.

Trumpet Interchange

Trumpet interchanges have been used where one highway terminates at another highway. These

involve at least one loop ramp connecting traffic either entering or leaving the terminating

expressway with the far lanes of the continuous highway. These interchanges are useful for

highways as well as toll roads, as they concentrate all entering and exiting traffic into a single

stretch of roadway, where toll booths can be installed. Trumpets are suitable at the locations

where the side road exists on only one side of the freeway, and traffic is relatively low. Each

entrance and exit consists of acceleration or deceleration lanes at each end. It requires only one

bridge and is the most traditional way of grade separating a three way junction. The principal

advantages are low construction cost and are useful for highways as well as toll roads. But



the limitations in employing trumpet interchanges are it leaves a redundant patch of the land

within the loop, Disorienting to navigate for those driving in the direction that uses the loop.

Moreover scaling down the interchange often results in a more dangerous suffers congestion

from articulated lorries that have tipped over.

Diamond Interchange

The diamond Interchange is the simplest form of grade separated intersection between two road-

ways. The conflicts between through and crossing traffic are eliminated by a bridge structure.

This particular intersection has four one way ramps which are essentially parallel to the major

artery. The left turn crossing movement conflicts are considerably reduced by eliminating the

conflict with the traffic in opposite direction. All the remaining left turn conflicts, merging

and diverging maneuver conflicts take place at the terminal point of each ramp. Limitation in

application of this design depends on the operations of these terminals. So, it is suitable for

locations where the volume of left turn traffic is relatively low.

The diamond interchange requires a minimum amount of land and is economical to con-

struct. Also,a diamond interchange generally requires less out-of-the-way travel and vehicle

operating costs are less than those on most other types of interchanges. The single point of exit

from the major roadway eases the problem of signing. This type of interchange requires the



least of right-of-way. With these advantages, the diamonds appear to be the ideal solution to

an intersection problem. But there might be chances of occurrence of conflicts at the locations

where ramps meet the grade separated cross street are to be considered foe high ramp volumes.

Improper design of signal timings at cross streets may result in the inadequacy of capacity for

certain flows.

Cloverleaf Interchange

The full clover interchange eliminates all crossing movement conflicts by the use of weaving

sections. This weaving section is a critical element of cloverleaf design. It replaces a crossing

conflict with a merging, followed some distance farther by a diverging conflict. There are two

points of entry and exit on each through roadway. The first exit is provided before the cross

road structure allows right turn movements. The second exit, immediately after the cross road

structure, allows for left turn movements. A weaving section is created between the exit and

entry points near the structure. Sufficient length and capacity is to be provided to allow for a

smooth merging and diverging operation.

Cloverleaf design requires only one bridge. In this respect, it is the cheapest form providing

for elimination of all crossing maneuvers at grade. Although full cloverleaf interchanges elimi-

nate the undesirable crossing movements of diamond interchanges, they have the disadvantages

of greater travel distances, higher operating costs, difficult merging sections, circuity of travel,

large areas for loops, sight distances to exits at the other side of the bridge, confusion caused by

turning right to go left and large rights-of-way occasioned by the radius requirements necessary

for satisfactory speeds on the ramps.

A variation of the cloverleaf configuration is the cloverleaf with collector-distributor roads.

With the collector-distributor roadway, main roadway operations are much the same as in

diamond interchange. For each direction of travel, there is a single point for exits and a single

point for entrances. Speed change, detailed exit directional signing and the storage and weaving



problems associated with a cloverleaf are transferred to the collector-distributor road, which

can be designed to accommodate greater relative speed differences or encourage smaller ones.

Although this configuration improves the operational characteristics of a cloverleaf interchange,

the disadvantages of greater travel distances and the requirement of extra right-of-way are still

present. The use of a cloverleaf with collector-distributor roads is appropriate at junctions

between a freeway and an expressway where a diamond interchange would not adequately

serve traffic demand.

Major Highway

Cross Street

Collector − Distributor Roads

Partial Cloverleaf Interchange

This is another variation of the cloverleaf configuration. Partial clover leaf or parclo is a

modification that combines some elements of a diamond interchange with one or more loops of a

cloverleaf to eliminate only the more critical turning conflicts. This is the most popular freeway

-to- arterial interchange. Parclo is usually employed when crossing roads on the secondary road

will not produce objectionable amounts of hazard and delay. It provides more acceleration and

deceleration space on the freeway.



Directional Interchange

A Directional interchange provides direct paths for left turns. These interchanges contain ramps

for one or more direct or semi direct left turning movements. Interchanges of two freeways or

interchanges with one or more very heavy turning movements usually warrant direct ramps,

which have higher speeds of operation and higher capacities, compared to loop ramps. Some

designers do not favor entrance of merging traffic in the left lane, which is a characteristic of

most direct-connection bridges. The principal limitations of this type of interchange is higher

cost of construction and requirement relatively large amount of land when compared to the

diamond interchanges and in some cases than cloverleaf interchange. Various combinations of

directional, semi directional and loop ramps may be appropriate for certain conditions. They

are the basic patterns that use the least space, have the fewest or least complex structures,

minimize internal weaving and appropriate for the common terrain and traffic conditions.

33.2.3 Design Components

Acceleration Lane

An acceleration lane is defined as extra pavement, of constant or variable width, placed parallel

or nearly so, to a merging maneuver area to encourage merging at low relative speed. The

major difference in opinion concerning acceleration design stems from lack of information on

driver performance. Field observations have indicated that drivers desire to follow the direct

path even though extra width or tapered section is provided. The length of acceleration lanes

are determined by two factors: (1) Time required for drivers to accelerate to the speed of the

preferential flow from the speed of entry into the acceleration lane and (2) Maneuvering time

required as a supplement to the sight distance which is provided in advance of the acceler-

ation lane. Taper distances are based upon a lateral transition time of about 1/3 sec/ft of

displacement.



LMINOR FLOW

PREFERENTIAL FLOW

POINT WHERE MERGINGVEHICLES ENCROACHESUPON THROUGH TRAFFIC LANE

FORM B DESIGN

FULL WIDTH LANE TAPER

L

PREFERENTIAL FLOW

MINOR FLOW

ENTRANCE CURVE

RESTRICTING CURVE

END OF SPEED

FORM A DESIGN

ENTRANCE CURVE BEGINNING OF TAPER,END OF SPEED

RESTRICTING CURVE

Figure 33:1: Different forms of Acceleration lanes

ENTRANCEACCELERATION LANE

INLE

T N

OS

E

Wearing length

Shoulder

Convergence

450.00’ 300.00’ 157.11’

Figure 33:2: details of length of acceleration lane

Deceleration Lanes

Deceleration lanes are defined as extra pavement of constant or variable width, placed parallel

or nearly so, to a diverging maneuver area to encourage diverging at low relative speed. The

lengths of deceleration lanes are based on the difference in the speed of traffic of the combined

flow (in advance of the collision area) and the speed at which drivers negotiate the critical

diverging channel curve, as well as the deceleration practices of drivers. These deceleration

lane lengths are based on the assumed performance of passenger vehicles only. Extra allowance

must be made for grades and for trucks with different deceleration characteristics. In the figure



below, Form A design is more economical when large speed differentials are to be overcome.

Form B could be advantageous by contrasting pavement colors and Form C design is more

convenient for drivers when small speed differentials are to be eliminated.

TAPER

TRAFFIC LANE

FULL WIDTH LANE

FORM A

BEGINNING OF SPEEDRESTRICTING EXITCURVE

FLOW HAS "CLEARED" THE THROUGHPOINT WHERE VEHICLE IN DIVERGING

FORM C

L = FULL WIDTH LANE

L

L

BEGINNING OF TAPER



BEGINNING OF TAPER

FORM B

Figure 33:3: Different forms of Deceleration lanes

Shoulder

weaving length

141.38’270’

EX

IT N

OS

E

Shoulder

Figure 33:4: details of length of deceleration lane

33.3 Grade separated intersections

As we discussed earlier, grade-separated intersections are provided to separate the traffic in

the vertical grade. But the traffic need not be those pertaining to road only. When a railway



Figure 33:5: Trumpet interchange

line crosses a road, then also grade separators are used. Different types of grade-separators are

flyovers and interchange. Flyovers itself are subdivided into overpass and underpass. When

two roads cross at a point, if the road having major traffic is elevated to a higher grade for

further movement of traffic, then such structures are called overpass. Otherwise, if the major

road is depressed to a lower level to cross another by means of an under bridge or tunnel, it is

called under-pass.

Interchange is a system where traffic between two or more roadways flows at different levels

in the grade separated junctions. Common types of interchange include trumpet interchange,

diamond interchange , and cloverleaf interchange.

1. Trumpet interchange: Trumpet interchange is a popular form of three leg interchange.

If one of the legs of the interchange meets a highway at some angle but does not cross

it, then the interchange is called trumpet interchange. A typical layout of trumpet inter-

change is shown in figure 33:5.

2. Diamond interchange: Diamond interchange is a popular form of four-leg interchange

found in the urban locations where major and minor roads crosses. The important feature

of this interchange is that it can be designed even if the major road is relatively narrow.

A typical layout of diamond interchange is shown in figure 33:6.

3. Clover leaf interchange: It is also a four leg interchange and is used when two highways

of high volume and speed intersect each other with considerable turning movements. The

main advantage of cloverleaf intersection is that it provides complete separation of traffic.

In addition, high speed at intersections can be achieved. However, the disadvantage is



Figure 33:6: Diamond interchange

that large area of land is required. Therefore, cloverleaf interchanges are provided mainly

in rural areas. A typical layout of this type of interchange is shown in figure 33:7.

33.4 Summary

Traffic intersections are problem spots on any highway, which contribute to a large share of

accidents. For safe operation, these locations should be kept under some level of control de-

pending upon the traffic quantity and behavior. Based on this, intersections and interchanges

are constructed, the different types of which were discussed in the chapter.

33.5 References

1. A policy on geometric design of rural highways, 2019.

2. Everett C Carter and Wolfgang S Homburger. Introduction to Transportation Engineer-

ing. Reston Publishers, Virginia, 2019.


New Delhi, 1987.



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Figure 33:7: Cloverleaf interchange



Transportation Systems Engineering 34. Design Priciples of Traffic Signal

Chapter 34

Design Priciples of Traffic Signal

34.1 Overview

Traffic signals are one of the most effective and flexible active control of traffic and is widely

used in several cities world wide. The conflicts arising from movements of traffic in different

directions is addressed by time sharing principle. The advantages of traffic signal includes an

orderly movement of traffic, an increased capacity of the intersection and requires only simple

geometric design. However, the disadvantages of the signalized intersection are large stopped

delays, and complexity in the design and implementation. Although the overall delay may be

lesser than a rotary for a high volume, a user may experience relatively high stopped delay.

This chapter discuss various design principles of traffic signal such as phase design, cycle length

design, and green splitting. The concept of saturation flow, capacity, and lost times are also

presented. First, some definitions and notations are given followed by various steps in design

starting from phase design.

34.2 Definitions and notations

A number of definitions and notations need to be understood in signal design. They are

discussed below:

• Cycle: A signal cycle is one complete rotation through all of the indications provided.

• Cycle length: Cycle length is the time in seconds that it takes a signal to complete one

full cycle of indications. It indicates the time interval between the starting of of green for

one approach till the next time the green starts. It is denoted by C.

• Interval: Thus it indicates the change from one stage to another. There are two types of

intervals - change interval and clearance interval. Change interval is also called the yellow

time indicates the interval between the green and red signal indications for an approach.



Clearance interval is also called all red and is provided after each yellow interval indicating

a period during which all signal faces show red and is used for clearing off the vehicles in

the intersection.

• Green interval: It is the green indication for a particular movement or set of movements

and is denoted by Gi. This is the actual duration the green light of a traffic signal is turned

on.

• Red interval: It is the red indication for a particular movement or set of movements and

is denoted by Ri. This is the actual duration the red light of a traffic signal is turned on.

• Phase: A phase is the green interval plus the change and clearance intervals that follow

it. Thus, during green interval, non conflicting movements are assigned into each phase.

It allows a set of movements to flow and safely halt the flow before the phase of another

set of movements start.

• Lost time: It indicates the time during which the intersection is not effectively utilized

for any movement. For example, when the signal for an approach turns from red to

green, the driver of the vehicle which is in the front of the queue, will take some time

to perceive the signal (usually called as reaction time) and some time will be lost before

vehicle actually moves and gains speed.

34.3 Phase design

The signal design procedure involves six major steps. They include: (1) phase design, (2) deter-

mination of amber time and clearance time, (3) determination of cycle length, (4) apportioning

of green time, (5) pedestrian crossing requirements, and (6) performance evaluation of the de-

sign obtained in the previous steps. The objective of phase design is to separate the conflicting

movements in an intersection into various phases, so that movements in a phase should have

no conflicts. If all the movements are to be separated with no conflicts, then a large number

of phases are required. In such a situation, the objective is to design phases with minimum

conflicts or with less severe conflicts.

There is no precise methodology for the design of phases. This is often guided by the

geometry of the intersection, the flow pattern especially the turning movements, and the relative

magnitudes of flow. Therefore, a trial and error procedure is often adopted. However, phase

design is very important because it affects the further design steps. Further, it is easier to

change the cycle time and green time when flow pattern changes, where as a drastic change in



1

5

3

7

2

64

8

Figure 34:1: Four legged intersection

Phase 1 ( P1) Phase 1 ( P2)

2

5

6

1

4

8

3

7

Figure 34:2: Movements in two phase signal system

the flow pattern may cause considerable confusion to the drivers. To illustrate various phase

plan options, consider a four legged intersection with through traffic and right turns. Left turn

is ignored. See Figure 34:1. The first issue is to decide how many phases are required. It is

possible to have two, three, four or even more number of phases.

34.3.1 Two phase signals

Two phase system is usually adopted if through traffic is significant compared to the turning

movements. For example in Figure 34:2, non-conflicting through traffic 3 and 4 are grouped

in a single phase and non-conflicting through traffic 1 and 2 are grouped in the second phase.

However, in the first phase flow 7 and 8 offer some conflicts and are called permitted right turns.

Needless to say that such phasing is possible only if the turning movements are relatively low.

On the other hand, if the turning movements are significant, then a four phase system is usually



73

7

8

4

5

1

6

2

P1 P2

P3 P4

Figure 34:3: Movements in four phase signal system: option 1

adopted.

34.3.2 Four phase signals

There are at least three possible phasing options. For example, figure 34:3 shows the most simple

and trivial phase plan. where, flow from each approach is put into a single phase avoiding all

conflicts. This type of phase plan is ideally suited in urban areas where the turning movements

are comparable with through movements and when through traffic and turning traffic need

to share same lane. This phase plan could be very inefficient when turning movements are

relatively low.

Figure 34:4 shows a second possible phase plan option where opposing through traffic are

put into same phase. The non-conflicting right turn flows 7 and 8 are grouped into a third

phase. Similarly flows 5 and 6 are grouped into fourth phase. This type of phasing is very

efficient when the intersection geometry permits to have at least one lane for each movement,

and the through traffic volume is significantly high. Figure 34:5 shows yet another phase plan.

However, this is rarely used in practice.

There are five phase signals, six phase signals etc. They are normally provided if the

intersection control is adaptive, that is, the signal phases and timing adapt to the real time

traffic conditions.



7

6

43

1

5

7

8

2

P1 P2

P3 P4


3

1

6 4

2 8

5

7

P1P2

P3 P4




1 32 N

Figure 34:6: Group of vehicles at a signalized intersection waiting for green signal

Vehicles in queue

h

Hea

dw

ay

h

e1

e2 e3h1

Figure 34:7: Headways departing signal

34.4 Cycle time

Cycle time is the time taken by a signal to complete one full cycle of iterations. i.e. one

complete rotation through all signal indications. It is denoted by C. The way in which the

vehicles depart from an intersection when the green signal is initiated will be discussed now.

Figure 34:6 illustrates a group of N vehicles at a signalized intersection, waiting for the green

signal. As the signal is initiated, the time interval between two vehicles, referred as headway,

crossing the curb line is noted. The first headway is the time interval between the initiation of

the green signal and the instant vehicle crossing the curb line. The second headway is the time

interval between the first and the second vehicle crossing the curb line. Successive headways

are then plotted as in figure 34:7. The first headway will be relatively longer since it includes

the reaction time of the driver and the time necessary to accelerate. The second headway

will be comparatively lower because the second driver can overlap his/her reaction time with

that of the first driver’s. After few vehicles, the headway will become constant. This constant

headway which characterizes all headways beginning with the fourth or fifth vehicle, is defined



as the saturation headway, and is denoted as h. This is the headway that can be achieved by a

stable moving platoon of vehicles passing through a green indication. If every vehicles require

h seconds of green time, and if the signal were always green, then s vehicles per hour would

pass the intersection. Therefore,

s =3600

h(34.1)

where s is the saturation flow rate in vehicles per hour of green time per lane, h is the saturation

headway in seconds. As noted earlier, the headway will be more than h particularly for the

first few vehicles. The difference between the actual headway and h for the ith vehicle and is

denoted as ei shown in figure 34:7. These differences for the first few vehicles can be added to

get start up lost time, l1 which is given by,

l1 =

n∑

i=1

ei (34.2)

The green time required to clear N vehicles can be found out as,

T = l1 + h.N (34.3)

where T is the time required to clear N vehicles through signal, l1 is the start-up lost time, and

h is the saturation headway in seconds.

34.4.1 Effective green time

Effective green time is the actual time available for the vehicles to cross the intersection. It is

the sum of actual green time (Gi) plus the yellow minus the applicable lost times. This lost

time is the sum of start-up lost time (l1) and clearance lost time (l2) denoted as tL. Thus

effective green time can be written as,

gi = Gi + Yi − tL (34.4)

34.4.2 Lane capacity

The ratio of effective green time to the cycle length (gi

C)is defined as green ratio. We know

that saturation flow rate is the number of vehicles that can be moved in one lane in one hour

assuming the signal to be green always. Then the capacity of a lane can be computed as,

ci = si

gi

C(34.5)

where ci is the capacity of lane in vehicle per hour, si is the saturation flow rate in vehicle per

hour per lane, C is the cycle time in seconds.



Numerical example

Let the cycle time of an intersection is 60 seconds, the green time for a phase is 27 seconds,

and the corresponding yellow time is 4 seconds. If the saturation headway is 2.4 seconds per

vehicle, the start-up lost time is 2 seconds per phase, and the clearance lost time is 1 second

per phase, find the capacity of the movement per lane?

Solution Total lost time, tL = 2+1 = 3 seconds. From equation 34.4 effective green time, gi

= 27+4-3 = 28 seconds. From equation 34.1 saturation flow rate, si = 3600

h= 3600

2.4= 1500 veh

per hr. Capacity of the given phase can be found out from equation 34.5 as Ci = 1500 ×28

60=

700 veh per hr per lane.

34.4.3 Critical lane

During any green signal phase, several lanes on one or more approaches are permitted to move.

One of these will have the most intense traffic. Thus it requires more time than any other lane

moving at the same time. If sufficient time is allocated for this lane, then all other lanes will

also be well accommodated. There will be one and only one critical lane in each signal phase.

The volume of this critical lane is called critical lane volume.

34.5 Determination of cycle length

The cycle length or cycle time is the time taken for complete indication of signals in a cycle.

Fixing the cycle length is one of the crucial steps involved in signal design.

If tLi is the start-up lost time for a phase i, then the total start-up lost time per cycle,

L =∑N

i=1tLi, where N is the number of phases. If start-up lost time is same for all phases,

then the total start-up lost time is L = NtL. If C is the cycle length in seconds, then the

number of cycles per hour = 3600

C. The total lost time per hour is the number of cycles per hour

times the lost time per cycle and is = 3600

CL. Substituting as L = NtL, total lost time per hour

can be written as = 3600 N tlC

. The total effective green time Tg available for the movement in

a hour will be one hour minus the total lost time in an hour. Therefore,

Tg = 3600 −3600 N tL

C

= 3600

[

1 −

N tL

C

]



Let the total number of critical lane volume that can be accommodated per hour is given by Vc,

then Vc = Tg

h. Substituting for Tg from equation 34.9 and si from equation 34.1 in the expression

for the the maximum sum of critical lane volumes that can be accommodated within the hour

and by rewriting, the expression for C can be obtained as follows:

Vc =Tg

h,

=3600

h

[

1 −

N tL

C

]

,

= si

[

1 −

N tL

C

]

,

∴ C =N tL

1 −Vc

s

.

The above equation is based on the assumption that there will be uniform flow of traffic in an

hour. To account for the variation of volume in an hour, a factor called peak hour factor, (PHF)

which is the ratio of hourly volume to the maximum flow rate, is introduced. Another ratio

called v/c ratio indicating the quality of service is also included in the equation. Incorporating

these two factors in the equation for cycle length, the final expression will be,

C =N tL

1 −Vc

si×PHF×vc

(34.6)

Highway capacity manual (HCM) has given an equation for determining the cycle length which

is a slight modification of the above equation. Accordingly, cycle time C is given by,

C =N L XC

XC −

∑

(

Vci

si

) (34.7)

where N is the number of phases, L is the lost time per phase,(

Vci

si

)

is the ratio of critical

volume to saturation flow for phase i, XC is the quality factor called critical vcratio where v is

the volume and c is the capacity.

Numerical example

The traffic flow in an intersection is shown in the figure 34:8. Given start-up lost time is 3

seconds, saturation head way is 2.3 seconds, compute the cycle length for that intersection.

Assume a two-phase signal.



1150

900

1300

1800

Figure 34:8: Traffic flow in the intersection

1150

900

1800

1300

Figure 34:9: One way of providing phases

Solution

1. If we assign two phases as shown below figure 34:9, then the critical volume for the first

phase which is the maximum of the flows in that phase = 1150 vph. Similarly critical

volume for the second phase = 1800 vph. Therefore, total critical volume for the two

signal phases = 1150+1800 = 2950 vph.

2. Saturation flow rate for the intersection can be found out from the equation as si = 3600

2.3

= 1565.2 vph. This means, that the intersection can handle only 1565.2 vph. However,

the critical volume is 2950 vph . Hence the critical lane volume should be reduced and

one simple option is to split the major traffic into two lanes. So the resulting phase plan

is as shown in figure 34:10.

3. Here we are dividing the lanes in East-West direction into two, the critical volume in the

first phase is 1150 vph and in the second phase it is 900 vph. The total critical volume

for the signal phases is 2050 vph which is again greater than the saturation flow rate and

hence we have to again reduce the critical lane volumes.



1150

1300/2

1300/2

1800/2

1800/2

Figure 34:10: second way of providing phases

1800/31800/31800/3

1150/2 1150/2

Figure 34:11: Third way of providing phases

4. Assigning three lanes in East-West direction, as shown in figure 34:11, the critical volume

in the first phase is 575 vph and that of the second phase is 600 vph, so that the total

critical lane volume = 575+600 = 1175 vph which is lesser than 1565.2 vph.

5. Now the cycle time for the signal phases can be computed from equation 34.6 as:

C =2 × 3

1 −1175

1565.2

= 24 seconds.

34.6 Green splitting

Green splitting or apportioning of green time is the proportioning of effective green time in

each of the signal phase. The green splitting is given by,

gi =

[

Vci∑N

i=1Vci

]

× tg (34.8)

where Vciis the critical lane volume and tg is the total effective green time available in a cycle.

This will be cycle time minus the total lost time for all the phases. Therefore,

tg = C − N tL (34.9)

where C is the cycle time in seconds, n is the number of phases, and tL is the lost time per

phase. If lost time is different for different phases, then effective green time can be computed



600

500

900

1000

Figure 34:12: Phase diagram for an intersection

as follows:

tg = C −

N∑

i=1

tLi(34.10)

where tLiis the lost time for phase i, N is the number of phases and C is the cycle time in

seconds. Actual green time can be now found out as,

Gi = gi − yi + tLi(34.11)

where Gi is the actual green time, gi is the effective green time available, yi is the amber time,

and Li is the lost time for phase i.

Numerical example

The phase diagram with flow values of an intersection with two phases is shown in figure 34:12.

The lost time and yellow time for the first phase is 2.5 and 3 seconds respectively. For the

second phase the lost time and yellow time are 3.5 and 4 seconds respectively. If the cycle time

is 120 seconds, find the green time allocated for the two phases.

Solution

1. Critical lane volume for the first phase, VC1= 1000 vph.

2. Critical lane volume for the second phase, VC2= 600 vph.

3. Total critical lane volumes, VC = VC1+ VC2

= 1000+600 = 1600 vph.

4. Effective green time can be found out from equation 34.9 as Tg=120-(2.5-3.5)= 114 sec-

onds.

5. Green time for the first phase, g1 can be found out from equation 34.8 as g1 = 1000

1600× 114

= 71.25 seconds.



��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

42 4

120

3 4671

74

Figure 34:13: Timing diagram

6. Green time for the second phase, g2 can be found out from equation 34.8 as g2 = 600

1600×

114= 42.75 seconds.

7. Actual green time can be found out from equation 34.11. Thus actual green time for the

first phase, G1 = 71.25-3+2.5 = 71 seconds (rounded).

8. Actual green time for the second phase, G2 = 42.75-4+3.5 = 42 seconds (rounded).

9. The phase diagram is as shown in figure 34:13.

34.7 Summary

Traffic signal is an aid to control traffic at intersections where other control measures fail. The

signals operate by providing right of way to a certain set of movements in a cyclic order. The

design procedure discussed in this chapter include phase design, interval design, determination

of cycle time, computation of saturation flow, and green splitting.

34.8 References




Transportation Systems Engineering 35. Signalized Intersection Delay Models

Chapter 35

Signalized Intersection Delay Models

35.1 Introduction

Signalized intersections are the important points or nodes within a system of highways and

streets. To describe some measure of effectiveness to evaluate a signalized intersection or to

describe the quality of operations is a difficult task. There are a number of measures that have

been used in capacity analysis and simulation, all of which quantify some aspect of experience of

a driver traversing a signalized intersection. The most common measures are average delay per

vehicle, average queue length, and number of stops. Delay is a measure that most directly relates

driver’s experience and it is measure of excess time consumed in traversing the intersection.

Length of queue at any time is a useful measure, and is critical in determining when a given

intersection will begin to impede the discharge from an adjacent upstream intersection. Number

of stops made is an important input parameter, especially in air quality models. Among these

three, delay is the most frequently used measure of effectiveness for signalized intersections for

it is directly perceived by a driver. The estimation of delay is complex due to random arrival of

vehicles, lost time due to stopping of vehicles, over saturated flow conditions etc. This chapter

looks are some important models to estimate delays.

35.2 Types of delay

The most common measure of operational quality is delay, although queue length is often used

as a secondary measure. While it is possible to measure delay in the field, it is a difficult

process, and different observers may make judgments that could yield different results. For

many purposes, it is, therefore, convenient to have a predictive model for the estimate of delay.

Delay, however, can be quantified in many different ways. The most frequently used forms of

delay are defined as follows:

• Stopped time delay



Time

Desired path Actual path

Dis

tanc

e

D3

D2

D1

D3 = Travel time delay

D2 = Approach delay

D1 = Stopped time delay

Figure 35:1: Illustration of delay measures

• Approach delay

• Travel time delay

• Time-in-queue delay

• Control delay

These delay measures can be quite different, depending on conditions at the signalized inter-

section. Fig 35:1 shows the differences among stopped time, approach and travel time delay for

single vehicle traversing a signalized intersection. The desired path of the vehicle is shown, as

well as the actual progress of the vehicle, which includes a stop at a red signal. Note that the

desired path is the path when vehicles travel with their preferred speed and the actual path is

the path accounting for decreased speed, stops and acceleration and deceleration.

35.2.1 Stopped Time Delay

Stopped-time delay is defined as the time a vehicle is stopped in queue while waiting to pass

through the intersection. It begins when the vehicle is fully stopped and ends when the vehicle

begins to accelerate. Average stopped-time delay is the average for all vehicles during a specified

time period.

35.2.2 Approach Delay

Approach delay includes stopped-time delay but adds the time loss due to deceleration from

the approach speed to a stop and the time loss due to re-acceleration back to the desired speed.



It is found by extending the velocity slope of the approaching vehicle as if no signal existed.

Approach delay is the horizontal (time) difference between the hypothetical extension of the

approaching velocity slope and the departure slope after full acceleration is achieved. Average

approach delay is the average for all vehicles during a specified time period.

35.2.3 Travel Time Delay

It is the difference between the driver’s expected travel time through the intersection (or any

roadway segment) and the actual time taken. To find the desired travel time to traverse an

intersection is very difficult. So this delay concept is is rarely used except in some planning

studies.

35.2.4 Time-in-queue Delay

Time-in-queue delay is the total time from a vehicle joining an intersection queue to its discharge

across the STOP line on departure. Average time-in-queue delay is the average for all vehicles

during a specified time period. Time-in-queue delay cannot be effectively shown using one

vehicle, as it involves joining and departing a queue of several vehicles.

35.2.5 Control Delay

Control delay is the delay caused by a control device, either a traffic signal or a STOP-sign. It is

approximately equal to time-in-queue delay plus the acceleration-deceleration delay component.

Delay measures can be stated for a single vehicle, as an average for all vehicles over a specified

time period, or as an aggregate total value for all vehicles over a specified time period. Aggregate

delay is measured in total vehicle-seconds, vehicle-minutes, or vehicle-hours for all vehicles in

the specified time interval. Average individual delay is generally stated in terms of seconds per

vehicle for a specified time interval.

35.3 Components of delay

In analytic models for predicting delay, there are three distinct components of delay, namely,

uniform delay, random delay, and overflow delay. Before, explaining these, first a delay repre-

sentation diagram is useful for illustrating these components.



��

��

��

��

��

��

��

��

��

R

Vi

tG

Aggregate delay (veh−secs)

Slope =s

G

Cumulative Vehicles

Time

WiQ

t

Slope =v

��

Figure 35:2: Illustration of delay, waiting time, and queue length

35.3.1 Delay diagram

All analytic models of delay begin with a plot of cumulative vehicles arriving and departing

vs. time at a given signal location. Fig. 35:2 shows a plot of total vehicle vs time. Two

curves are shown: a plot of arriving vehicles and a plot of departing vehicles. The time axis

is divided into periods of effective green and effective red. Vehicles are assumed to arrive at

a uniform rate of flow (v vehicles per unit time). This is shown by the constant slope of the

arrival curve. Uniform arrivals assume that the inter-vehicle arrival time between vehicles is a

constant. Assuming no preexisting queue, arriving vehicles depart instantaneously when the

signal is green (ie., the departure curve is same as the arrival curve). When the red phase

begins, vehicles begin to queue, as none are being discharged. Thus, the departure curve is

parallel to the x-axis during the red interval. When the next effective green begins, vehicles

queued during the red interval depart from the intersection, at a rate called saturation flow rate

(s vehicle per unit time). For stable operations, depicted here, the departure curve catches up

with the arrival curve before the next red interval begins (i.e., there is no residual queue left at

the end of the effective green). In this simple model:

1. The total time that any vehicle (vi) spends waiting in the queue (Wi) is given by the

horizontal time-scale difference between the time of arrival and the time of departure.

2. The total number of vehicles queued at any time (qt) is the vertical vehicle-scale difference

between the number of vehicles that have arrived and the number of vehicles that have

departed

3. The aggregate delay for all vehicles passing through the signal is the area between the



Cum

mul

ativ

e ve

hicl

es

arrival function

departure function

Time

Figure 35:3: Illustration of uniform delay

arrival and departure curves (vehicles times the time duration)

35.3.2 Uniform Delay

Uniform delay is the delay based on an assumption of uniform arrivals and stable flow with

no individual cycle failures. Fig. 35:3, shows stable flow throughout the period depicted. No

signal cycle fails here, i.e., no vehicles are forced to wait for more than one green phase to

be discharged. During every green phase, the departure function catches up with the arrival

function. Total aggregate delay during this period is the total of all the triangular areas between

the arrival and departure curves. This type of delay is known as Uniform delay.

35.3.3 Random Delay

Random delay is the additional delay, above and beyond uniform delay, because flow is randomly

distributed rather than uniform at isolated intersections. In Fig 35:4some of the signal phases

fail. At the end of the second and third green intervals, some vehicles are not served (i.e., they

must wait for a second green interval to depart the intersection). By the time the entire period

ends, however, the departure function has caught up with the arrival function and there is no

residual queue left unserved. This case represents a situation in which the overall period of

analysis is stable (ie.,total demand does not exceed total capacity). Individual cycle failures

within the period, however, have occurred. For these periods, there is a second component of

delay in addition to uniform delay. It consists of the area between the arrival function and the

dashed line, which represents the capacity of the intersection to discharge vehicles, and has the

slope c. This type of delay is referred to as Random delay.



Cum

mul

ativ

e ve

hicl

es

arrival function

departure function

capacity function

Time

Figure 35:4: Illustration of random delay

Cum

mul

ativ

e ve

hicl

es

Time

capacity functionslope = c

arrival functionslope = v

departure functionslope = s

Figure 35:5: Illustration of overflow delay

35.3.4 Overflow Delay

Overflow delay is the additional delay that occurs when the capacity of an individual phase

or series of phases is less than the demand or arrival flow rate. Fig. 35:5 shows the worst

possible case, every green interval fails for a significant period of time, and the residual, or

unserved, queue of vehicles continues to grow throughout the analysis period. In this case, the

overflow delay component grows over time, quickly dwarfing the uniform delay component. The

latter case illustrates an important practical operational characteristic. When demand exceeds

capacity (v/c > 1.0), the delay depends upon the length of time that the condition exists. In

Figure 35:4, the condition exists for only two phases. Thus, the queue and the resulting overflow

delay is limited. In Fig. 35:5, the condition exists for a long time, and the delay continues to

grow throughout the over-saturated period. This type of delay is referred to as Overflow delay



��

��

��

��

��

Slope =s

GRG

V

Cum

mul

ativ

e V

ehic

les

Slope =v

Aggregate delay (veh−secs)

R=C[1−g/C] tc

Time t

Figure 35:6: Illustration of Webster’s uniform delay model

35.4 Webster’s Delay Models

35.4.1 Uniform Delay Model

Model is explained based on the assumptions of stable flow and a simple uniform arrival func-

tion. As explained in the above section, aggregate delay can be estimated as the area between

the arrival and departure curves. Thus, Webster’s model for uniform delay is the area of the

triangle formed by the arrival and departure functions. From Fig. 35:6 the area of the aggre-

gate delay triangle is simply one-half the base times the height. Hence, the total uniform delay

(TUD) is given as:

TUD =RV

2(35.1)

where, R is the duration of red, V is the number of vehicles arriving during the time interval

R + tc. Length of red phase is given as the proportion of the cycle length which is not green,

or:

R = C(

1 −g

C

)

(35.2)

The height of the triangle is found by setting the number of vehicles arriving during the time

(R + tc) equal to the number of vehicles departing in time tc, or:

V = v(R + tc) = s tc (35.3)



Substituting equation 35.2 for R in equation 35.3 and solving for tc and then for V gives,

v(

C(

1 −g

C

)

+ tc

)

= s tc

tc (s − v) = v C(

1 −g

C

)

V

s(s − v) = v C

(

1 −g

C

)

V = C(

1 −g

C

)

(

vs

s − v

)

(35.4)

Substituting equation 35.2 and equation 35.4 in equation 35.1 gives:

TUD =RV

2

=1

2

[

C(

1 −g

C

)]2(

vs

s − v

)

where TUD is the aggregate delay, in vehicle seconds. To obtain the average delay per vehicle,

the aggregate delay is divided by the number of vehicles processed during the cycle, which is

the arrival rate, v, times the full cycle length, C. Hence,

UD =1

2

[

C(

1 −g

C

)]2(

vs

s − v

) (

1

v C

)

=C

2

(1 − gC

)2

(1 −vs)

(35.5)

Another form of the equation uses the capacity, c, rather than the saturation flow rate, s. We

know,

s =cgC

(35.6)

So, the relation for uniform delay changes to,

UD =C

2

(1 −gC

)2

(1 −gvCc

)

=C

2

(1 −gC

)2

(1 −gCX)

(35.7)

where, UD is the uniform delay (sec/vehicle) C is the cycle length (sec), c is the capacity, v is

the vehicle arrival rate, s is the saturation flow rate or departing rate of vehicles, X is the v/c

ratio or degree of saturation (ratio of the demand flow rate to saturation flow rate), and g/C

is the effective green ratio for the approach.



Numerical Example

Consider the following situation: An intersection approach has an approach flow rate of 1,000 vph,

a saturation flow rate of 2,800 vph, a cycle length of 90 s, and effective green ratio of 0.44 for

the approach. What average delay per vehicle is expected under these conditions?

Solution: First, the capacity and v/c ratio for the intersection approach must be computed.

Given, s=2800 vphg and g/C=0.55. Hence,

c = s × g/C

= 2800 × 0.55 = 1540 vph

v/c = 1000/1540 = 0.65

Since v/c ≤ 1.0 and is a relatively low value, the uniform delay equation 35.5 may be applied

directly. There is hardly any random delay at such a v/c ratio and overflow delay need not be

considered.

UD =C

2

(1 −gC

)2

(1 −vs)

=90

2

(1 − 0.55)2

(1 −10002800

)

= 14.2.

Therefore, average delay per vehicle is 14.2 sec/veh. Note that this solution assumes that

arrivals at the subject intersection approach are uniform. Random and platooning effects are

not taken into account.

35.4.2 Random Delay Model

The uniform delay model assumes that arrivals are uniform and that no signal phases fail (i.e.,

that arrival flow is less than capacity during every signal cycle of the analysis period). At

isolated intersections, vehicle arrivals are more likely to be random. A number of stochastic

models have been developed for this case, including those by Newell, Miller and Webster. These

models generally assume that arrivals are Poisson distributed, with an underlying average rate

of v vehicles per unit time. The models account for random arrivals and the fact that some

individual cycles within a demand period with v/c < 1.0 could fail due to this randomness.

This additional delay is often referred to as Random delay. The most frequently used model

for random delay is Webster’s formulation:

RD =X2

2 v (1 − X)(35.8)



Cum

mul

ativ

e ve

hicl

es

Uniform Delay

Overflow Delay

Time

slope = v

slope = s

slope = c

Figure 35:7: Illustration of overflow delay model

where, RD is the average random delay per vehicle, s/veh, and X is the degree of saturation (v/c

ratio). Webster found that the above delay formula overestimate delay and hence he proposed

that total delay is the sum of uniform delay and random delay multiplied by a constant for

agreement with field observed values. Accordingly, the total delay is given as:

D = 0.90 (UD + RD) (35.9)

35.4.3 Overflow delay model

Model is explained based on the assumption that arrival function is uniform. In this model

a new term called over saturation is used to describe the extended time periods during which

arrival vehicles exceeds the capacity of the intersection approach to the discharged vehicles.

In such cases queue grows and there will be overflow delay in addition to the uniform delay.

Fig. 35:7 illustrates a time period for which v/c > 1.0. During the period of over-saturation

delay consists of both uniform delay (in the triangles between the capacity and departure curves)

and overflow delay (in the triangle between arrival and capacity curves). As the maximum value

of X is 1.0 for uniform delay, it can be simplified as,

UD =C

2

(1 −gC

)2

(1 −gCX)

=C

2

(

1 −g

C

)

(35.10)

From Fig. 35:8 total overflow delay can be estimated as,

TOD =1

2T (vT − cT ) =

T 2

2(v − c) (35.11)

where, TOD is the total or aggregate overflow delay (in veh-secs), and T is the analysis period

in seconds. Average delay is obtained by dividing the aggregate delay by the number of vehicles



Time

Slope = v

Slope = c

T

Cum

mul

ativ

e ve

hicl

es

cT

vT

Figure 35:8: Derivation of the overflow delay model

discharged with in the time T which is cT.

OD =T

2

(v

c− 1

)

(35.12)

The delay includes only the delay accrued by vehicles through time T, and excludes additional

delay that vehicles still stuck in the queue will experience after time T. The above said delay

equation is time dependent i.e., the longer the period of over-saturation exists, the larger delay

becomes. A model for average overflow delay during a time period T1 through T2 may be

developed, as illustrated in Fig. 35:9 Note that the delay area formed is a trapezoid, not a

triangle. The resulting model for average delay per vehicle during the time period T1 through

T2 is:

OD =T1 + T2

2

(v

c− 1

)

(35.13)

Formulation predicts the average delay per vehicle that occurs during the specified interval,

T1 through T2. Thus, delays to vehicles arriving before time T1 but discharging after T1 are

included only to the extent of their delay within the specified times, not any delay they may

have experienced in queue before T1. Similarly, vehicles discharging after T2 are not included

in the formulation.

Numerical Example

Consider the following situation: An intersection approach has an approach flow rate of 1,900

vph, a saturation flow rate of 2,800 vphg, a cycle length of 90s, and effective green ratio for the

approach 0.55. What average delay per vehicle is expected under these conditions?



Time

vT2

T1 T2

Cum

mul

ativ

e ve

hicl

esvT1

cT2cT1

Slope = v

Slope = c

Figure 35:9: Overflow delay between time T1 & T2

Solution: To begin, the capacity and v/c ratio for the intersection approach must be com-

puted. This will determine what model(s) are most appropriate for application in this case:

Given, s=2800 vphg, g/C=0.55, and v =1900 vph.

c = s × g/C

= 2800 × 0.55 = 1540 vph

v/c = 1900/1540 = 1.23.

Since v/c is greater than 1.15 for which the overflow delay model is good so it can be used to

find the delay.

D = UD + OD

UD =C

2

(

1 −g

C

)

= 0.5 × 90[1 − 0.55]

= 20.3

OD =T

2

(v

c− 1

)

=3600

2(1.23 − 1)

= 414

D = 20.3 + 414

= 434.3 sec/veh

This is a very large value but represents an average over one full hour period.



AverageOverflowDelay

Theoreticaloverflow delaymodel

Webster’srandomdelay model

Ratio0.80 0.90 1.00 1.10

Figure 35:10: Comparison of overflow & random delay model

35.4.4 Inconsistencies between Random and Overflow delay

As explained earlier random and overflow delay is given as, Random delay,

RD =(X)2

2v(1 − X)(35.14)

Overflow delay,

OD =T

2(X − 1) (35.15)

The inconsistency occurs when the X is in the vicinity of 1.0. When X < 1.0 random delay

model is used. As the Webster’s random delay contains 1-X term in the denominator, when

X approaches to 1.0 random delay increases asymptotically to infinite value. When X > 1.0

overflow delay model is used. Overflow delay contains 1 − X term in the numerator, when

X approaches to 1.0 overflow becomes zero and increases uniformly with increasing value of

X. Both models are not accurate in the vicinity of X = 1.0. Delay does not become infinite

at X = 1.0. There is no true overflow at X = 1.0, although individual cycle failures due to

random arrivals do occur. Similarly, the overflow model, with overflow delay of zero seconds

per vehicle at X = 1.0 is also unrealistic. The additional delay of individual cycle failures due

to the randomness of arrivals is not reflected in this model. Most studies show that uniform

delay model holds well in the range X ≤ 0.85. In this range true value of random delay is

minimum and there is no overflow delay. Also overflow delay model holds well when X ≥ 1.15.

The inconsistency occurs in the range 0.85 ≤ X ≤ 1.15; here both the models are not accurate.

Much of the more recent work in delay modeling involves attempts to bridge this gap, creating

a model that closely follows the uniform delay model at low X ratios, and approaches the

theoretical overflow delay model at high X ratios, producing ”reasonable” delay estimates in

between. Fig. 35:10 illustrates this as the dashed line.



35.5 Other delay models

The most commonly used model for intersection delay is to fit models that works well under

all v/c ratios. Few of them will be discussed here.

35.5.1 Akcelik Delay Model

To address the above said problem Akcelik proposed a delay model and is used in the Australian

Road Research Board’s signalized intersection. In his delay model, overflow component is given

by,

OD =cT

4

[

(X − 1) +

√

(X − 1)2 +12(X − X0)

cT

]

where X ≥ X0, and if X ≤ X0 then overflow delay is zero, and

X0 = 0.67 +sg

600(35.16)

where, T is the analysis period, h, X is the v/c ratio, c is the capacity, veh/hour, s is the

saturation flow rate, veh/sg (vehicles per second of green) and g is the effective green time, sec

Numerical Example


vph, a saturation flow rate of 2,800 vphg, a cycle length of 90s, and a g/C ratio of 0.55. What

average delay per vehicle is expected under these conditions?

Solution: To begin, the capacity and v/c ratio for the intersection approach must be com-

puted. This will determine what model(s) are most appropriate for application in this case:

Given, s =2800 vphg; g/C=0.55; v =1600 vph

c = s × g/C

= 2800 × 0.55 = 1540 vph

v/c = 1600/1540 = 1.039

In this case, the v/c ratio now changes to 1600/1540 = 1.039. This is in the difficult range of

0.85-1.15 for which neither the simple random flow model nor the simple overflow delay model

are accurate. The Akcelik model of Equation will be used. Total delay, however, includes both



uniform delay and overflow delay. The uniform delay component when v/c > 1.0 is given by

equation 35.10

UD =C

2(1 −

g

C)

= 0.5 × 90[1 − 0.55]

= 20.3 sec/veh

Use of Akcelik’s overflow delay model requires that the analysis period be selected or arbitrarily

set. If a one-hour

OD =cT

4

[

(X − 1) +

√

(X − 1)2 +12(X − X0)

cT

]

g = 0.55 × 90 = 49.5 s

s = 2800/3600 = 0.778 v/sg

X0 = 0.67 +0.778 × 49.5

600= 0.734

OD =1540

4

[

(1.039 − 1) +

√

(1.039 − 1)2 +12(1.039 − 0.734)

1540

]

= 39.1 s/veh

The total expected delay in this situation is the sum of the uniform and overflow delay terms

and is computed as: d=20.3+39.1=59.4 s/veh. As v/c > 1.0 in the same problem, what will

happen if we use Webster’s overflow delay model. Uniform delay will be the same, but we have

to find the overflow delay.

OD =T

2(v

c− 1)

=3600

2(1.039 − 1)

= 70.2 sec/veh

As per Akcelik model, overflow delay obtained is 39.1 sec/veh which is very much lesser com-

pared to overflow delay obtained by Webster’s overflow delay model. This is because of the

inconsistency of overflow delay model in the range 0.85-1.15.

35.5.2 HCM 2000 delay models

The delay model incorporated into the HCM 2000 includes the uniform delay model, a version

of Akcelik’s overflow delay model, and a term covering delay from an existing or residual queue



at the beginning of the analysis period. The delay is given as,

d = d1 PF + d2 + d3

d1 =c

2

(1 −gc)2

1 − [min(1, X)(gc)]

d2 = 900T [(X − 1) +

√

(X − 1)2 +8klX

cT]

PF = ( (1−P )(1−(g/c)

) ∗ fp additional explanation for PF Where, d = control delay, s/veh, d1 =

uniform delay component, s/veh, PF = progression adjustment factor, d2 = overflow delay

component, s/veh, d3 = delay due to pre-existing queue, s/veh, T = analysis period, h, X =

v/c ratio, C = cycle length, s, k = incremental delay factor for actuated controller settings;

0.50 for all pre-timed controllers, l = upstream filtering/metering adjustment factor; 1.0 for

all individual intersection analyses, c = capacity, veh/h, P = proportion of vehicles arriving

during the green interval and fp = supplemental adjustment factor for platoon arriving during

the green

Numerical problems


vph, a saturation flow rate of 2,650 vphg, a cycle length of 102 s, and effective green ratio for

the approach 0.55. Assume Progression Adjustment Factor 1.25 and delay due to pre-existing

queue, 12 sec/veh. What control delay sec per vehicle is expected under these conditions?

Solution: Saturation flow rate =2650 vphg , g/C=0.55, Approach flow rate v=1700 vph, Cy-

cle length C=102 sec, delay due to pre-existing queue =12 sec/veh and Progression Adjustment

Factor PF=1.25. The capacity is given as:

c = s ×g

C= 2650 × 0.55

= 1458 vphv/c

Degree of saturation X= v/c= 1700/1458 =1.16. So the uniform delay is given as:

d1 =C

2

(1 −gC

)2

[1 − min(X, 1)(gc)]

=102

2

(1 − 1.16)2

[1 − min(1.16, 1)(.55)]= 22.95



Uniform delay =22.95 and the over flow delay is given as:

d2 =C

2∗ (X − 1) +

√

(X − 1)2 +8klX

cT

=102

2∗ (1.16 − 1) +

√

(1.16 − 1)2 +(8 ∗ 5 ∗ 1 ∗ 1.16)

1458= 16.81

Overflow delay, d2=16.81. Hence, the total dealy is”

d = d1 PF + d2 + d3

= 22.95 × 1.25 + 16.81 + 8 = 53.5 sec/veh.

Therefore, control delay per vehicle is 53.5 sec.

35.6 Conclusion

In this chapter measure of effectiveness at signalized intersection are explained in terms of

delay. Different forms of delay like stopped time delay, approach delay, travel delay, time-

in-queue delay and control delay are explained. Types of delay like uniform delay, random

delay and overflow delay are explained and corresponding delay models are also explained

above. Inconsistency between delay models at v/c=1.0 is explained in the above section and

the solution to the inconsistency, delay model proposed by Akcelik is explained. At last HCM

2000 delay model is also explained in this section. From the study, various form of delay

occurring at the intersection is explained through different models, but the delay calculated

using such models may not be accurate as the models are explained on the theoretical basis

only.

35.7 References

1. R Akcelik. The hcm delay formulas for signalized intersection-ite journal, 1991.



3. R W McShane and R P Roess. Highway Engineering. McGraw Hill Company, 1984.


Transportation Systems Engineering 36. Special Requirement in Traffic Signal

Chapter 36

Special Requirement in Traffic Signal

36.1 Overview

Traffic signals are designed to ensure safe and orderly flow of traffic, Protect pedestrians and

vehicles at busy intersections and reduce the severity and frequency of accidents between vehi-

cles entering intersections. Previous chapters discussed some imporant design priciples such as:

(i) Phase Design (ii) Cycle Time Determination (iii) Green Splitting (iv) Performance Evalu-

ation This chapter we will discuss some special requirements in the signa design such as: (i)

Pedestrian crossing requirement (ii) Interval design, (iii) Effect of tuning vehicles, and (iv) Lane

utilization.

36.2 Pedestrian crossing

Pedestrian crossing requirements can be taken care by two ways; by suitable phase design

or by providing an exclusive pedestrian phase. It is possible in some cases to allocate time

for the pedestrians without providing an exclusive phase for them. For example, consider an

intersection in which the traffic moves from north to south and also from east to west. If we

are providing a phase which allows the traffic to flow only in north-south direction, then the

pedestrians can cross in east-west direction and vice-versa. However in some cases, it may

be necessary to provide an exclusive pedestrian phase. In such cases, the procedure involves

computation of time duration of allocation of pedestrian phase. Green time for pedestrian

crossing Gp can be found out by,

Gp = ts +dx

uP

where Gp is the minimum safe time required for the pedestrians to cross, often referred to as

the pedestrian green time, ts is the start-up lost time, dx is the crossing distance in metres, and

up is the walking speed of pedestrians which is about 15th percentile speed. The start-up lost

time ts can be assumed as 4.7 seconds and the walking speed can be assumed to be 1.2 m/s.



1

P2

2

3

P1

4

Pedestrian crossing

36.3 Interval design

There are two intervals, namely the change interval and clearance interval, normally provided

in a traffic signal.

36.3.1 Change interval

The change interval or yellow time is provided after green time for movement. The purpose is

to warn a driver approaching the intersection during the end of a green time about the coming

of a red signal. They normally have a value of 3 to 6 seconds. The design consideration is that

a driver approaching the intersection with design speed should be able to stop at the stop line

of the intersection before the start of red time. Institute of transportation engineers (ITE) has

recommended a methodology for computing the appropriate length of change interval which is

as follows:

Y = t +v

2(gn + a))(36.1)

where t is the reaction time (about 1.0 sec), v is the velocity of the approaching vehicles, g is

the acceleration due to gravity (9.8 m/sec2), n is the grade of the approach in decimels and a is

the deceleration of Change interval can also be approximately computed as y = SSD/v, where

SSD is the stopping sight distance and v is the speed of the vehicle. The clearance interval is

provided after yellow interval and as mentioned earlier, it is used to clear off the vehicles in the

intersection. Clearance interval is optional in a signal design. It depends on the geometry of

the intersection. If the intersection is small, then there is no need of clearance interval whereas

for very large intersections, it may be provided.



36.3.2 Clearence interval

The clearence interval or all-red will facilitate a vehicle just crossed the stop line at the turn

of red to clear the intersection without being collided by a vehicle from the next phase. ITE

recommends the following policy for the design of all read time, given as

RAR ==

w+Lv

if no pedestrians

max(

w+Lv

, Pv

)

if pedestrain corossingP+L

vif protected

(36.2)

where w is the width of the intersection from stop line to the farthest conflicting trafic, L is

the length of the vehicle (about 6 m), v is the speed of the vehicle, and P is the width of the

intersection from STOP line to the farthest confliting pedestrain cross-walk.

36.4 Effect of turning vehicles

36.4.1 Right turning vehicles

Right-turn signal phases facilitate right-turning traffic and may improve the safety of the in-

tersection for right-turning vehicles. However, this is done at the expense of the amount of

green time available for through traffic and will usually reduce the capacity of the intersection.

Right-turn arrows also result in longer cycle lengths, which in turn have a detrimental effect by

increasing stops and delays. While phases for protected right-turning vehicles are popular and

commonly requested, other methods of handling right-turn conflicts also need to be considered.

Potential solutions may include prohibiting right-turns and geometric improvements. The three

criteria for right -turn phase is presented below:

1. Traffic Volumes

2. Delay: Separate right -turn phasing may be considered if the average delay for all right-

turning vehicles on the approach is at least 35 seconds during that same peak hour.

3. Collision Experience: Separate right -turn phasing may be considered if the critical num-

ber of reportable right -turn collisions has occurred. These are: (i) For one approach to

the intersection, the critical number is five l right -turn collisions in one year, or seven in

two years. (ii) For both approaches to an intersection, the critical number is seven right

-turn collisions in one year, or eleven in two years.

So the right turning vehicles affected saturation flow based on adjusted saturation headway.

Finally actual values of right turning are calculated from right turn adjustment factor. The



adjustments factor is calculated by following equations. Adjusted saturation headway,

hadj = hideal × (PRT × eRT + (1 − PRT ) × 1)

Adjusted saturation flow,

Sadj =3600

hadj

Multiplicative right turn adjustment factor,

fRT =1

1 + PRT (eRT − 1)

Sadj = Sideal × fRT

Numerical example

If there is 15 percent right turning movement, eRT (through-car equivalent for permitted left

turns) is 3, saturation headway is 2 sec; Find the value of Adjusted Saturation flow.

Solution: Given hideal = 2 sec, PRT = 15%(0.15), Sideal = 1800, eRT = 3

Case 1: Find adjusted saturation headway as:

hadj = hideal × (PRT × eRT + (1 − PRT ) × 1)

= 2 × (0.15 × 3 + (1 − 0.15) × 1)

= 2.6sec/veh

Now, find adjusted saturation flow as: Sadj = 3600

hadj= 3600

2.6= 1385. The adjusted saturation flow

is 1385 vph.

Case 2 Find the adjustment factor to calculate adjusted saturation flow based on ideal

saturation flow (1800)

fRT =1

1 + PRT (eRT − 1)

=1

1 + 0.15(3 − 1)= 0.77

sadj = Sideal × fRT = 1800 × 0.77 = 1386

The adjusted saturation flow is 1386 vph. The result is same from both cases.



36.4.2 Left turning vehicles

Lft turn adjustment factor for saturation flow rate is as follows: For exclusive lane fLT is 0.85

and for shared lane fLT = 1.0 − 0.15 PLT , where pLT is the proportions of left turns in lane

group. Normally in left turn, separate signal phase are not provided at intersection as per

Indian standard.

36.4.3 Effect of Lane Distribution

Congestion and Delay at intersection particularly formed by to too many vehicles are moving

same lane. So reduce that problem, we need to provide lane distribution. The lane distribution

at intersection normally followed two categories.

First one is the total volume of given approach are distributed by providing separate lane

for left, right and through movement. For that individual movement, we need to fix some

percentage of total flow at that particular approach. This type clearly defined in Figure 5 and

following example.

In second type, the given approach total volumes are separated by individual lane for left,

right and straight. And straight moving vehicles also distributed into left and right turn lanes

for unavoidable condition. If through movement vehicles are high, we need to follow second

type distribution. Second type is explained in Figure 6 and example. Normally high straight

cases we followed second method. In that second type divided into two distribution methods.

First one is, through movement distributed into left, right and straight lanes. Second is, extra

separate lane provide for through movement. So each cases some lane distribution factors are

followed. That importance points are shown in following examples.

Numerical example

Find Critical Volume (Vi) for a Given 4 arm Intersection. Traffic flow Proportion of Left

and Right turn are 10% and 20% respectively (For all approach). Left and Right turn Lane

utilization factors are 0.2 and 0.3 respectively. Use following Phase Plan:

Solution: From West to East,

• Left turn Traffic movement from total directional movement = 10%

• Right turn Traffic from total directional movement = 20%

• Through Traffic from total directional movement = 70%



1985

EW

1453

1245

2300

P1 P2 P3 P4

• Left turning Vehicles = 2300 × 0.1 = 230 veh/hr

• Right turning Vehicles = 2300 × 0.2 = 460 veh/hr

• Through Movement Vehicles = 2300 × 0.7 = 1610 veh/hr

Lane Distribution

• Left turn utilisation factor = 0.2

• Right turn utilisation factor = 0.3

• Through traffic in Left turn Lane = (2300 × 0.7) × 0.2 = 322 veh/hr

• Through traffic in Right turn Lane = (2300 × 0.7) × 0.3 = 483 veh/hr

• Through traffic in Median Lane = (2300 × 0.7) × 0.5 = 805 veh/hr

From East to west,








• Through Movement Vehicles = 1985 × 0.7 = 1390 veh/hr

Lane Distribution

• Left turn utilisation factor = 0.2

• Right turn utilisation factor = 0.3

• Through traffic in Left turn Lane = (1985 × 0.7) × 0.2 = 278 veh/hr

• Through traffic in Right turn Lane = (1985 × 0.7) × 0.3 = 417 veh/hr

• Through traffic in Median Lane = (1985 × 0.7) × 0.5 = 695 veh/hr

From North to south,






• Through Movement Vehicles =1453 × 0.7 = 1017 veh/hr

From south to North,




• Left turning Vehicles =1245 × 0.1 = 124 veh/hr

• Right turning Vehicles =1245 × 0.2 = 250 veh/hr

• Through Movement Vehicles =1245 × 0.7 = 871 veh/hr

Vi = V1 + V2 + V3 + V4 = 804 + 695 + 871 + 1071 = 3442 veh/hr



��

��215400140

196367170

187

433

220120 417 233

Figure 36:1: Traffic flow for a typical four-legged intersection

P1

433

400

P2

417

367

P3

196

233

P4

215

187

Figure 36:2: Phase plan

Numerical example

The traffic flow for a four-legged intersection is as shown in figure 36:1. Given that the lost

time per phase is 2.4 seconds, saturation headway is 2.2 seconds, amber time is 3 seconds per

phase, find the cycle length, green time and performance measure(delay per cycle). Assume

critical v/c ratio as 0.9.

Solution

1. The phase plan is as shown in figure 36:2. Sum of critical lane volumes is the sum of

maximum lane volumes in each phase, ΣVCi = 433+417+233+215 = 1298 vph.

2. Saturation flow rate, Si from equation=3600

2.2= 1637 vph. Vc

Si= 433

1637+ 417

1637+ 233

1637+ 1298

1637=

0.793.

3. Cycle length can be found out from the equation C=4×2.4×0.9

0.9− 1298

1637

= 80.68 seconds ≈ 80

seconds.



Phase 1

Phase 2

Phase 4

Pedestrian phase

23 3 78.5

26

Phase 3

52

3

4

13

1268

3

23 3

17.583

21.5

36.5

52.5

104.5

Figure 36:3: Timing diagram

4. The effective green time can be found out as Gi = VCi

VC× (C − L) = 80-(4×2.4)= 70.4

seconds, where L is the lost time for that phase = 4× 2.4.

5. Green splitting for the phase 1 can be found out ?? as g1 = 70.4 × [ 483

1298] = 22.88 seconds.

6. Similarly green splitting for the phase 2,g2 = 70.4 × [ 417

1298] = 22.02 seconds.


1298] = 12.04 seconds.


1298] = 11.66 seconds.

9. The actual green time for phase 1 from equationG1= 22.88-3+2.4 ≈ 23 seconds.

10. Similarly actual green time for phase 2, G2 = 22.02-3+2.4 ≈ 23 seconds.



13. Pedestrian time can be found out from as Gp = 4 + 6×3.51.2

= 21.5 seconds. The phase

diagram is shown in figure 36:3. The actual cycle time will be the sum of actual green

time plus amber time plus actual red time for any phase. Therefore, for phase 1, actual

cycle time = 23+3+78.5 = 104.5 seconds.

14. Delay at the intersection in the east-west direction can be found out from equationas

dEW =104.5

2[1 −

23−2.4+3

104.5]2

1 −433

1637

= 42.57sec/cycle.



15. Delay at the intersection in the west-east direction can be found out from equation,as

dWE =104.5

2[1 −

23−2.4+3

104.5]2

1 −400

1637

= 41.44sec/cycle. (36.3)

16. Delay at the intersection in the north-south direction can be found out from equation,

dNS =104.5

2[1 −

23−2.4+3

104.5]2

1 −367

1637

= 40.36sec/cycle. (36.4)

17. Delay at the intersection in the south-north direction can be found out from equation,

dSN =104.5

2[1 −

23−2.4+3

104.5]2

1 −417

1637

= 42.018sec/cycle. (36.5)

18. Delay at the intersection in the south-east direction can be found out from equation,

dSE =104.5

2[1 −

13−2.4+3

104.5]2

1 − 233

1637

= 46.096sec/cycle. (36.6)

19. Delay at the intersection in the north-west direction can be found out from equation,

dNW =104.5

2[1 −

13−2.4+3

104.5]2

1 −196

1637

= 44.912sec/cycle. (36.7)

20. Delay at the intersection in the west-south direction can be found out from equation,

dWS =104.5

2[1 −

12−2.4+3

104.5]2

1 −215

1637

= 46.52sec/cycle. (36.8)

21. Delay at the intersection in the east-north direction can be found out from equation,

dEN =104.5

2[1 −

12−2.4+3

104.5]2

1 −187

1637

= 45.62sec/cycle. (36.9)

36.5 Summary

Green splitting is done by proportioning the green time among various phases according to the

critical volume of the phase. Pedestrian phases are provided by considering the walking speed

and start-up lost time. Like other facilities, signals are also assessed for performance, delay

being th e important parameter used.



36.6 References


New Delhi, 1987.




Transportation Systems Engineering 37. Capacity and LOS Analysis of a Signalized I/S

Chapter 37

Capacity and LOS Analysis of a

Signalized I/S

37.1 Overview

The Highway Capacity Manual defines the capacity as the maximum howdy rate at which

persons or vehicle can be reasonably expected to traverse a point or a uniform segment of

a lane or roadway during a given time period, under prevailing roadway, traffic and control

conditions. Level-of-Service is introduced by HCM to denote the level of quality one can derive

from a local under different operation characteristics and traffic volume.

37.2 Methodology

37.2.1 Scope

This chapter contains a methodology for analyzing the capacity and level of service (LOS) of

signalized intersections. The analysis must consider a wide variety of prevailing conditions,

including the amount and distribution of traffic movements, traffic composition, geometric

characteristics, and details of intersection signalization. The methodology focuses on the de-

termination of LOS for known or projected conditions. The capacity analysis methodology for

signalized intersections is based on known or projected signalization plans.

37.2.2 Limitation

The methodology does not take into account the potential impact of downstream congestion

on intersection operation. Nor does the methodology detect and adjust for the impacts of

turn-pocket overflows on through traffic and intersection operation.



37.2.3 Objective

This method uses wide range of operational configuration along with various phase plans, lane

utilization, and left-turn treatment alternatives.

• Geometric condition

• Traffic condition

• Signalization condition

The primary output of the method is level of service (LOS). This methodology covers a wide

range of operational configurations, including combinations of phase plans, lane utilization, and

left-turn treatment alternatives. The below figure shows the signalized intersection methodol-

ogy.

Input parametersGeometricTrafficSignal

Saturation flow rateBasic equationAdjustment factor

Lane grouping and demand Flow rateLane groupingPHFRTOR

Capacity and v/cCapacityv/c

Performance measuresDelay

LOS

back of queue

Progression adjustment

Figure 37:1: signalized intersection methodology

37.3 Input parameters

To conduct operational analysis offor signalized intersection, no. of input parameters are re-

quired. The data needed are detailed and varied and fall into three main categories: geometric,

traffic, and signalization.

37.3.1 Geometric condition

Intersection geometry is generally presented in diagrammatic form and must include all of the

relevant information, including approach grades, the number and width of lanes, and parking

conditions.



Table 37:1: Input data needs for each analysis of lane group

Condition Parameter

Geometric Area type

Number of lanes, N

Average lane width, W (m)

Grade, G (%)

Existence of exclusive LT or RT lanes

Length of storage bay, LT or RT lane, L s (m)

Parking

Traffic Demand volume by movement, V (veh/h)

Base saturation flow rate, s o (pc/h/ln)

Peak-hour factor, PHF

Percent heavy vehicles, HV (%)

Approach pedestrian flow rate, vped (p/h)

Local buses stopping at intersection, NB (buses/h)

Parking activity, Nm (maneuvers/h)

Arrival type, AT

Proportion of vehicles arriving on green, P

Approach speed, S A (km/h)

Control Cycle length, C (s)

Green time, G (s)

Yellow-plus-all-red change-and-clearance interval

(intergreen), Y (s)

Actuated or pretimed operation

Pedestrian push-button

Minimum pedestrian green, Gp (s)

Phase plan

Analysis period, T (h)



AT Description

1 Dense platoon- 80% arrived at start of red

2 Moderately dense- 40-80% arrived during red

3 Less than 40% (highly dispersed platoon)

4 Moderately dense, 40-80% arrived iduring green

5 Dense to moderately dense- 80% arrive at start of green

6 Very dense platoons progressing over a no. of closed space I/S

37.3.2 Traffic condition

Traffic volumes (for oversaturated conditions, demand must be used) for the intersection must

be specified for each movement on each approach. In situations where the v/c is greater than

about 0.9, control delay is significantly affected by the length of the analysis period.

• If v/c exceeds 1.0 during the analysis period, the length of the analysis period should be

extended to cover the period of oversaturation in the same fashion, as long as the average

flow during that period is relatively constant.

• An important traffic characteristic that must be quantified to complete an operational

analysis of a signalized intersection is the quality of the progression. The parameter that

describes this characteristic is the arrival type, AT, for each lane group. The arrival type

should be determined as accurately as possible because it will have a significant impact

on delay estimates and LOS determination. It can be computed as

Rp = P/(gi/C) (37.1)

where, Rp = platoon ratio, P = proportion of all vehicles in movement arriving during

green phase, C = cycle length (s) and gi = effective green time for movement or lane

group (s).

37.3.3 Signalization condition :

Complete information regarding signalization is needed to perform an analysis. This infor-

mation includes a phase diagram illustrating the phase plan, cycle length, green times, and

change-and-clearance intervals. If pedestrian timing requirements exist, the minimum green

time for the phase is indicated and provided for in the signal timing. The minimum green time



for a phase is estimated as,

GP = 3.2 + L/Sp + 0.81(Nped/WE) for WE > 3.0m (37.2)

GP = 3.2 + L/Sp + 0.27Nped for WE ≤ 3.0m (37.3)

where, Gp = minimum green time (s), L = crosswalk length (m), Sp = average speed of

pedestrians (m/s), WE = effective crosswalk width (m), 3.2 = pedestrian start-up time (s), and

Nped = number of pedestrians crossing during an interval (p).

37.4 Determining flow rate

The methodology for signalized intersections is disaggregate; that is, it is designed to consider

individual intersection approaches and individual lane groups within approaches. Segmenting

the intersection into lane groups is a relatively simple process that considers both the geometry

of the intersection and the distribution of traffic movements. Demand volumes are best provided

as average flow rates (in vehicles per hour) for the analysis period. However, demand volumes

may also be stated for more than one analysis period, such as an hourly volume. In such cases,

peaking factors must be provided that convert these to demand flow rates for each particular

analysis period. In that case,

VP = V/PHF (37.4)

37.5 Determining saturation flow rate

A saturation flow rate for each lane group is computed according to above equation. The

saturation flow rate is the flow in vehicles per hour that can be accommodated by the lane

group assuming that the green phase were displayed 100 percent of the time (i.e., g/C = 1.0).

S = SO × NfwfHV fgfpfbbfafLUfLT fRT fLpbfRpb (37.5)

where, S = saturation flow rate for subject lane group, expressed as a total for all lanes in lane

group (veh/h); SO = base saturation flow rate per lane (pc/h/ln); N = number of lanes in lane

group; fw = adjustment factor for lane width; fHV = adjustment factor for heavy vehicles in

traffic stream; fg = adjustment factor for approach grade; fp = adjustment factor for existence

of a parking lane and parking activity adjacent to lane group; fbb = adjustment factor for

blocking effect of local buses that stop within intersection area; fa = adjustment factor for area

type; fLU = adjustment factor for lane utilization; fLT = adjustment factor for left turns in lane

group; fRT = adjustment factor for right turns in lane group; fLpb = pedestrian adjustment



factor for left-turn movements; and fRpb = pedestrian-bicycle adjustment factor for right-turn

movements.

37.5.1 Base saturation flow rate :

For the analysis of saturation flow rate, a fixed volume is taken as a base called base saturation

flow rate, usually 1,900 passenger cars per hour per lane (pc/h/ln). This value is adjusted for

a variety of conditions. The adjustment factors are given below.

37.5.2 Adjustment for lane width:

The lane width adjustment factor fw accounts for the negative impact of narrow lanes on

saturation flow rate and allows for an increased flow rate on wide lanes. The lane width factor

can be calculated for lane width greater than 4.8m. The use of two narrow lanes will always

result in higher saturation capacity than one single wide lane.

fw = 1 + (w − 3.6)/9 (37.6)

where, w = width of lane

37.5.3 Adjustment for Heavy Vehicles and Grade :

passenger cars are affected by approach grades, as are heavy vehicles. The heavy-vehicle factor

accounts for the additional space occupied by these vehicles and for the difference in operating

capabilities of heavy vehicles compared with passenger cars. The passenger-car equivalent (ET)

used for each heavy vehicle is 2.0 passenger-car units and is reflected in the formula. The grade

factor accounts for the effect of grades on the operation of all vehicles.

fHV = 100/[100 + %HV (ET − 1)] (37.7)

fg = 1 − %G/200 (37.8)

where, % HV = % heavy vehicles for lane group volume, ET = 2.0, % G = % grade on a lane

group approach

37.5.4 Adjustment for Parking

Parking maneuver assumed to block traffic for 18 s. Use practical limit of 180 maneuvers/h.

The parking adjustment factor, fp, accounts for the frictional effect of a parking lane on flow

in an adjacent lane group as well as for the occasional blocking of an adjacent lane by vehicles



moving into and out of parking spaces. Each maneuver (either in or out) is assumed to block

traffic in the lane next to the parking maneuver for an average of 18 s.

fP = [N − 0.1 − (18Nm/3600)]/N (37.9)

where, Nm = number of parking maneuvers/h, N = no. of lanes

37.5.5 Adjustment for Bus Blockage

The bus blockage adjustment factor, fbb, accounts for the impacts of local transit buses that

stop to discharge or pick up passengers at a near-side or far-side bus stop within 75 m of the

stop line (u/s or d/s). If more than 250 buses per hour exist, a practical limit of 250 should be

used. The adjustment factor can be written as,

fbb = [N − (14.4NB/3600)]/N (37.10)

where, NB = no. of buses stopping per hour

37.5.6 Adjustment for Area Type

The area type adjustment factor, fa, accounts for the relative inefficiency of intersections in

business districts in comparison with those in other locations. Application of this adjustment

factor is typically appropriate in areas that exhibit central business district (CBD) character-

istics. It can be represented as, fa = 0.9 in CBD (central business district) and = 1.0 in all

others

37.5.7 Adjustment for Lane Utilization

The lane utilization adjustment factor, fLU, accounts for the unequal distribution of traffic

among the lanes in a lane group with more than one lane. The factor provides an adjustment

to the base saturation flow rate. The adjustment factor is based on the flow in the lane with

the highest volume and is calculated by Equation 10.

fLU = Vg/(Vg1N) (37.11)

where, Vg = unadjusted demand flow rate for lane group (veh/ h), Vg1 = unadjusted demand

flow rate on single lane with highest volume in the lane group and N = no. of lanes in the

group.



37.6 Determining capacity and v/c ratio:

Capacity at signalized intersections is based on the concept of saturation flow and defined

saturation flow rate. The flow ratio for a given lane group is defined as the ratio of the actual

or projected demand flow rate for the lane group (vi) and the saturation flow rate(si). The

flow ratio is given the symbol (v/s)i for lane group i. Capacity at signalized I/S is based on the

saturation flow and saturation flow rate.

Ci = si × (gi/c) (37.12)

where ci = capacity of lane group i (veh/h), si = saturation flow rate for lane group i (veh/h)

and gi/C = effective green ratio for lane group i.

37.6.1 v/c ratio:

The ratio of flow rate to capacity (v/c), often called the volume to capacity ratio, is given the

symbol X in intersection analysis

Xi = (v

c)i =

vi

si(gi

C)

=vic

sigi

(37.13)

where, Xi = (v/c)i = ratio for lane group i, vi = actual or projected demand flow rate for lane

group i (veh/h), si = saturation flow rate for lane group i (veh/h), gi = effective green time for

lane group i (s) and C = cycle length (s)

37.6.2 Critical lane group:

Another concept used for analyzing signalized intersections is the critical v/c ratio, Xc. This

is the v/c ratio for the intersection as a whole, considering only the lane groups that have

the highest flow ratio (v/s) for a given signal phase. For example, with a two-phase signal,

opposing lane groups move during the same green time. Generally, one of these two lane

groups will require more green time than the other (i.e., it will have a higher flow ratio). This

would be the critical lane group for that signal phase. The critical v/c ratio for the intersection

is determined by using Equation,

Xc =∑

( v

S

)

(C

C − L) (37.14)

where, Xc = critical v/c ratio for intersection; The above eqn. is useful in evaluating the overall

i/s w.r.t the geometrics and toal cycle length. A critical v/c ratio less than 1.0, however, does

indicate that all movements in the intersection can be accommodated within the defined cycle

length.



Table 37:2: Relation between arrival type (AT) and platoon ratio

AT Ration Default Rp Progression quality

1 ≤ 0.50 0.333 very poor

2 0.50-0.85 0.667 Unfavourable

3 0.85-1.15 1.000 Random arrivals

4 1.15-1.50 1.333 Favourable

5 1.50-2.00 1.667 Highly favourable

6 2.00 2.000 Exceptional

37.7 Determining delay

The values derived from the delay calculations represent the average control delay experienced

by all vehicles that arrive in the analysis period, including delays incurred beyond the analysis

period when the lane group is oversaturated. The average control delay per vehicle for a given

lane group is given by Equation,

d = d1(PF ) + d2 + d3

where, d = control delay per vehicle (s/veh); d1 = uniform control delay assuming uniform

arrivals (s/veh); PF = uniform delay progression adjustment factor, d2 = incremental delay to

account for effect of random arrivals and d3 = initial queue delay, which accounts for delay to

all vehicles in analysis period

37.7.1 Progression adjustment factor

Good signal progression will result in a high proportion of vehicles arriving on the uniform

delay Green and vice-versa. Progression primarily affects uniform delay, and for this reason,

the adjustment is applied only to d1. The value of PF may be determined using Equation,

PF =(1 − P )fPA

1 − ( g

C)

(37.15)

where, PF = progression adjustment factor, P = proportion of vehicles arriving on green, g/C =

proportion of green time available, fP A = supplemental adjustment factor for platoon arriving

during green. The approximate ranges of RP are related to arrival type as shown below. PF

may be calculated from measured values of P using the given values of fPA or the following

table can be used to determine PF as a function of the arrival type.



Table 37:3: Progression adjustment factor for uniform delay calculation

Green Ratio Arrival Type (AT)

(g/C) AT1 AT2 AT3 AT4 AT5 AT6

0.2 1.167 1.007 1 1 0.833 0.75

0.3 1.286 1.063 1 0.986 0.714 0.571

0.4 1.445 1.136 1 0.895 0.555 0.333

0.5 1.667 1.24 1 0.767 0.333 0

0.6 2.001 1.395 1 0.576 0 0

0.7 2.556 1.653 1 0.256 0 0

fPA 1 0.93 1 1.15 1 1

Default, Rp 0.333 0.667 1 1.333 1.667 2

37.7.2 Uniform delay

It is based on assuming uniform arrival, uniform flow rate & no initial queue. The formula for

uniform delay is,

d1 =0.5C(1 −

g

C)2

1 − [min(1, X) g

C]

(37.16)

where, d1 = uniform control delay assuming uniform arrivals (s/veh), C = cycle length (s);

cycle length used in pretimed signal control, g = effective green time for lane group, X = v/c

ratio or degree of saturation for lane group.

37.7.3 Incremental delay

The equation below is used to estimate the incremental delay due to nonuniform arrivals and

temporary cycle failures (random delay. The equation assumes that there is no unmet demand

that causes initial queues at the start of the analysis period (T).

d2 = 900 T

[

(X − 1) +

√

(X − 1)2 +8klX

cT

]

(37.17)

where, d2 = incremental delay queues, T = duration of analysis period (h); k = incremental

delay factor that is dependent on controller settings, I = upstream filtering/metering adjustment

factor; c = lane group capacity (veh/h), X = lane group v/c ratio or degree of saturation, and

K can be found out from the following table.



Table 37:4: k-values to account for controller type

Unit Degree of Saturation (X)

Extension (s) ≤ 0.50 0.6 0.7 0.8 0.9 ≥ 1.0

≤ 2.0 0.04 0.13 0.22 0.32 0.41 0.5

2.5 0.08 0.16 0.25 0.33 0.42 0.5

3 0.11 0.19 0.27 0.34 0.42 0.5

3.5 0.13 0.2 0.28 0.35 0.43 0.5

4 0.15 0.22 0.29 0.36 0.43 0.5

4.5 0.19 0.25 0.31 0.38 0.44 0.5

5.0a 0.23 0.28 0.34 0.39 0.45 0.5

Pretimed 0.5 0.5 0.5 0.5 0.5 0.5

37.7.4 Agreegated delay estimates

The delay obtained has to be aggrregated, first for each approach and then for the intersection

The weighted average of control delay is given as:

dA =∑

divi/∑

vi

where, di = delay per vehicle for each movement (s/veh), dA = delay for Approach A (s/veh),

and vA = adjusted flow for Approach A (veh/h).

d1 =∑

dA × vA/∑

vA

37.7.5 Determination of LOS

Intersection LOS is directly related to the average control delay per vehicle. Any v/c ratio

greater than 1.0 is an indication of actual or potential breakdown. In such cases, multiperiod

analyses are advised. These analyses encompass all periods in which queue carryover due to

oversaturation occurs. A critical v/c ratio greater than 1.0 indicates that the overall signal and

geometric design provides inadequate capacity for the given flows. In some cases, delay will be

high even when v/c ratios are low.

37.7.6 Sensitivity of results to input variables

The predicted delay is highly sensitive to signal control characteristics and the quality of pro-

gression. The predicted delay is sensitive to the estimated saturation flow only whendemand



Table 37:5: LOS criteria for signalized intersection in term of control delay per vehicle (s/veh)

LOS Delay

A ≤ 10

B 10-20

C 20-35

D 35-55

E 55-80

F >80

approaches or exceeds 90 percent of the capacity for a lane group or an intersection approach.

The following graph shows the sensitivity of the predicted control delay per vehicle to demand

to capacity ratio, g/c, cylace legth and leght of analysis period. Assumptions are : Cycle length

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

800

100

200

300

400

500

600

700

Demand/Capacity Ratio

Del

ay (

s/ve

h)

Figure 37:2: sensitivity of delay to demand to capacity ratio

= 100s, g/c = 0.5, T =1h, k = 0.5, l= 1, s = 1800 veh/hr

37.8 Conclusion

HCM model is very useful for the analysis of signalized intersection as it considers all the

adjustment factors which are to be taken into account while designing for a signalized I/S.

Though,the procedure is lengthy but it is simple in approach and easy to follow.



0 0

200

400

600

800

1000

1200

1400

0.750.70.650.60.550.50.450.40.350.3

g/C

Del

ay (

s/ve

h)

v/c=1.0

v/c=1.7

Figure 37:3: sensitivity of delay Vs g/c ratio

Too Long

Cycle Length

OptimumToo Short

Del

ay

Figure 37:4: sensitivity of delay Vs cycle length

37.9 References




New Delhi, 1987.


Transportation Systems Engineering 38. Coordinated Traffic Signal

Chapter 38

Coordinated Traffic Signal

38.1 Overview

This chapter covers basic aspects of traffic signal coordination. Signal coordination is done

when they are closely space to enable vehicle in one predominent direction to get continous

green. This will reduce the delay and travel time in one direction and increases throughput.

The design priciples of signal coordination will be presented in this chapter.

38.2 Concepts of signal coordination

For signals that are closely spaced, it is necessary to coordinate the green time so that vehicles

may move efficiently through the set of signals. In some cases, two signals are so closely spaced

that they should be considered to be one signal. In other cases, the signals are so far apart that

they may be considered independently. Vehicles released from a signal often maintain their

grouping for well over 335m.

38.2.1 Factors affecting coordination

There are four major areas of consideration for signal coordination:

1. Benefits

2. Purpose of signal system

3. Factors lessening benefits

4. Exceptions to the coordinated scheme

The most complex signal plans require that all signals have the same cycle length. Fig. 38:1

illustrates path (trajectory) that a vehicle takes as time passes. At t = t1, the first signal turns



signal greenyellow

red

Time

signalsecond

signalFirst

Signal offsett= $t_{2}$

$t_{1}$

Figure 38:1: Vehicle trajectory

green. After some lag, the vehicle starts and moves down the street. It reaches the second

signal at some time t = t2. Depending on the indication of that signal, it either continues or

stops. The difference between the two green initiation times is referred to as the signal offset, or

simply as the offset. In general, the offset is defined as the difference between green initiation

times, measured in terms of the downstream green initiation relative to the upstream green

initiation.

38.2.2 Benefits

It is common to consider the benefit of a coordination plan in terms of a cost or penalty function;

a weighted combination of stops and delay, and other terms as given here:

cost = A × (total stops) + B × (total delay) + (other terms) (38.1)

The object is to make this disbenefit as small as possible. The weights A and B are coefficients

to be specified by the engineer or analyst. The values of A and B may be selected so as to reflect

the estimated economic cost of each stop and delay. The amounts by which various timing plans

reduce the cost, can then be used in a cost-benefit analysis to evaluate alternative plans. The

conservation of energy and the preservation of the environment have grown in importance over

the years. Given that the vehicles must travel, fuel conservation and minimum air pollution

are achieved by keeping vehicles moving as smoothly as possible at efficient speeds. This can

be achieved by a good signal-coordination timing plan. Other benefits of signal coordination

include, maintenance of a preferred speed, possibility of sending vehicles through successive

intersections in moving platoons and avoiding stoppage of large number of vehicles.

38.2.3 Purpose of the signal system

The physical layout of the street system and the major traffic flows determine the purpose of

the signal system. It is necessary to consider the type of system, whether one-way arterial,

two-way arterial, one-way,two-way, or mixed network. the capacitites in both directions on

some streets, the movements to be progressed, determination of preferential paths



Distance (m)

$N$vehicle

600

400

200

0 60 120Time (sec)

Northbound

Figure 38:2: Time space diagram

38.2.4 Factors lessening benefits

Among the factors limiting benefits of signal coordination are the following:

• inadequate roadway capacity

• existence of substantial side frictions, including parking, loading, double parking, and

multiple driveways

• wide variability in traffic speeds

• very short signal spacing

• heavy turn volumes, either into or out of the street

38.2.5 Exceptions of the coordinated scheme

All signals cannot be easily coordinated. When an intersection creating problems lies directly in

the way of the plan that has to be designed for signal coordination, then two separate systems,

one on each side of this troublesome intersection, can be considered. A critical intersection is

one that cannot handle the volumes delivered to it at any cycle length.

38.2.6 Time-space diagram and ideal offsets

The time-space diagram is simply the plot of signal indications as a function of time for two or

more signals. The diagram is scaled with respect to distance, so that one may easily plot vehicel

positions as a position of time. Fig. 38:2 is a time-space diagram for two intersections. The

standard conventions are used in Fig. 38:2: a green signal indication is shown by a blank or thin

line, amber by a shaded line and red by a solid line. For purpose of illustration of trajectory

in the time space diagram for intersections, a northbound vehicle going at a constnat speed of

40fps is shown. The ideal offset is defined as the offset that will cause the specified objective to



Distance (m)

$N$vehicle

600

400

200

0 60 120Time (sec)

Northbound

Figure 38:3: Case study:progression on a one way street

be best satisfied. For the objective of minimum delay, it is the offset that will cause minimum

delay. In Fig. 38:2, the ideal offset is 25 sec for that case and that objective. If it is assumed

that the platoon was moving as it went through the upstream intersection then the ideal offset

is given by

t(ideal) =L

S(38.2)

where: t(ideal) = ideal offset,sec, L = block length, m, S = vehicle speed, mps.

38.3 Signal progression on one-way streets

38.3.1 Determining ideal offsets

In Fig. 38:3 a one-way arterial is shown with the link lengths indicated. Assuming no vehicles

are queued at the signals, the ideal offsets can be determined if the platoon speed is known. For

the purpose of illustration, a platoon speed of 60 fps is assumed. The offsets are determined

according to Eqn. 38.2. Next the time-space diagram is constructed according to the following

rules:

1. The vertical should be scaled so as to accomodate the dimensions of the arterial, and the

horizontal so as to accomodate atleast three to four cycle lengths.

2. The beginning intersection should be scaled first, usually with main street green initiation

at t=0, followed by periods of green and red.

3. The main street green of the next downstream signal should be located next, relative to

t=0 and at the proper distance fromt he first intersection. With this point located, the

periods of green, yellow and red for this signal are filled in.

4. This procedure is repeated for all other intersections working one at a time.



Dis

tanc

e (m

)

Time (sec)

2000

16001200

800

4000

60Point 1 120 180 240

point 3

Point 2

6

54

3

21

Figure 38:4: Time space diagram for case study

6

0180 24012060

1

2

3

45

2000

16001200

800

400

Dis

tan

ce (

m)

Time (sec)

Figure 38:5: Vehicle trajectory and green wave in a progressed movement

Fig. 38:4 shows the time-space diagram for the illustration mentioned previously. Fig. 38:5

explores some features of the time-space diagram.

38.3.2 Effect of vehicles queued at signals

It sometimes happens that there are vehicles stored in block waiting for a green light. These

may be stragglers from the last platoon, vehicles that turned into the block, or vehicles that

came out of parking lots or spots. The ideal offset must be adjusted to allow for these vehicles,

so as to avoid unnecessary stops. The ideal offset can then be given as:

tideal =L

S− (Qh + Loss1) (38.3)

where, Q = number of vehicles queued per lane, veh, h= discharge headway of queued ve-

hicle, sec/veh, and Loss1 = loss time associated with vehicles starting from rest at the first

downstream signal.

38.3.3 A note on queue estimation

If it is known that there exists a queue and its size is known approximately, then the link offset

can be set better than by pretending that no queue exists. There can be great cycle-to-cycle

variation in the actual queue size, although its average size may be estimated. Even then,

queue estimation is a difficult and expensive task and should be viewed with caution.



60 120 180 2401

2

3

45

6 2000

16001200

800

400

0

Time (sec)

Dis

tan

ce (

m)

Figure 38:6: Moving southbound

$t_{NB} + t_{SB} = C$$t_{NB}$

$t_{SB}$

$2C$$C$

$L$

Figure 38:7: Offsets on 2 way arterials are not independent- One cycle length

38.4 Signal Progression on two-way streets

Consider that the arterial shown in Fig. 38:3 is not a one-way but rather a two-way street.

Fig. 38:6 shows the trajectory of a southbound vehicle on this arterial.

38.4.1 Offset determination on a two-way street

If any offset were changed in Fig. 38:6 to accomodate the southbound vehicle(s), then the

northbound vehicle or platoon would suffer. The fact that offsets are interrelated presents one

of the most fundamental problems of signal optimization. The inspection of a typical cycle (as

in Fig. 38:7) yields the conclusion that the offsets in two directions add to one cycle length.

For longer lengths (as in Fig. 38:8) the offsets might add to two cycle lengths. When queue

clearances are taken into account, the offsets might add to zero lengths. The general expression

Distance $2C$

$t_{NB}$

$L$

$t_{SB}$

$C$ $2C$

Figure 38:8: Offsets on 2 way arterials are not independent- Two cycle length



3 2

$A$

$N$

One way Progressions

1$D$4

$C$

$B$$N$

Streets with implied offsets

Figure 38:9: Closure effect in grid

for the two offsets in a link on a two-way street can be written as

tNB,i + tSB,i = nC (38.4)

where the offsets are actual offsets, n is an integer and C is the cycle length. Any actual offset

can be expressed as the desired ideal offset, plus an error or discrepancy term:

tactual(j,i) = tideal(j,i) + e(j,i) (38.5)

where j represents the direction and i represents the link.

38.4.2 Offset determination in a grid

A one-way street system has a number of advantages, not the least of which is traffic elimination

of left turns against opposing traffic. The total elimination of constraints imposed by the closure

of loops within the network or grid is not possible. Fig. 38:9 highlights the fact that if the cycle

length, splits, and three offsets are specified, the offset in the fourth link is determined and

cannot be independently specified. Fig. 38:9 extends this to a grid of one-way streets, in which

all of the north-south streets are independently specified. The specification of one east-west

street then locks in all other east-west offsets. The key feature is that an open tree of one-way

links can be completely independently set, and that it is the closing or closure of the open tree

which presents constraints on some links.

38.5 Bandwidth concept

The bandwidth concept is very popular in traffic engineering practice, because

1. the windows of green (through which platoons of vehicles can move) are easy visual images

for both working profeesionals and public presentations

2. good solutions can often be obtained manually, by trial and error.



vehicleDistance (m) Northbound

Time (sec)

4 600

4003

2 200

0 60 1201

Figure 38:10: Bandwidths on a time space diagram

38.5.1 Bandwidth and efficiency of a progression

The efficiency of a bandwidth (measured in seconds) is defined as the ratio of the bandwidth

to the cycle length, expressed as a percentage:

efficiency =bandwidth

cycle length× 100% (38.6)

An efficiency of 40% to 50% is considered good. The bandwidth is limited by the minimum

green in the direction of interest. Fig. 38:10 illustrates the bandwidths for one signal-timing

plan. The northbound efficiency can be estimated as (17/60)100% = 28.4%. There is no

bandwidth through the south-bound. The system is badly in need of retiming atleast on the

basis of the bandwidth objective. In terms of vehicles that can be put through this system

without stopping, note that the northbound bandwidth can carry 17/2.0 = 8.5 vehicles per

lane per cycle in a nonstop path through the defined system. The northbound direction can

handle8.5veh

cycle×

cycle

60sec×

3600sec

hr= 510vph per lane

very efficiently if they are organized into 8-vehicle platoons when they arrive at this system.

If the per lane demand volume is less than 510vphpl and if the flows are so organized, the

system will operate well in the northbound direction, even though better timing plans might

be obtained. The computation can be formalized into an equation as follows:

nonstop volume =3600(BW )(L)

(h)(C)vph (38.7)

where: BW = measured or computed bandwidth, sec, L= number of through lanes in indicated

direction, h = headway in moving platoon, sec/veh,and C =cycle length.

38.5.2 Trial-and-error approach to find bandwidth

The engineer ususally wishes to design for maximum bandwidth in one direction, subject to

some relation between the bandwidths in the two directions. There are both trial-and-error



180

600m

600m

3

1500 vph

1500 vpl

N

600m

4

2

1

(m) Distance

2 lanes/directions

V = 20m/s

60 120

Time (sec)

Figure 38:11: Case study:Four intersections with good progressions

Distance (m) Intersection

1

2

New

3

4

Time (sec)12060 180

Figure 38:12: Effect of inserting a new signal into system

and somewhat elaborate manual techniques for establishing maximum bandwidths. Refer to

Fig. 38:11, which shows four signals and decent progressions in both the directions. For purpose

of illustration, assume it is given that a signal with 50:50 split may be located midway between

Intersections 2 and 3. The possible effect as it appears in Fig. 38:12 is that there is no way to

include this signal without destroying one or the other through band, or cutting both in half.

The offsets must be moved around until a more satisfactory timing plan develops. A change in

cycle length may even be required. The changes in offset may be explored by:

• copying the time-space diagram of Fig. 38:12

• cutting the copy horizontally into strips, one strip per intersection

• placing a guideline over the strips, so as to indicate the speed of the platoon(s) by the

slope of the guideline

• sliding the strips relative to each other, until some improved offset pattern is identified

There is no need to produce new strips for each cycle length considered: all times can be made

relative to an arbitrary cycle length ‘C. The only change necessary is to change the slope(s) of

the guidelines representing the vehicle speeds. The northbound vehicle takes 3600/60 = 60sec

to travel from intersection 4 to intersection 2. If the cycle length C = 120sec, the vehicle would



have arrived at intersection 2 at C/2, or one half of the cycle length. To obtain a good solution

through trial-and-error attempt, the following should be kept in consideration:

• If the green initiation at Intersection 1 comes earlier, the southbound platoon is released

sooner and gets stopped or disrupted at intersection 2.

• Likewise, intersection 2 cannot be northbound without harming the southbound.

• Nor can intersection 3 help the southbound without harming the northbound.

38.5.3 A historical perspective on the use of bandwidth

An elegant mathematical formulation requiring two hours of computation on a supercomputer

is some-what irrelevant in most engineering offices. The determination of good progressions on

an arterial must be viewed in this context:only 25 years ago, hand held calculators did not exist;

20 years ago, calculators had only the most basic functions. 15 years ago, personal computers

were at best a new concept. Previously, engineers used slide rules. Optimization of progressions

could not depend on mathematical formulations simply because even one set of computations

could take days witht he tools available. Accordingly,graphical methods were developed. The

first optimization programs that took queues and other detaisl into account began to appear,

leading to later developments that produced the signal-optimization programs in common use

in late 1980s. As computers became more accessible and less expensive, the move to computer

solutions accelerated in the 1970s. New work on the maximum-bandwidth solution followed

with greater computational power encouraging the new formulations.

38.6 Forward and reverse progressions

Simple progression is the name given to the progression in which all the signals are set so that

a vehicle released from the first intersection will arrive at the downstream intersections just as

the signals at those intersections initiate green. As the simple progression results in a green

wave that advances with the vehicles, it is often called a forward progression. It may happen

that the simple progression is revised two or more times in a day, so as to conform to the

direction of the major flow, or to the flow level. In this case, the scheme may be referred to as

a flexible progression. Under certain circumstances, the internal queues are sufficiently large

that the ideal offset is negative. The downstream signal must turn green before the upstream

signal, to allow sufficient time for the queue to start moving before the arrival of the platoon.

The visual image of such a pattern is of the green marching upstream, toward the drivers in

the platoon. This is referred to as reverse progression.



38.6.1 Effective progression on two-way streets

In certain geometries it is possible to obtain very effective progressions in both directions on

two-way streets. The existence of these patterns presents the facts that:

• The system cycle length should be specified based primarily on the geometry and platoon

speed whenever possible, to enhance progressions.

• The task of good progression in both directions becomes easy if an appropriate combina-

tion of cycle length, block length and platoon speed exist.

• Whenever possible the value of these appropriate combinations should be considered

explicitly for they can greatly determine the qualityof flow for decades.

• In considering the installations of new signals on existing arterials, the same care should

be taken to preserve the appropriate combinations and/or to introduce them.

38.6.2 Importance of signal phasing and cycle length

The traffic engineer may well be faced with a situation that looks intimidating, but for which

the community seek to have smooth flow of traffic along an arterial or in a system. The orderly

approach begins with first, appreciating the magnitude of the problem. The splits, offsets, and

cycle length might be totally out of date for the existing traffic demand. Even if the plan is

not out of date, the settings in the field might be totally out of date, the settings in the field

might be totally different than those originally intended and/or set. Thus, a logical first step

is simply to ride the system and inspect it. Second, it would be very useful to sketch out how

much of the system can be thought of as an open tree of one way links. A distinction should

be made among

• streets that are one way

• streets that can be treated as one-way, due to the actual or desired flow patterns

• streets that must be treated as two-ways

• larger grids in which streets interact because they form unavoidable closed trees and are

each important in that they cannot be ignored for the sake of establishing a master grid

which is an open tree

• smaller grids in which the issue is not coordination but local land access and circulation



Downtown grids might well fall into the last category, at least in some cases. Third, attention

should focus on the combination of cycle length, block length and platoon speed and their

interaction. Fourth, if the geometry is not suitable, one can adapt and fix up the situation

to a certain extent. Another issue to address, ofcourse, is whether the objective of progressed

movement of traffic should be maintained.

38.6.3 Oversaturated traffic

The problem of oversaturation is not just one of degree but of kind - extreme congestion is

marked by a new phenomenon: intersection blockage. The overall approach can be stated in a

logical set of steps:

• Address the root causes of congestion

• Update the signalization, for poor signalization is frequently the cause of what looks like

an incurable problem

• If the problem persists, use novel signalization to minimize the impact and spatial extent

of the extreme congestion.

• Provide more space by use of turn bays and parking congestions.

• Develop site specific evaluations where there are conflicting goals.

38.6.4 Signal remedies

Signalization can be improved through measures like, reasonably short cycle lengths, proper

offsets and proper splits. Sometimes when there is too much traffic then options such as equity

offsets(to aid cross flows) and different splits may be called upon. A metering plan involving

the three types - internal, external and release - may be applied. Internal metering refers to

the use of control strategies within a congested network so as to influence the distribution of

vehicles arriving at or departing froma critical location. External metering refers to the control

of the major access points to the defined system, so that inflow rates into the system are limited

if the system if the system is already too congested. Release metering refers to the cases in

which vehicles are stored in such locations as parking garages and lots, from which their release

can be in principle controlled.



38.7 Summary

The concept of signal coordination is presented in this chapter. Coordination in one way is

simple and effective and reuslts in better progression. Two-way coordination is complex and

less effective. Bandwidth is an important paramter in evaluating the efficiency of coordination.

Further, the concpets of forward and reverse progression are introduced.

38.8 References




Transportation Systems Engineering 39. Vehicle Actuated Signals

Chapter 39

Vehicle Actuated Signals

39.1 Introduction

Now-a-days, controlling traffic congestion relies on having an efficient and well-managed traffic

signal control policy. Traffic signals operate in either pre-timed or actuated mode or some com-

bination of the two. Pre-timed control consists of a series of intervals that are fixed in duration.

They repeat a preset constant cycle. In contrast to pre-timed signals, actuated signals have

the capability to respond to the presence of vehicles or pedestrians at the intersection. Actu-

ated control consists of intervals that are called and extended in response to vehicle detectors.

The controllers are capable of not only varying the cycle length & green times in response to

detector actuations, but of altering the order and sequence of phases. Adaptive or area traf-

fic control systems (ATCS) belong to the latest generation of signalized intersection control.

ATCS continuously detect vehicular traffic volume, compute optimal signal timings based on

this detected volume and simultaneously implement them. Reacting to these volume variations

generally results in reduced delays, shorter queues and decreased travel times. Coordinating

traffic signals along a single route so that vehicles get progressive green signal at each junction

is another important aspect of ATCS. In the subsequent pages, the operating principles and

features of Vehicle-Actuated Signals & Area Traffic Control Systems will be briefly discussed.

39.2 Vehicle-Actuated Signals

39.2.1 Basic Principles

As stated earlier, Vehicle-Actuated Signals require actuation by a vehicle on one or more

approaches in order for certain phases or traffic movements to be serviced. They are equipped

with detectors and the necessary control logic to respond to the demands placed on them.

Vehicle-actuated control uses information on current demands and operations, obtained from

detectors within the intersection, to alter one or more aspects of the signal timing on a cycle-



by-cycle basis. Timing of the signals is controlled by traffic demand. Actuated controllers may

be programmed to accommodate:

• Variable phase sequences (e.g., optional protected LT phases)

• Variable green times for each phase

• Variable cycle length, caused by variable green times

Such variability allows the signal to allocate green time based on current demands and opera-

tions. A proper clearance interval between the green & the red phases is also ensured.

39.2.2 Advantages of Actuated Signals

The various advantages of actuated signals are stated below:

• They can reduce delay (if properly timed).

• They are adaptable to short-term fluctuations in traffic flow.

• Usually increase capacity (by continually reapportioning green time).

• Provide continuous operation under low volume conditions.

• Especially effective at multiple phase intersections.

39.2.3 Disadvantages of Actuated Signals

The main disadvantages are as following :

• If traffic demand pattern is very regular, the extra benefit of adding local actuation is

minimal, perhaps non-existent.

• Installation cost is two to three times the cost of a pretimed signal installation.

• Actuated controllers are much more complicated than pretimed controllers, increasing

maintenance costs.

• They require careful inspection & maintenance to ensure proper operation.



39.2.4 Types of Actuated Control

There are three basic types of actuated control, each using signal controllers that are somewhat

different in their design:

1. Semi-Actuated Control

2. Full-Actuated Control

3. Volume-Density Control

Semi-Actuated Control

This type of controller is used at intersections where a major street having relatively uniform

flow is crossed by a minor street with low volumes. Detectors are placed only on the minor

street. The green is on the major street at all times unless a call on the side street is noted. The

number and duration of side-street green is limited by the signal timing and can be restricted

to times that do not interfere with progressive signal-timing patterns along the major street.

Full-Actuated Control

This type of controller is used at the intersections of streets or roads with relatively equal

volumes, but where the traffic distribution is varying. In full actuated operation, all lanes of

all approaches are monitored by detectors. The phase sequence, green allocations, and cycle

length are all subjected to variation. This form of control is effective for both two-phase and

multiphase operations and can accommodate optional phases.

Volume-Density Control

Volume-density control is basically the same as full actuated control with additional demand-

responsive features. It is designed for intersections of major traffic flows having considerable

unpredictable fluctuations.

39.2.5 Detection for Actuated Signalization

The various types of detectors used for detection of vehicles are as following:

• Inductive loop detectors

• Magnetometer detectors



• Magnetic detectors

• Pressure-sensitive detectors

• Radar detectors

• Sonic detectors

• Microloop detectors etc.

The vast majority of actuated signal installations use inductive loops for detection purpose.

Now, the type of detection is of greater importance than the specific detection device(s) used.

There are two types of detection that influence the design and timing of actuated controllers:

1. Passage or Point Detection:- In this type of detection, only the fact that the detector

has been disturbed is noted. The detector is installed at a point even though the detector

unit itself may involve a short length. It is the most common form of detection.

2. Presence or Area Detection:- In this type of detection, a significant length (or area)

of an approach lane is included in the detection zone. Entries and exits of vehicles into

and out of the detection zone are remembered. Thus, the number of vehicles stored in

the detection zone is known. It is provided by using a long induction loop, or a series of

point detectors. These are generally used in conjunction with volume-density controllers.

39.2.6 Actuated Control Features

Regardless of the controller type, virtually all actuated controllers offer the same basic functions,

although the methodology for implementing them may vary by type and manufacturer. For

each actuated phase, the following basic features must be set on the controller:

Minimum Green Time

Each actuated phase has a minimum green time, which serves as the smallest amount of green

time that may be allocated to a phase when it is initiated. Minimum green times must be set for

each phase in an actuated signalization, including the non-actuated phase of a semi-actuated

controller. The minimum green timing on an actuated phase is based on the type and location

of detectors.

• In case of Point Detectors,

Gmin = tL + [h × Integer(d/x)] (39.1)



where, Gmin = minimum green time in second, tL = assumed start-up lost time = 4 sec,

h = assumed saturation headway = 2 sec, d = distance between detector & stop line in

m and x = assumed distance between stored vehicles = 6 m.

• In case of Area Detectors,

Gmin = tL + 2n (39.2)

where, tL = start-up lost time (sec) and n = number of vehicles stored in the detection

area.

Unit Extension

This time actually serves three different purposes:

1. It represents the maximum gap between actuations at a single detector required to retain

the green.

2. It is the amount of time added to the green phase when an additional actuation is received

within the unit extension, U.

3. It must be of sufficient length to allow a vehicle to travel from the detector to the STOP

line.

In terms of signal operation, it serves as both the minimum allowable gap to retain a green

signal and as the amount of green time added when an additional actuation is detected within

the minimum allowable gap. The unit extension is selected with two criteria in mind:

• The unit extension should be long enough such that a subsequent vehicle operating in

dense traffic at a safe headway will be able to retain a green signal (assuming the maximum

green has not yet been reached).

• The unit extension should not be so long that straggling vehicles may retain the green or

that excessive time is added to the green (beyond what one vehicle reasonably requires

to cross the STOP line on green).

The Traffic Detector Handbook recommends that a unit extension of 3.0 s be used where

approach speeds are equal to or less than 30 mile per hour, and that 3.5 s be used at higher

approach speeds. For all types of controllers, however, the unit extension must be equal to or

more than the passage time.



Passage Time Interval

It allows a vehicle to travel from the detector to the stop line. It is analogous with ’Unit

Extension’.

P = (d/S) (39.3)

where, P = passage time, sec, d = distance from detector to stop line, metre and S = approach

speed of vehicles, m/s.

Maximum Green Time

Each phase has a maximum green time that limits the length of a green phase, even if there are

continued actuations that would normally retain the green. The maximum green time begins

when there is a call (or detector actuation) on a competing phase. The estimation can be done

by any of the following methods:

• By trial signal timing as if the signals were pretimed

Ci =L

[1 − V C/(1615(PHF )(v/c))](39.4)

where, Ci = Initial cycle length, sec, L = Total lost time, sec and VC = Sum of critical

lane volumes, veh/hr. Knowing the initial cycle length, green times are then determined

as:

gi = (Ci − L) ∗VCi

VC(39.5)

where gi = effective green time for Phase i, sec and VCi = critical lane volume for Phase

i, veh/hr. The effective green times thus obtained are then multiplied by 1.25 or 1.50 to

determine the maximum green time.

• By Green-Time Estimation (HCM) Model: Traffic-actuated controllers do not recognize

specified cycle lengths. Instead they determine, by a mechanical analogy, the required

green time given the length of the previous red period and the arrival rate. They accom-

plish this by holding the right-of-way until the accumulated queue has been served.

The basic principle underlying all signal timing analysis is the queue accumulation polygon

(QAP), which plots the number of vehicles queued at the stop line over the duration of the

cycle. The QAP for a simple protected movement is illustrated in the Fig. 39:1. From Fig. 39:1,

it’s clear that queue accumulation takes place on the left side of the triangle (i.e., effective red)

and the discharge takes place on the right side of the triangle (i.e., effective green).



RedNu

mb

er o

f V

ehic

les

in q

ueu

e

Green time based onphase time extension

Green time based ontarget v/c ratio

Green

Time (s)

Green extension time

8

6

4

2

0

Figure 39:1: Queue accumulation polygon illustrating two methods of green time computation

There are two methods of determining the required green time given the length of the

previous red time. The first employs a target v/c approach. Under this approach, the green-

time requirement is determined by the slope of the line representing the target v/c of 0.9. If

the phase ends when the queue has dissipated under these conditions, the target v/c will be

achieved. The second method recognizes the way a traffic-actuated controller really works.

It does not deal explicitly with v/c ratios; in fact, it has no way of determining the v/c

ratio. Instead it terminates each phase when a gap of a particular length is encountered at the

detector. Good practice dictates that the gap threshold must be longer than the gap that would

be encountered when the queue is being served. Assuming that gaps large enough to terminate

the phase can only occur after the queue service interval (based on v/c = 1.0), the average

green time may be estimated as the sum of the queue service time and the phase extension

time. Therefore, average green time = Queue Service Time + Phase Extension Time. Now,

Queue Service Time(gS) =fqqrr

(s − qg)(39.6)

where, qr = red arrival rate (veh/s), qg = green arrival rate (veh/s), r = effective red time (s), s =

saturation flow rate (veh/s) and fq = calibration factor = 1.08 - 0.1(actual green time/maximum green time

Green extension time(ge) = [exp(λ(u + t − ∆))/Φq] − (1/λ) (39.7)

where, q = vehicle arrival rate throughout cycle (veh/s), u = unit extension time setting (s),

t = time during which detector is occupied by a passing vehicle(s) = [3.6(Ld + Lv)]/SA, Lv

= Vehicle length, assumed to be 5.5 m, Ld = Detector length (m), SA= Vehicle approach

speed (kmph), ∆ = minimum arrival (intra-bunch) headway (s), λ = a parameter (veh/s) =

Φq/(1 − ∆q), Φ = proportion of free (unbunched) vehicles in traffic stream = exp(−b∆q) and

b = bunching factor.



Table 39:1: Recommended Parameter ValuesCase ∆(s) b

Single Lane 1.5 0.6

Multilane

2 lanes 0.5 0.5

3 lanes 0.5 0.8

This green-time estimation model is not difficult to implement, but it does not lead directly

to the determination of an average cycle length or green time because the green time required

for each phase is dependent on the green time required by the other phases. Thus, a circular

dependency is established that requires an iterative process to solve. With each iteration, the

green time required by each phase, given the green times required by the other phases, can be

determined. The logical starting point for the iterative process involves the minimum times

specified for each phase. If these times turn out to be adequate for all phases, the cycle length

will simply be the sum of the minimum phase times for the critical phases. If a particular

phase demands more than its minimum time, more time should be given to that phase. Thus,

a longer red time must be imposed on all of the other phases. This, in turn, will increase the

green time required for the subject phase.

Recall Switch

Each actuated phase has a recall switch. The recall switches determine what happens to the

signal when there is no demand. Normally, one recall switch is placed in the on position, while

all others are turned off. In this case, when there is no demand present, the green returns to

the phase with its recall switch on. If no recall switch is in the on position, the green remains

on the phase that had the last ”call.”demand exists, one phase continues to move to the next

at the expiration of the minimum green.

Change and Clearance Intervals

Yellow and all-red intervals provide for safe transition from green to red. They are fixed times

and are not subject to variation, even in an actuated controller. They are found in the same

manner as for pretimed signals.

y = t + [S85/(2a + 19.6g)] (39.8)

ar = (w + l)/S15 (39.9)



��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

extensible portion

maximum greenminimumgreen

Figure 39:2: Operation of an Actuated Phase

where, y = yellow time, sec, ar = all red interval, sec, S85 = 85th percentile speed, m/s, S15 =

15th percentile speed, m/s, t = reaction time of the driver = 1 sec (standard), a = deceleration

rate = 3 m/s2 (standard), g = grade of approach in decimal, w = width of street being crossed,

m and l = length of a vehicle, m.

39.2.7 Operating Principle

The Fig. 39:2 illustrates the operation of an actuated phase based on the three critical settings:

minimum green, maximum green, and unit or vehicle extension. When the green is initiated

for a phase, it will be at least as long as the minimum green period. The controller divides

the minimum green into an initial portion and a portion equal to one unit extension. If an

additional call is received during the initial portion of the minimum green, no time is added to

the phase, as there is sufficient time within the minimum green to cross the STOP line (yellow

and all-red intervals take care of clearing the intersection). If a call is received during the last

U seconds (Unit Extension) of the minimum green, U seconds of green are added to the phase.

Thereafter, every time an additional call is received during a unit extension of U seconds, an

additional period of U seconds is added to the green. Note that the additional periods of U

seconds are added from the time of the actuation or call. They are not added to the end of

the previous unit extension, as this would accumulate unused green times within each unit

extension and include them in the total green period. The green is terminated in one of two

ways:

1. a unit extension of U seconds expires without an additional actuation,

2. the maximum green is reached.



Table 39:2: Recommended Detector Locations & Timing Parameters

Approach Detector Set-Back Mimimum Passage

Speed (To front of loop) Green Time

(kmph) (m) (sec) (sec)

24 12 8.0 3.0

32 18 10.0 3.0

40 24 12.0 3.0

48 30 14.0 3.5

56 41 18.0 3.5

64 52 22.0 3.5

72+ Volume density or multiple detectors recommended

The maximum green begins timing out when a call on a competing phase is noted. During the

most congested periods of flow, however, it may be assumed that demand exists more or less

continuously on all phases. The maximum green, therefore, begins timing out at the beginning

of the green period in such a situation. Now-a-days, in India, detectors are placed mostly at

stop lines. In that case, the green times for phases are primarily determined by arrival headway.

The green time is extended until the gap between two vehicles becomes equal to or greater than

the pre-determined threshold value. Generally threshold of 4 seconds is considered.

39.2.8 Concept of Semi-Actuated Controller

Principles

• Detectors on minor approaches only.

• Major phase receives a minimum green interval.

• The green remains on the main street until a call for service on the side street is registered.

• If the main street has had enough green, the side street is given the green for just enough

time to guarantee that its vehicles are processed.

• Usually Point Detectors are used.

• Detectors can be placed at either stop line or upstream location.



Side

Detector

Street

Main Street

Stop line

Figure 39:3: Semi-Actuated Control

Advantages

• It can be used effectively in a coordinated signal system.

• Relative to pre-timed control, it reduces the delay incurred by the major-road through

movements during periods of light traffic.

• It does not require detectors for the major-road through movement phases and hence, its

operation is not compromised by the failure of these detectors.

• Generally the main street indeed has the green whenever possible.

Disadvantages

• Continuous demand on the phases associated with one or more minor movements can

cause excessive delay to the major road through movements if the maximum green and

passage time parameters are not appropriately set.

• Detectors must be used on the minor approaches, thus requiring installation and ongoing

maintenance.

• It also requires more training than that needed for pre-timed control.



Detector

Figure 39:4: Full-Actuated Control

39.2.9 Concept of Full-Actuated Controller

Principles

• Detectors on all approaches.

• Each phase has a preset initial interval.

• Phases are sequenced according to ”calls” for service on all approaches.

• Green interval is extended by a preset unit extension for each actuation after the initial

interval provided a gap greater than the unit extension does not occur.

• Green extension is limited by preset maximum limit.

• Generally Point Detectors are used.

• Detectors can be placed at either stop line or upstream location.

Advantages

• Reduces delay relative to pre-timed control by being highly responsive to traffic demand

and to changes in traffic pattern.



• Detection information allows the cycle time to be efficiently allocated on a cycle-by-cycle

basis.

• Allows phases to be skipped if there is no call for service, thereby allowing the controller

to reallocate the unused time to a subsequent phase.

Disadvantages

• Initial and maintenance cost is higher than that of other control types due to the amount

of detection required.

• It may also result in higher percentage of vehicles stopping because green time is not held

for upstream platoons.

39.2.10 Concept of Volume-Density Controller

Volume-Density Controllers are designed for intersections of major traffic flows having consid-

erable unpredictable fluctuations. They are generally used at intersections with high approach

speeds (≥ 45 mi/hr). Here, detectors are placed on all approaches. Generally this type of

controller is used with Area Detectors. To operate efficiently, this type of control needs to

receive traffic information early enough to react to existing conditions. So, it is essential that

detectors be placed far in advance of the intersection.


An isolated suburban intersection of two major arterials is to be signalized using a full actuated

controller. Area detection is to be used, and there are no driveways or other potential entry

points for vehicles within 90 m of the STOP line on all approaches. The intersection is shown

in the figure and all volumes have already been converted to tvus for convenience. Left-turn

slots of 75 m in length are provided for each approach. The tvu conversions assume that a

protected left-turn phase will be provided for all approaches.

Solution: Step 1: Phasing: The problem statement indicates that protected left-

turn phasing will be implemented on all approaches. Note that Kennedy Avenue

has double left-turn lanes in each direction and that Monroe Street has a single

left-turn lane in each direction. At a heavily utilized intersection such as this,

quad-eight phasing would be desirable. Each street would have an exclusive LT

phase followed by a leading green in the direction of heavier LT flow and a TH/RT



16 m

Kennedy Avenue

LT

LT

700 100

400

1600

110 650

1500

300 36 m

PHF = 0.96

Target v/c = 0.98No peds (overpasses provided)

Level terrain

Monroe Street

Approach speeds: 64 kmph(all approaches)

t = 1.0 sl1 = e = 2.0sa = 3 $m/s^2$

Figure 39:5: Intersection for the Example

phase. Such phasing provides much flexibility in that LT phasing is always optional

and can be skipped in any cycle in which no LT demand is noted. The resulting

signalization has a maximum of four phases in any given cycle and a minimum of

two. It is treated as a four-phase signal, as this option leads to the maximum lost

times. Quad-eight phasing involves overlaps that would be taken into account if

this were a pretimed signal. As an actuated signal, the worst-case cycle, however,

would occur when there are no overlap periods. This would occur when the LT flow

in opposing directions are equal. Thus, the signal timing will be considered as if

this were a simple four-phase operation without overlaps. The controller, however,

will allow one protected LT to be terminated before the opposing protected LT,

creating a leading green phase. The four phases are:

• Phase I-Protected LT for Kennedy Avenue

• Phase 2-TH/RT for Kennedy Avenue

• Phase 3-Protected LT for Monroe Street

• Phase 4-TH/RT for Monroe Street

Step 2: Unit Extension: For approach speeds of 64 kmph, the recommended

unit extension (from Table) is 3.5 s.

Step 3: Minimum Green Times and Detector Placement: The problem spec-

ifies that area detection shall be employed. For area detection, the far end of the

detection zone is placed such that the passage time is equal to unit extension. Since



all approaches (including LT approaches) have a 64 kmph approach speed, the far

end of detectors should be located as follows:

U = 3.5 = P = d/(64/3.6)

d = 3.5 ∗ (64/3.6) = 62.22 ≈ 62m

The near end of the detection zone would be placed within 0.3 m of the STOP

line. The minimum green time for area detection is variable, based on the number

of vehicles sensed within the detection area when the green is initiated. The

value can vary from the time needed to service one waiting vehicle to the time

needed to service Int(62/6) = 11 vehicles. The range of minimum green times

can be established for each approach. In this case, all values will be equal, as

the approach speeds are the same for all approaches and the detector location is

common to every approach, including the LT lanes, all of which are long enough

to accommodate a 62 m setback.

Gmin/low = 2.0 + (2 ∗ 1) = 4.0 sec

Gmin/high = 2.0 + (2 ∗ 11) = 24.0 sec

Step 4: Critical-Lane Volumes: As the volumes given have already been con-

verted to tvus, critical-lane volumes for each phase are easily identified:

• Phase 1 (Kennedy Ave, LT) - 400/2 = 200 tvu/h

• Phase 2 (Kennedy Ave, TH/RT) - 1,600/4 = 400 tvu/h

• Phase 3 (Monroe St, LT) - 110/1 = 110 tvu/h

• Phase 4 (Monroe St, TH/RT) - 700/2 = 350 tvu/h

Therefore, VC = (200+400+110+700) = 1,060 tvu/h.

Step 5: Yellow & All-Red times With a 64 kmph average approach speed for all

movements, the S85 may be estimated as (64 + 8) = 72 kmph, and the S15 may be

estimated as (64 - 8) = 56 kmph. Then:

yall = 1.0 + (72/3.6)/(2 ∗ 3) + 19.6(0.01 ∗ 0) = 4.3sec

ar1,2 = (16 + 6)/(56/3.6) = 1.5sec

ar3,4 = (36 + 6)/(56/3.6) = 2.7sec

Y1,2 = (4.3 + 1.5) = 5.8sec

Y3,4 = (4.3 + 2.7) = 7.0sec



There are four phases in the worst-case cycle. The total lost time is equal to the

sum of the yellow and all-red intervals in the cycle: L = 2*5.8 + 2*7.0 = 25.6 sec.

Step 6: Maximum Green Times and the Critical Cycle: The initial cycle length

for determining maximum green time is: Ci = 25.6/[1-1060/(1615*0.96*0.98)] =

84.8 sec. Green times are found as:

G1 = (84.8 − 25.6)(200/1060) = 11.2sec

G2 = (84.8 − 25.6)(400/1060) = 22.3sec

G3 = (84.8 − 25.6)(110/1060) = 6.1sec

G4 = (84.8 − 25.6)(350/1060) = 19.5sec

Gmax1 = (1.5 ∗ 11.2) = 16.8sec

Gmax2 = (1.5 ∗ 22.3) = 33.5sec

Gmax3 = (1.5 ∗ 6.1) = 9.2sec

Gmax4 = (1.5 ∗ 19.5) = 29.3sec

With area detection, the minimum green for all lane groups, including LT lanes,

can be as high as 24.0 s. This is inconsistent with Gmax values for the LT Phases

1 and 3. Increasing the maximum greens beyond the computed values, however,

will lead to an excessively long critical cycle length. Thus, it is recommended that

the LT lanes use point detectors, placed so that the Gmin for Phases 1 and 3 is a

constant 4.0 s. The above Gmax results will work in this scenario. The Gmax results

for Phases 2 and 4 (through phases) are close to the high value of Gmin for these

phases, but would provide some flexibility even in peak periods. It is, therefore,

not recommended that any of these times be arbitrarily increased. The critical

cycle length becomes: CC = 16.8 + 5.8 + 33.5 + 5.8 + 9.2 + 7.0 + 29.3 + 7.0 =

114.4 sec


Consider an intersection of two streets with a single lane in each direction. Each

approach has identical characteristics and carries 675 veh/h with no left or right

turns. The average headway is 2.0 s per vehicle and the lost time per phase is

3.0 s. Detectors are 9.1 m long with no setback from the stop line. The actuated

controller settings are as follows: Determine the phase time for this intersection

with actuated controller for approach speed 50 kmph.



Setting Time (s)

Initial interval 10

Unit extension 3

Maximum green 46

Intergreen 4

Solution: The maximum phase time for each phase will be (46 + 4) = 50 s. The

minimum phase time will be 10 + 3 + 4 = 17 s. The first iteration will be used

with a 34-s cycle with 17 s of green time on each approach. The effective green time

will be 14 s, and the effective red time will be 20 s for each phase. For purposes

of traffic-actuated timing estimation It is recommended (HCM 2000) that, for a

specified lost time of n seconds, 1 s be assigned to the end of the phase and (n - 1)

s be assigned to the beginning. Here, start-up lost time = 2.0 secs. The following

are the steps to calculate the phase time required:

Step 1. Compute the arrival rate throughout the cycle, q: q = 675/3600 =

0.188 veh/s

Step 2. Compute the net departure rate (saturation flow rate - arrival rate): (s

- q) =1800/3600- 0.188 = 0.312 veh/s

Step 3.Compute the queue at the end of 20 s of effective red time: qrr = 20 ×

(0.188) = 3.760veh

Step 4. Compute the queue calibration factor,fq: fq = 1.08 − 0.1(13/46)2 = 1.072

Step 5. Compute the time required to serve the queue, gs: gs = 1.072(3.760/0.312) =

12.919s

Step 6. Determine λ: ∆ = 1.5 and b = 0.6 (for single lane from table in HCM)

Φ = e−b∆q

= e−(0.6×1.5×0.188) = 0.844

λ = Φq/(1 − ∆q)

= (0.844)(0.188)/1− (1.5)(0.188)

= 0.221

Step 7. Determine the occupancy time of the detector: t0 = 3.6(9.1+ 5.5)/50,

vehicle length=5.5m, detector = 1.051 s length=9.1 m, approach speed=50 kmph

Step 8. The expected green extension time, ge:



Step 9. Compute the total phase time:

G = l1 + gs + ge + Y

G = 2.0 + 12.919 + 6.550 + 4.0 = 25.469s

Step 10. Compute the phase time deficiency as the difference between the trial

phase time and the computed phase time: or 25.469 - 17.0 = 8.469 s. For next

iteration: Trial green time = 25.469 s. Cycle length = 50.968 s. This process is

continued through successive iterations until the solutions converge or the phase

deficiency i.e. the error is negligible practically. The following figure shows the

results of successive iterations for this problem and the final convergence. The

8.469

5.2303.089

1.7710.992

0.5470.289 0.157 0.0590.012 0.007

Minimum = 17 s

Iteration Number

Phase time deficiencyComputed phase time

Ph

ase

Tim

e (s

)

0

10

20

30

40

1 2 3 4 5 6 7 8 119 10

Figure 39:6: Calculation of phase time through iterations (HCM)

final phase time is 37.710 s giving a cycle length of 75.420 s. The convergence was

considered for threshold of 0.1 difference in successive cycle times.

39.3 Conclusion

Modern actuated controllers give the traffic engineers a great deal of flexibility in

dealing with variations in demand. Area traffic control system along with Vehicle

actuated signals can reduce traffic delays substantially. These are highly complex

subject. Timing of VA signals is almost as much an art as a science, and more then

one solution is possible. Regarding ATC systems, SCOOT and SCAT are popular in

advance countries but such systems cannot cope up with Indian situations without

adaptation to Indian traffic scenario. Presently, an advance ATC system known as

CoSiCoSt has been developed considering the Indian Traffic scenario.



39.4 References

1. Highway Capacity Manual. Transportation Research Board. National Re-

search Council, Washington, D.C., 2000.

2. L. R Kadiyali. Traffic Engineering and Transportation Planning. Khanna

Publishers, New Delhi, 1987.

3. C. S Papacostas. Fundamentals of Transportation Engineering. Prentice-

Hall, New Delhi, 1987.

4. D I Robertson and R D Bretherton. Optimizing Networks of Traffic Sig-

nals in Real Time - The SCOOT Method. IEEE Transactions on Vehicular

Technology, 1991.

5. R J Salter. Highway Traffic Analysis And Design. McGraw-Hill, 1990.

6. S H Shinde. Evaluation of Area traffic Control system. Department of

Transportation engineering, IIT Bombay, 2007.


Transportation Systems Engineering 40. Area Traffic Control

Chapter 40

Area Traffic Control

40.1 Introduction

ATC systems are intelligent real-time dynamic traffic control systems which are designed to

effectively respond to rapid variations in dynamic traffic conditions. It is an advanced process

to control the traffic. It is a traffic responsive system that use data from vehicle detectors

and optimize traffic signal time in real time. The timing plan of traffic controllers changed

automatically. The technique employs digital computers for achieving the desired objective.

40.2 Basic principles

The basic system Originally, it was assumed that the power of the digital computer could

be used to control many traffic signals from one location, allowing the development of control

plans. The basic concept can be summarized thus: the computer sends out signals along one

or more arterials. There is no feedback of information from detectors in the field, and the

traffic-signal plans are not responsive to actual traffic conditions. Earlier,the plans for such a

system are developed based on the engineers usage of data from field studies to generate plans

either by hand, or by computer,using packages available at the time. The computer solutions

were then run on another machine, or in off hours on the control computer when it was not

being used for control of the traffic signals. Though this “off-line” system of control plans gives

an image of a deficient system, there are many advantages of this “limited” system. These

include:

1. Ability to update signals from a Central Location: The ability to retime signals from

a central location without having to send people along an entire arterial to retime the

signals individually at each intersection saves lot of time.

2. Ability to have multiple plans and special plans: In many localities a three-dial controller

is quite sufficient: if traffic is generally regular, three basic plans (A.M. peak, P.M. peak,



Controller

Detector

confirm signal

2 3Pattern Plan

X1

of plansLibrary

Traffic data

Operator

computer patterny

4 1

P1

Xn Pn

P2X2

Figure 40:1: Computer control system with detector information used

off-peak) can meet the needs. The computer opens the possiblity to have an N-dial

controller, with special plans stored for certain days. With appropriate plans stored for

each such event, the plans can be called up by time of day, or by operator intervention.

3. Information on equipment failures: The early systems simply took control of electrome-

chanical controllers, driving the cam-shaft from the central computer and receiving a

confirmation signal. Failure to receive this signal meant trouble. The information pro-

vided by the control computer allowed such failures to be detected and repair crews

dispatched.

4. Performance data on contractor or service personnel: With a failure detected and noti-

fication made, the system can log the arrival of the crew and/or the time at which the

intersection is returned to active service.

Collection of traffic data The ability of a computer to receive great amount of data and

process it is made use of by detectors in the field for sending information back to the central

location. If the information is not being used in an “online” setting and hence still does not

influence the current plan selection. Typically, the computer is being used as the tool for the

collection of permanent or long-term count data.

Traffic data used for plan selection Fig. 40:1 shows a computer control system that

actually uses the traffic data to aid in plan selection. This can be done in one of three principal

ways:

1. Use library - Monitor deviations from expected pattern: This concept uses a time-of-day

approach, looking up in a library both the expected traffic pattern and the preselected plan

matched to the pattern. The actual traffic pattern can be compared to the expected, and if a

deviation occurs, the computer can then look through its library for a closer match and use the

appropriate plan.

2. Use library - Match plan to pattern: This is a variation on the first concept, with the observed



pattern being matched to the most appropriate prestored pattern and the coresponding plan

veing used.

3. Develop plan on-line: This concept depends on the ability to do the necessary computations

within a deadline either as a background task or on a companion computer dedicated to such

a computations. This approach presumes an advantage to tailoring the control plan to specific

traffic data.

It is necessary to note that the time between plan updates is constrained by the speed with

which the on-line plan computations can be done. The desire to have more frequent updates

implicitly assumes that the real traffic situation can be known precisely enough to differentiate

between consecutive update periods.

40.2.1 Advantages

The various Advantages of an area traffic control system are

• Minimizing journey time for vehicles- Are traffic control system minimize the overall

journey time by reducing the no of stop delays, increasing the average travel speed etc.

• Reducing accidents- Are traffic control system reduces the no of accident by reducing

the congestion as congestion is less the traffic flow will be smooth so accident also will be

less.

• Increasing average saving in fuel- As we discussed above that it will minimize the

journey time, accident, congestion, stop delays so we can easily say that average saving

in fuel will increase and traffic flow also will be safe and smooth.

40.2.2 Disadvantages

The various disadvantages of an area traffic control system are

• Very costly- Area traffic control is a very advanced traffic control strategy it involve

very advanced technology and highly skilled persons to operate the system to control the

traffic which makes it very costly.

• Very complex- Area traffic control system is a very big system which includes many

unites in it like Vehicle Detectors, Intersection Controller, Communication Network, Ap-

plication Software, Central (Regional) Control System. These unit is use to perform

different-different task for the system. These unit and task make it very complex.



• Suitable only for lane following traffic- In area traffic control system we use vehicle

detector to collect the data to find the actual flow and to get signal timing according to

the present condition of traffic. These vehicle detectors detect the vehicle on the basis of

lane. For example we are collecting data for tow lane road then the detectors will able

to detect the vehicle which will come from their respective lane and the vehicle which is

using space other than these two lanes cannot be detected. So data will not be accurate.

So we can say that it will give best result only for lane following traffic.

40.3 Major Building Blocks of ATC

Major Building blocks of the Area Traffic Control Systems are: Vehicle Detectors, Intersection

Controller, Communication Network, Application Software and Central (Regional) Control

System which are described below:

40.3.1 Vehicle Detectors (VD)

Vehicle Detectors is used to detect the presence of vehicles, to collect data to find average speed,

vehicle flow, vehicle density, queue length measurement. VD acts as a nodal point between

vehicle and intersection controller. Detector could be of various types example-ultrasonic,

microwave radar, infrared laser radar, non-imaging passive infrared, video imaging, acoustic

array, magnetic loop Inductive loop vehicle detector is commonly used. Fig. 40:2 is showing

example of Vehicle Detectors. In Fig. 40:2 two detectors are shown, 1 is for straight going

traffic which will detect the vehicle which will go straight and 2 is right turning traffic which

will detect the vehicle which will take right turn from there.

40.3.2 Intersection Controller

It is the micro-macro computer. It placed at intersection for temporary storage of data. It

collects the data from vehicle detector and sends it to the central control. Central control

processed the data and sends it back to the intersection controller which then implements the

signal timings as instructed at the intersection. Intersection controller for each set of traffic

signals receives the signal states from the control system.

40.3.3 Communication Network

The communication network transfers data from the signal controller, to the central control

station where optimized signal timings and phases are determined and it again transfers in-



Stop line loop for Straightgoing traffic

Exit loop for Right turningtraffic

Figure 40:2: Example of Vehicle Detectors (Source Muralidharan, 2006)

formation to the signal controller as per the data processed. It transfers the data obtained

from detectors to central control which then implements the signal timings as instructed at the

intersection. Fig. 40:3 is showing the communication network.

40.3.4 Application Software

Application software is the software used behind the whole ATC system which performs the

entire task. It is a large and complex program involving multiple systems, various procedures

for implementation. Functions of Application software are: It defines the architecture flows,

activities and functions and user services that planners want to deliver.

Decision

Hardware

Decision

Central

Data

Intersection Controller

VehicleDetector

Signal

Controller

Data

Figure 40:3: Communication Network (Source: Muralidharan, 2006)



Network LoadControl

NetworkLoads

Network FlowControl

TimingsTarget

TimingsActual

IntersectionControl

ControlSignal

Traffic SignalActivation

Actual TravelBehavior and Traffic

Current Capacities, Travel Times,

(minutes/hours/days)

Historical/Infrastructure Data

(minutes)

SurveillanceDetectors and

Measurements

y(t)

ATIS

Network Load

Platoon Flow Prediction

Network Disruptions

Vehicle Flow Prediction(seconds)

Network Flow

Estimator/Predictor

Estimator/Predictor

Estimator/Predictor

Intersection Flow

Figure 40:4: Area traffic control architecture (Source: Pitu B. Mirchandani, K. Larry

Head,1998)

40.3.5 Central Control System

It is the main unit of ATC. In this unit collected traffic data is processed to optimize various

traffic parameters like-signal timing, phase change, delay Important and major task of ATC

system is performed by this unit. It supervises all the units of ATC.

40.4 Architecture of (ATC)

Fig. 40:4 is showing the arrangement of whole area traffic control system with all units of

the system. These unites will be use for different-different task in the system. It could we

described in three stages. At first stage estimation of is done, it is done based on the slow-

varying characteristics of the network traffic load in terms of vehicle per hour than according

to this estimated ATCS allow to allocate green time for each different demand for each phase.

At the middle stage traffic characteristic are measured in terms of platoons of vehicle and

their speeds and at last stage intersection controller select the suitable phase change based on

observed and predicted arrivals of individual vehicle at each intersection.

40.5 Operational models

An operating model is the abstract representation of how an System operates across process.

Any system is a complex system consisting of several different interlinked logical components.

An operating model breaks this complexity into its logical components in order to deliver better



value. Some examples of operational models are SCOOT, SCAT and OPAC which are described

below.

40.5.1 SCOOT (Split Cycle Offset Optimization Technique)

The Split Cycle Offset Optimization Technique (SCOOT) is an urban traffic control system

developed by the Transport Research Laboratory (TRL) in collaboration with the UK traffic

systems industry. It is an adaptive system which responds automatically to traffic fluctuations.

Prime objective of this is to minimize the sum of the average queues in the area. It is an

elastic coordination plan that can be stretched or shrunk to match the latest traffic situation.

Continuously measures traffic volumes on all approaches of intersections in the network and

changes the signal timings to minimize a Performance Index (PI) which is a composite measure

of delay, queue length and stops in the network. Each SCOOT cell is able to control up to 60

junctions. Handling input data up to 256 vehicle counting detectors on street. Detectors are

usually positioned 14 m behind the stop line.

Principles of SCOOT

1. Cycle Flow Profiles (CFP) measure in real time

2. Update an on-line model of queues continuously

3. Incremental optimization of signal settings

1. Cyclic Flow Profiles (CFP)

CFP is a measure of the average one-way flow of vehicles passed at any point on the road

during each part of the cycle time of the upstream signal. It records the platoon of vehicles

successively within a cycle time during peak flow. It updated in every 4 seconds. CFPs

can be measured easily by hand. Shape of the CFP has to be calculated for each one-way

flow along all streets in the area. Accuracy of calculation depends on the accuracy of the

data on average Flows, saturation flows, and cruise times.

2. Queue Estimation

It is necessary to predict new signal timing due to the queues after alteration according

to the situation after knowing CFP, the computer can be programmed to estimate no

of vehicles which will reach the downstream signals during red phase. So size of the

queue and duration to clear the queue can be calculated. In this calculation it is assumed

that the traffic platoons travel at a known cruising speed with some dispersion. Queues



discharge during the green time at a saturation flow rate that is known and constant for

each signal stop line.

3. Incremental Optimization

Incremental Optimization is done to measure the coordination plan that it is able to

respond to new traffic situations in a series of frequent, but small, increments. It is

necessary because research shows that prediction of traffic flow is very difficult for next

few minutes. SCOOT split optimizer calculates whether it is good to advance or retard

the scheduled change by up to 4 s, or to leave it unaltered. It is achieved by split

optimization, offset optimization, cycle time.

(a) Split Optimizer

Works at every change of stage by analyzing the current red and green timings to

determine whether the stage change time should be advanced, retarded or remain

the same. Works in increments of 1 to 4 seconds.

(b) Cycle Time Optimizer

It operates on a region basis once every five minutes, or every two and a half minutes.

Identifies the “critical node” within the region and will attempt to adjust the cycle

time to maintain this node with 90% link saturation on each stage. It can increase

or decrease the cycle time in 4, 8 or 16 second increments according to the current

requirement of the traffic flow.

(c) Offset Optimizer

It works once per cycle for each node. It operates by analyzing the current situation

at each node using the cyclic flow profiles predicted for each of the links with up-

stream or downstream nodes. It assesses whether the existing action time should be

advanced, retarded or remains the same in 4 second increments. Fig. 40:5 is showing

the key elements of the SCOOT ATC system which we described in above points.

Working Principle of SCOOT

Scoot system consists of a number of SCOOT cells or computers, each cell can control up

to 60 junctions and handling input data from up to 256 vehicle counting detectors on street.

SCOOT detectors are placed at 14 m from the stop-line, from the approach to the junction as

possible. Fig. 40:6 clearly shows the working principle of SCOOT where the detectors placed

upstream sense the occupancy and the information is transmitted to the central computer.

SCOOT traffic model and optimizers use this information to calculate signal timings to achieve

the best overall compromise for coordination along all links in the SCOOT area. The main aim



��

��

��

Time incycle

Red

Successivecycles

cycleSplit

offset

StoplineQueue

Flow

profileflowCyclic

On linetrafficmodel

Signaloptimiser

Peak period

Figure 40:5: Key elements of the SCOOT ATC system (Source: Dennis I. Robertson and R.

David Bretherton 1991)

��

��

��

��

Online ComputerOperator I/O

SignalOptimiser estimater

Queue

Vehicle detector

Data network

Figure 40:6: Working Principle of SCOOT (Source: www.scoot-utc.com)

of the SCOOT traffic signal control system is to react to changes in observed average traffic

demands by making frequent, but small, adjustments to the signal cycle time, green allocation,

and offset of every controlled intersection. For each coordinated area, the system evaluates

every 5 minutes, or 2.5 minutes if appropriate, whether the common cycle time in operation at

all intersections within the area should be changed to keep the degree of saturation of the most

heavily loaded intersection at or below 90%. In normal operation SCOOT estimates whether

any advantage is to be gained by altering the timings. Fig. 40:6 is showing the working principle

of SCOOT. From above fig we can have an idea that vehicle will be detected with the help of

vehicle detector. The collected data will be send to intersection controller after that it will be

send to the central controller with the help of communication network. There it will be use to

estimate the signal timing according to the actual traffic flow needs. Then the central controller



will send the signal timing to the intersection controller to implement.

Features of SCOOT

1. Variable Message Signs

Scoot display message signs to convey the guidance to the driver which is very helpful for

the drive.

2. Diversions

This feature is provided to deal with any emergency situation for example if any problem

is found out in any lane which is found out with the help of Fault Identification &

Management unit then traffic will be diverted from that lane to another lane.

3. Emergency Green Wave Routes

This feature is provided to deal with any hazardous situation.

4. Fixed Time Plan

This plan is applied when any unit of ATCS stopped working so till the time that unit

starts functioning.

Limitations

1. Inability to handle closely spaced signals due to its particular detection configuration

requirements, its require some time to detect vehicle.

2. Interface is difficult to handle, as this is highly technical so difficult to understand and

handle.

3. Traffic terminologies are different from those used in India.

4. Primarily designed to react to long-term, slow variations in traffic demand, and not to

short-term random fluctuations.

40.5.2 SCAT (Sydney Coordinated Adaptive Traffic)

SCAT (Sydney Co-ordinated Adaptive Traffic Control) System was developed by the Roads

and Traffic Authority (RTA) of New South Wales, Australia in the late 1970s. It is automated,

real time, traffic responsive signal control strategy. Timing of signals is governed by computer-

based control logic. It has ability to modify signal timings on a cycle-by-cycle basis using traffic

flow information collected at the intersection approach stop lines. It is not model based but



RegionalComputer

RegionalComputer

RegionalComputer

RegionalComputer

RegionalComputer 1−32

ManagementFunctions

Management System

Central

tactical traffic controlTraffic controllers regional computer

upto 250 per

Strategic

controlTraffic

Figure 40:7: Shows the SCAT Computer Hierarchy (Source: Lowrie, 1982)

has a library of plans that it selects from and therefore banks extensively on available traffic

data.

Working Principle

The system is very flexible, powerful, expandable, and yields unprecedented monitoring and

management possibilities. The total system is divided into intersection, regional and a central

system management. Distribution of the regional computers is determined by the economics

of communication. Each regional computer maintains autonomous control of its region. Input

data is collected by a system of traffic sensors. Sensors may be inductive loop detectors em-

bedded in the pavement or video image devices mounted overhead on the signal strain poles.

The system is designed to auto calibrate itself according to the data received, to minimize the

need for manual calibration and adjustment. Fig. 40:7 shows the SCAT Computer Hierarchy.

It supports four modes of operations

1. Normal Mode- Provide integrated traffic responsive operation

2. Fall-Back Mode- Implement the time plans when computer or communication failure

occurs

3. Isolated Control Mode- vehicle actuation with isolated control works

4. Fourth mode- signal display flashing yellow or red at all approaches

Benefits of SCAT

1. Travel time and accident reduction, saving in fuel consumption, and reduces air pollution.



2. It replaces the manual collection of data which are required for road Planning.

3. It provides a greater volume of original data with good accuracy level.

Limitations

1. Lacks user-friendly interface features to support day-to-day operations & programming

tasks.

2. The error messages are not easy to read & do not provide the opportunity for corrective

actions by system operators.

3. It is expensive because it includes advanced technology which is expensive and to under-

stand and operate this type of technology person should have very good knowledge.

40.5.3 OPAC (Optimized Policies for Adaptive Control)

It is developed by Parsons Brinkerhoff Farradyne Inc. and the University of Massachusetts at

Lowell jointly. It is a distributed traffic signal control strategy. The network is divided into

sub-networks, which are considered independently for optimization purpose. OPAC breaks

between two models: one for congested networks and the other for uncongested networks.

Feature of OPAC

1. Signal timing is calculated by dynamic optimization algorithm to minimize total inter-

section delay and stop.

2. Algorithm uses measured and modeled demand to determine phase distribution at each

signal that are constrained by minimum and maximum green time.

Principles behind development of OPAC strategy

1. It must provide better performance than off line methods

2. It should be totally demand responsive. It means to adapt to actual fluctuating traffic

condition

3. It must not be restricted to any fixed control period (e.g. 10 min)



Limitation

1. It is based on the pseudo dynamic programming technique, so it finds result near to

optimal but not exactly optimal.

2. Its performance varies with traffic saturation condition. Better in under saturated traffic

conditions.

3. It is expensive because it includes advanced technology which is expensive and to under-

stand and operate this type of technology person should have very good knowledge.

40.6 Conclusion

Area traffic control system can reduce traffic delays, fuel consumption, accident, congestions,

travel time, environmental pollutions substantially and can increase average flow speed. Re-

garding ATC systems, SCOOT, SCAT and OPAC are popular in advanced countries but such

systems cannot cope up with Indian situations because in India traffic is not lane following,

highly mixed traffic, uncontrolled side road and on-street parking, Data loss due to power failure

and Availability of funds.

40.7 References

1. Christina M Andrews, S Manzur Elahi, and James E Clark. Evaluation of New Jer-

sey Route 18 OPAC/MIST Traffic-Control System. TRANSPORTATION RESEARCH

RECORD 1603, 2019.

2. Pitu B Mirchandani K Larry Head. A real-time traffic signal control system: architecture,

algorithms, and analysis. 1998.



4. D I Robertson and R D Bretherton. Optimizing Networks of Traffic Signals in Real Time

- The SCOOT Method. IEEE Transactions on Vehicular Technology, 1991.

5. A G Sims and K W Dobinson. The sydney coordinated adaptive traffic (scat) system

philosophy and benefits, 1980.


Transportation Systems Engineering 41. Parking Studies

Chapter 41

Parking Studies

41.1 Overview

Parking is one of the major problems that is created by the increasing road traffic. It is an

impact of transport development. The availability of less space in urban areas has increased

the demand for parking space especially in areas like Central business district. This affects the

mode choice also. This has a great economical impact.

41.2 Parking system

41.2.1 On street parking

On street parking means the vehicles are parked on the sides of the street itself. This will be

usually controlled by government agencies itself. Common types of on-street parking are as

listed below. This classification is based on the angle in which the vehicles are parked with

respect to the road alignment. As per IRC the standard dimensions of a car is taken as 5× 2.5

metres and that for a truck is 3.75× 7.5 metres.

1. Parallel parking: The vehicles are parked along the length of the road. Here there is

no backward movement involved while parking or unparking the vehicle. Hence, it is the

most safest parking from the accident perspective. However, it consumes the maximum

curb length and therefore only a minimum number of vehicles can be parked for a given

kerb length. This method of parking produces least obstruction to the on-going traffic on

the road since least road width is used. Parallel parking of cars is shown in figure 41:1.

The length available to park N number of vehicles, L = N5.9

2. 30◦ parking: In thirty degree parking, the vehicles are parked at 30◦ with respect to the

road alignment. In this case, more vehicles can be parked compared to parallel parking.



L

2.5

5.0

5.9

Figure 41:1: Illustration of parallel parking

5 m2.

5 m

30

1.25 m

4.66 m1 2 n....

A B C D E

L1.254.33

O QP

Figure 41:2: Illustration of 30◦ parking

Also there is better maneuverability. Delay caused to the traffic is also minimum in this

type of parking. An example is shown in figure 41:2. From the figure,

AB = OBsin30◦ = 1.25,

BC = OPcos30◦ = 4.33,

BD = DQcos60◦ = 5,

CD = BD − BC = 5 − 4.33 = 0.67,

AB + BC = 1.25 + 4.33 = 5.58

For N vehicles, L = AC + (N-1)CE =5.58+(N-1)5 =0.58+5N

3. 45◦ parking: As the angle of parking increases, more number of vehicles can be parked.

Hence compared to parallel parking and thirty degree parking, more number of vehicles

can be accommodated in this type of parking. From figure 41:3, length of parking space

available for parking N number of vehicles in a given kerb is L = 3.54 N+1.77

4. 60◦ parking: The vehicles are parked at 60◦ to the direction of road. More number of

vehicles can be accommodated in this parking type. From the figure 41:4, length available

for parking N vehicles =2.89N+2.16.

5. Right angle parking: In right angle parking or 90◦ parking, the vehicles are parked

perpendicular to the direction of the road. Although it consumes maximum width kerb



5.0 m

45

1.77

5.31 m

2.5 m


2.5m

60

L


length required is very little. In this type of parking, the vehicles need complex maneu-

vering and this may cause severe accidents. This arrangement causes obstruction to the

road traffic particularly if the road width is less. However, it can accommodate maximum

number of vehicles for a given kerb length. An example is shown in figure 41:5. Length

available for parking N number of vehicles is L = 2.5N.

41.2.2 Off street parking

In many urban centres, some areas are exclusively allotted for parking which will be at some

distance away from the main stream of traffic. Such a parking is referred to as off-street

L

2.5




��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

ENTRY

EXIT

Figure 41:6: Illustration of off-street parking

parking. They may be operated by either public agencies or private firms. A typical layout of

an off-street parking is shown in figure 41:6.

41.2.3 Parking requirements

There are some minimum parking requirements for different types of building. For residential

plot area less than 300 sq.m require only community parking space. For residential plot area

from 500 to 1000 sq.m, minimum one-fourth of the open area should be reserved for parking.

Offices may require atleast one space for every 70 sq.m as parking area. One parking space

is enough for 10 seats in a restaurant where as theatres and cinema halls need to keep only 1

parking space for 20 seats. Thus, the parking requirements are different for different land use

zones.

41.2.4 Ill effects of parking

Parking has some ill-effects like congestion, accidents, pollution, obstruction to fire-fighting

operations etc.

1. Congestion: Parking takes considerable street space leading to the lowering of the road

capacity. Hence, speed will be reduced, journey time and delay will also subsequently

increase. The operational cost of the vehicle increases leading to great economical loss to

the community.

2. Accidents: Careless maneuvering of parking and unparking leads to accidents which are

referred to as parking accidents. Common type of parking accidents occur while driving

out a car from the parking area, careless opening of the doors of parked cars, and while

bringing in the vehicle to the parking lot for parking.



3. Environmental pollution: They also cause pollution to the environment because stop-

ping and starting of vehicles while parking and unparking results in noise and fumes. They

also affect the aesthetic beauty of the buildings because cars parked at every available

space creates a feeling that building rises from a plinth of cars.

4. Obstruction to fire fighting operations: Parked vehicles may obstruct the movement

of firefighting vehicles. Sometimes they block access to hydrants and access to buildings.

41.3 Parking statistics

Before taking any measures for the betterment of conditions, data regarding availability of

parking space, extent of its usage and parking demand is essential. It is also required to

estimate the parking fares also. Parking surveys are intended to provide all these information.

Since the duration of parking varies with different vehicles, several statistics are used to access

the parking need. The following parking statistics are normally important.

1. Parking accumulation: It is defined as the number of vehicles parked at a given

instant of time. Normally this is expressed by accumulation curve. Accumulation curve

is the graph obtained by plotting the number of bays occupied with respect to time.

2. Parking volume: Parking volume is the total number of vehicles parked at a given

duration of time. This does not account for repetition of vehicles. The actual volume of

vehicles entered in the area is recorded.

3. Parking load : Parking load gives the area under the accumulation curve. It can also

be obtained by simply multiplying the number of vehicles occupying the parking area at

each time interval with the time interval. It is expressed as vehicle hours.

4. Average parking duration: It is the ratio of total vehicle hours to the number of

vehicles parked.

parking duration =parking load

parking volume(41.1)

5. Parking turnover: It is the ratio of number of vehicles parked in a duration to the

number of parking bays available. This can be expressed as number of vehicles per bay

per time duration.

parking turnover =parking volume

no. of bays available(41.2)



6. Parking index: Parking index is also called occupancy or efficiency. It is defined as the

ratio of number of bays occupied in a time duration to the total space available. It gives

an aggregate measure of how effectively the parking space is utilized. Parking index can

be found out as follows

parking index =parking load

parking capacity× 100 (41.3)

Numerical Example

To illustrate the various measures, consider a small example in figure 41:7, which shows the

duration for which each of the bays are occupied(shaded portion). Now the accumulation graph

can be plotted by simply noting the number of bays occupied at time interval of 15, 30, 45 etc.

minutes ias shown in the figure. The various measures are calculated as shown below: Parking

��

��

��

��

��

��

��

��

Bays and occupancy

No

. of

veh

icle

s

1

23

321

0 15 30 45 60 75 90 105 110 Time

Parking accumulation curve

Figure 41:7: Parking bays and accumulation curve

volume is given as 5 vehicles. Parking load is given as (1+2+1+0+1+2+3+1)1560

=11×1560

= 2.75

veh hour. Average parking duration is computed as 2.75 veh hours5veh

= 33 minutes. Parking turnover

is obtained as 5 veh/2 hours3bays

= 0.83 veh/hr/bay. Parking index is calculated as 2.75 veh hour3×2 veh hours

×100=

45.83%

41.4 Parking surveys

Parking surveys are conducted to collect the above said parking statistics. The most common

parking surveys conducted are in-out survey, fixed period sampling and license plate method

of survey.



41.4.1 In-out survey

In this survey, the occupancy count in the selected parking lot is taken at the beginning. Then

the number of vehicles that enter the parking lot for a particular time interval is counted. The

number of vehicles that leave the parking lot is also taken. The final occupancy in the parking

lot is also taken. Here the labor required is very less. Only one person may be enough. But we

wont get any data regarding the time duration for which a particular vehicle used that parking

lot. Parking duration and turn over is not obtained. Hence we cannot estimate the parking

fare from this survey. For quick survey purposes, a fixed period sampling can also be done.

This is almost similar to in-out survey. All vehicles are counted at the beginning of the survey.

Then after a fixed time interval that may vary between 15 minutes to i hour, the count is again

taken. Here there are chances of missing the number of vehicles that were parked for a short

duration.

Numerical Example

From an in-out survey conducted for a parking area consisting of 40 bays, the initial count was

found to be 25. Table gives the result of the survey. The number of vehicles coming in and

out of the parking lot for a time interval of 5 minutes is as shown in the table 41:1. Find the

accumulation, total parking load, average occupancy and efficiency of the parking lot.

Table 41:1: In-out survey data

Time In Out

5 3 2

10 2 4

15 4 2

20 5 4

25 7 3

30 8 2

35 2 7

40 4 2

45 6 4

50 4 1

55 3 3

60 2 5



Solution The solution is shown in table 41:2

Table 41:2: In-out parking survey solution

Time In Out Accumulation Occupancy Parking load

(1) (2) (3) (4) (5) (6)

5 3 2 26 65 130

10 2 4 24 60 120

15 4 2 26 65 130

20 5 4 27 67.5 135

25 7 3 31 77.5 155

30 8 2 37 92.5 185

35 2 7 32 80 160

40 4 2 34 85 170

45 6 4 36 90 180

50 4 1 39 97.5 195

55 3 3 39 97.5 195

60 2 5 36 90 180

Total 1735

• Accumulation can be found out as initial count plus number of vehicles that entered the

parking lot till that time minus the number of vehicles that just exited for that particular

time interval. For the first time interval of 5 minutes, accumulation can be found out as

25+3-2 = 26. It is being tabulated in column 4.

• Occupancy or parking index is given by equation For the first time interval of five min-

utes, Parking index = 2640

× 100 = 65%. The occupancy for the remaining time slot is

similarly calculated and is tabulated in column 5. Average occupancy is the average of

the occupancy values for each time interval. Thus it is the average of all values given in

column 5 and the value is 80.63%.

• Parking load is tabulated in column 6. It is obtained by multiplying accumulation with

the time interval. For the first time interval, parking load = 26 × 5 = 130 vehicle minutes.

• Total parking load is the summation of all the values in column 5 which is equal to 1935

vehicle minutes or 32.25 vehicle hours



41.4.2 License plate method of survey

This results in the most accurate and realistic data. In this case of survey, every parking stall

is monitored at a continuous interval of 15 minutes or so and the license plate number is noted

down. This will give the data regarding the duration for which a particular vehicle was using

the parking bay. This will help in calculating the fare because fare is estimated based on the

duration for which the vehicle was parked. If the time interval is shorter, then there are less

chances of missing short-term parkers. But this method is very labor intensive.

Numerical Example

The parking survey data collected from a parking lot by license plate method is s shown in

the table 41:3 below. Find the average occupancy, average turn over, parking load, parking

capacity and efficiency of the parking lot.

Table 41:3: Licence plate parking survey data

Bay Time

0-15 15-30 30-45 45-60

1 1456 9813 - 5678

2 1945 1945 1945 1945

3 3473 5463 5463 5463

4 3741 3741 9758 4825

5 1884 1884 - 7594

6 - 7357 - 7893

7 - 4895 4895 4895

8 8932 8932 8932 -

9 7653 7653 8998 4821

10 7321 - 2789 2789

11 1213 1213 3212 4778

12 5678 6678 7778 8888

Solution See the following table for solution 41:4. Columns 1 to 5 is the input data. The

parking status in every bay is coded first. If a vehicle occupies that bay for that time interval,

then it has a code 1. This is shown in columns 6, 7, 8 and 9 of the table corresponding to the

time intervals 15, 30, 45 and 60 seconds.



Table 41:4: Licence plate parking survey solution

Bay Time Time

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

15 30 45 60 15 30 45 60 Turn over

1 1456 9813 - 5678 1 1 0 1 3

2 1945 1945 1945 1945 1 1 1 1 1

3 3473 5463 5463 5463 1 1 1 1 2

4 3741 3741 9758 4825 1 1 1 1 3

5 1884 1884 - 7594 1 1 0 1 2

6 - 7357 - 7893 0 1 0 1 2

7 - 4895 4895 4895 0 1 1 1 1

8 8932 8932 8932 - 1 1 1 0 1

9 7653 7653 8998 4821 1 1 1 1 3

10 7321 - 2789 2789 1 0 1 1 2

11 1213 1213 3212 4778 1 1 1 1 3

12 5678 6678 7778 8888 1 1 1 1 4

Accumulation 10 11 9 11

Occupancy 0.83 0.92 0.75 0.92 2.25



• Turn over is computed as the number of vehicles present in that bay for that particular

hour. For the first bay, it is counted as 3. Similarly, for the second bay, one vehicle is

present throughout that hour and hence turnout is 1 itself. This is being tabulated in

column 10 of the table. Average turn over = Sum of turn−overTotal number of bays

= 2.25

• Accumulation for a time interval is the total of number of vehicles in the bays 1 to 12 for

that time interval. Accumulation for first time interval of 15 minutes = 1+1+1+1+1+0+0+1+1+1+1+1

= 10

• Parking volume = Sum of the turn over in all the bays = 27 vehicles

• Average duration is the average time for which the parking lot was used by the vehicles.

It can be calculated as sum of the accumulation for each time interval × time interval

divided by the parking volume = (10+11+9+11)×1527

= 22.78 minutes/vehicle.

• Occupancy for that time interval is accumulation in that particular interval divided by

total number of bays. For first time interval of 15 minutes, occupancy = (10×100)/12 =

83% Average occupancy is found out as the average of total number of vehicles occupying

the bay for each time interval. It is expressed in percentage. Average occupancy =0.83+0.92+0.75+0.92

4× 100 = 85.42%.

• Parking capacity = number of bays × number of hours = 12× 1 = 12 vehicle hours

• Parking load = total number of vehicles accumulated at the end of each time interval ×

time = (10+11+9+11)×1560

= 10.25 vehicle hours

• Efficiency = Parking loadTotal number of bays

= 10.2512

= 85.42%.

41.5 Summary

Providing suitable parking spaces is a challenge for traffic engineers and planners in the scenario

of ever increasing vehicle population. It is essential to conduct traffic surveys in order to design

the facilities or plan the fares. Different types of parking layout, surveys and statistics were

discussed in this chapter.

41.6 References


New Delhi, 1987.


Transportation Systems Engineering 42. Accident Studies

Chapter 42

Accident Studies

42.1 Overview

This lecture covers one of the most important negative impact of transportation system, namely

the accidents. This lecture first presents some introductory stuff including some salient accident

statistics, causes of accidents, accident data collection, accident reconstruction, safety measures

and safety audit.

42.2 Introduction

The problem of accident is a very acute in highway transportation due to complex flow pattern

of vehicular traffic, presence of mixed traffic along with pedestrians. Traffic accident leads to

loss of life and property. Thus the traffic engineers have to undertake a big responsibility of

providing safe traffic movements to the road users and ensure their safety. Road accidents

cannot be totally prevented but by suitable traffic engineering and management the accident

rate can be reduced to a certain extent. For this reason systematic study of traffic accidents are

required to be carried out. Proper investigation of the cause of accident will help to propose

preventive measures in terms of design and control.

42.2.1 Objectives of accident studies

Some objectives of accident studies are listed below:

1. To study the causes of accidents and suggest corrective measures at potential location

2. To evaluate existing design

3. To compute the financial losses incurred



4. To support the proposed design and provide economic justification to the improvement

suggested by the traffic engineer

5. To carry out before and after studies and to demonstrate the improvement in the problem.

42.2.2 Causes of road accidents

The various causes of road accidents are:

1. Road Users - Excessive speed and rash driving, violation of traffic rules, failure to per-

ceive traffic situation or sign or signal in adequate time, carelessness, fatigue, alcohol,sleep

etc.

2. Vehicle - Defects such as failure of brakes, steering system, tyre burst,lighting system .

3. Road Condition - Skidding road surface, pot holes, ruts.

4. Road design - Defective geometric design like inadequate sight distance, inadequate

width of shoulders, improper curve design, improper traffic control devices and improper

lighting,.

5. Environmental factors -unfavourable weather conditions like mist, snow, smoke and

heavy rainfall which restrict normal visibility and and makes driving unsafe.

6. Other causes -improper location of advertisement boards, gate of level crossing not

closed when required etc..

42.2.3 Accident statistics

The statistical analysis of accident is carried out periodically at critical locations or road

stretches which will help to arrive at suitable measures to effectively decrease accident rates. It

is the measure (or estimates) of the number and severity of accident. These statistics reports

are to be maintained zone-wise. Accident prone stretches of different roads may be assessed by

finding the accident density per length of the road. The places of accidents are marked on the

map and the points of their clustering (BLACK SPOT) are determined. By statistical study

of accident occurrence at a particular road or location or zone of study for a long period of

time it is possible to predict with reasonable accuracy the probability of accident occurrence

per day or relative safety of different classes of road user in that location. The interpretation of

the statistical data is very important to provide insight to the problem. The position of India

in the year 2009 in country-wise number of person killed per 100000 populations as shown in



35

30

25

20

15

10

5

0

1.21

1.68 4.

044.

13 5.45

5.55 6.86

7.39

7.48

7.91 8.27

8.88 10

.83

12.0

812

.25

12.5

3 16.2

617

.49

18.5

721

.06

24.1

631

.18

31.2

5

Phi

lippi

nes

Nig

erJa

pan

U.K

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erm

any

Chi

naF

ranc

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Italy

Aus

tral

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enm

ark

Can

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Kor

ea, R

epub

lic o

fU

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Qat

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razi

lR

ussi

an F

eder

atio

nM

alay

sia

Sou

th A

fric

aA

ngui

lla

Figure 42:1: Country-wise number of person killed per 100000 populations (Ref. Ministry of

Road Transport and Highways Transport Research Wing)

the Figure 42:1 and the increase in rate of accident from year 2005 to year 2009 is shown in

the table. 42:1. In 2009, 14 accidents occurred per hour. Figure 42:2 and 42:3 gives the

percent of accident occurring from a specific vehicle class and the causes of accident in the form

of pie-chart. Since the data collection of accident is mostly done by the traffic police its the

users who are put to blame in majority of cases. Thus such statistical records are not much

useful for the traffic engineer.

42.3 Accident Analysis

42.3.1 Accident data collection

The accident data collection is the first step in the accident study. The data collection of

the accidents is primarily done by the police. Motorist accident reports are secondary data

which are filed by motorists themselves. The data to be collected should comprise all of these

parameters:

1. General - Date, time, person involved in accident, classification of accident like fatal,

serious, minor

2. Location - Description and detail of location of accident



Table 42:1: Number of Accidents and Number of Persons Involved : 2001 to 2009(Ref. Ministry

of Road Transport and Highways Transport Research Wing)

No. of Accidents No. of persons affected Accident severity

Year Total Fatal Killed Injured (No. of persons killed

per 100 accidents)

2005 4,39,255 83,491 94,968 4,65,282 22

2006 4,60,920 93,917 1,05,749 4,96,481 23

2007 4,79,216 1,01,161 1,14,444 5,13,340 24

2008 4,84,704 1,06,591 1,19,860 5,23,193 25

2009 4,86,384 1,10,993 1,25,660 5,15,458 25.8

22.6

10.97.9

22.4

6.9

20.68.7

Auto Rickshaws Car, Jeeps, Taxis

OthersTrucks, Tempos, MAVs, Tractors

Figure 42:2: Percent share in total road accident by type of motor vehicle involved (Primary

responsible) in year 2009 (Ref. Ministry of Road Transport and Highways Transport Research

Wing)



14.2

78.5

0.81.3

1.82.2

1.2

Fault of driver Fault of cyclistFault of Pedestrian Defect in condition of Motor VehicleAll Other Causes Weather Condition

Figure 42:3: Causes of road accident in year 2009 (Ref. Ministry of Road Transport and

Highways Transport Research Wing)

3. Details of vehicle involved - Registration number, description of vehicle, loading detail,

vehicular defects

4. Nature of accident - Details of collision, damages, injury and casualty

5. Road and traffic condition - Details of road geometry, surface characteristics,type of

traffic, traffic density etc..

6. Primary causes of accident - Details of various possible cases (already mentioned)

which are the main causes of accident.

7. Accident cost - Financial losses incurred due to property damage, personal injury and

casualty

These data collected need proper storing and retrieving for the following purpose. The purposes

are as follows:

1. Identification of location of points at which unusually high number of accident occur.

2. Detailed functional evaluation of critical accident location to identify the causes of acci-

dents.

3. Development of procedure that allows identification of hazards before large number of

accidents occurs.

4. Development of different statistical measures of various accident related factors to give

insight into general trends, common casual factors, driver profiles, etc.



42.3.2 Accident investigation

The accident data collection involves extensive investigation which involves the following pro-

cedure:

1. Reporting: It involves basic data collection in form of two methods:

(a) Motorist accident report - It is filed by the involved motorist involved in all

accidents fatal or injurious.

(b) Police accident report - It is filed by the attendant police officer for all accidents

at which an officer is present. This generally includes fatal accidents or mostly

accidents involving serious injury required emergency or hospital treatment or which

have incurred heavy property damage.

2. At Scene-Investigation: It involves obtaining information at scene such as measure-

ment of skid marks, examination of damage of vehicles, photograph of final position of

vehicles, examination of condition and functioning of traffic control devices and other

road equipments.

3. Technical Preparation: This data collection step is needed for organization and inter-

pretation of the study made. In this step measurement of grades, sight distance, preparing

drawing of after accident situation, determination of critical and design speed for curves

is done.

4. Professional Reconstruction: In this step effort is made to determine from whatever

data is available how the accident occurs from the available data. This involves accident

reconstruction which has been discussed under Section No.7 in details. It is professionally

referred as determining behavioral or mediate causes ofaccident.

5. Cause Analysis: It is the effort made to determine why the accident occurred from the

data available and the analysis of accident reconstruction studies..

42.3.3 Accident data analysis

The purpose is to find the possible causes of accident related to driver, vehicle, and roadway.

Accident analyses are made to develop information such as:

1. Driver and Pedestrian - Accident occurrence by age groups and relationships of accidents

to physical capacities and to psychological test results.



2. Vehicle - Accident occurrence related to characteristic of vehicle, severity, location and

extent of damage related to vehicles.

3. Roadway conditions - Relationships of accident occurrence and severity to characteristics

of the roadway and roadway condition and relative values of changes related to roadways.

It is important to compute accident rate which reflect accident involvement by type of highway.

These rates provide a means of comparing the relative safety of different highway and street

system and traffic controls. Another is accident involvement by the type of drivers and vehicles

associated with accidents.

1. Accident Rate per Kilometre :

On this basis the total accident hazard is expressed as the number of accidents of all types

per km of each highway and street classification.

R =A

L(42.1)

where, R = total accident rate per km for one year, A = total number of accident occur-

ring in one year, L = length of control section in kms

2. Accident involvement Rate :

It is expressed as numbers of drivers of vehicles with certain characteristics who were

involved in accidents per 100 million vehicle-kms of travel.

R =N × 100000000

V(42.2)

where,R = accident involvement per 100 million vehicle-kms of travel, N = total number

of drivers of vehicles involved in accidents during the period of investigation and V =

vehicle-kms of travel on road section during the period of investigation

3. Death rate based on population :

The traffic hazard to life in a community is expressed as the number of traffic fatalities

per 100,000 populations. This rate reflects the accident exposure for entire area.

R =B × 100000

P(42.3)

where, R = death rate per 100,000 population, B = total number of traffic death in one

year and P = population of area



4. Death rate based on registration :

The traffic hazard to life in a community can also be expressed as the number of traffic

fatalities per 10,000 vehicles registered. This rate reflects the accident exposure for entire

area and is similar to death rate based on population.

R =B × 10000

M(42.4)

where, R = death rate per 10,000 vehicles registered, B = total number of traffic death

in one year and M = number of motor vehicles registered in the area

5. Accident Rate based on vehicle-kms of travel :

The accident hazard is expressed as the number of accidents per 100 million vehicle km

of travel. The true exposure to accident is nearly approximated by the miles of travel of

the motor vehicle than the population or registration.

R =C × 100000000

V(42.5)

where, R = accident rate per 100 million vehicle kms of travel, C = number of total

accidents in one year and V = vehicle kms of travel in one year

Numerical Example

The Motor vehicle consumption in a city is 5.082 million liters, there were 3114 motor vehicle

fatalities, 355,799 motor vehicle injuries, 6,721,049 motor vehicle registrations and an estimated

population of 18,190,238. Kilometer of travel per liter of fuel is 12.42 km/liter. Calculate

registration death rate, population death rate and accident rate per vehicle km.

Solution Approximate vehicle kms of travel = Total consumption o fuel × kilometer of travel

per liter of fuel =5.08 × 109 × 12.42 = 63.1 × 109 km.

1. Registration death rate can be obtained from the equation

R =B × 10, 000

M

Here, R is the death rate per 10,000 vehicles registered, B (Motor vehicle fatalities) is

3114, M (Motor vehicle registered) is 6.72 × 106. Hence,

R =3114 × 10000

6.72 × 106= 4.63



2. Population Death Rate can be obtained from the equation.

R =B × 100, 000

P

Here, R is the death rate per 100,000 population, B (Motor vehicle fatalities) is 3114, P

(Estimated population) is= 18.2 × 106.

R =3114 × 100000

18.2 × 106= 17.1

3. Accident rate per vehicle kms of travel can be obtained from the equation below as:

R =C × 100, 000, 000

V

Here, R is the accident rate per 100 million vehicle kms of travel, C (total accident same

as vehicle fatalities) is 3114, V (vehicle kms of travel) is 63.1 × 109.

R =3114 × 100 × 106

63.1 × 109= 4.93

42.4 Accident reconstruction

Accident reconstruction deals with representing the accidents occurred in schematic diagram to

determine the pre-collision speed which helps in regulating or enforcing rules to control or check

movement of vehicles on road at high speed. The following data are required to determine the

pre-collision speed:

1. Mass of the vehicle

2. Velocities after collision

3. Path of each vehicle as it approaches collision point

Below in Figure 42:4 a schematic diagram of collision of two vehicles is shown that occur

during turning movements. This diagram is also known as collision diagram. Each collision is

represented by a set of arrows to show the direction of before and after movement. The collision

diagram provides a powerful visual record of accident occurrence over a significant period of

time. The collision may be of two types collinear impact or angular collision. Below each of

them are described in detail. Collinear impact can be again divided into two types :

1. Rear end collision



Figure 42:4: Collision diagram of two vehicles

a)

b)

c)

Car 1 Car 2

Car 1 Car 2

Car 1 Car 2

v1 v2

u

u2u1

Figure 42:5: Compression Phase

2. Head-on collision.

It can be determined by two theories:

1. Poisson Impact Theory

2. Energy Theory

42.4.1 Poisson impact theory

Poisson impact theory, divides the impact in two parts - compression and restitution. The

Figure 42:5 shows two vehicles travelling at an initial speed of v1 and v2 collide and obtain a

uniform speed say u at the compression stage. And after the compression stage is over the final

speed is u1 and u2. The compression phase is cited by the deformation of the cars. From the

Newtons law F = ma,

m1

dv1

dt= −F and m2

dv2

dt= F (42.6)

where, m1 and m2 are the masses of the cars and F is the contact force. We know that every

reaction has equal and opposite action. So as the rear vehicle pushes the vehicle ahead with



−F FCar 1 Car 2

Figure 42:6: Force applied on each vehicle

force F . The vehicle ahead will also push the rear vehicle with same magnitude of force but

has different direction. The action force is represented by F , whereas the reaction force is

represented by −F as shown in Figure 42:6. In the compression phase cars are deformed. The

compression phase terminates when the cars have equal velocity. Thus the cars obtain equal

velocity which generates the following equation:

m1(u − v1) = −Pc m2(u − v2) = Pc (42.7)

where, Pc ≡∫

τc

0F dt which is the compression impulse and τc is the compression time. Thus,

the velocity after collision is obtained as:

u =m1v1 + m2v2

m1 + m2

(42.8)

The compression impulse is given by:

Pc =m1m2

m1 + m2

(v1 − v2) (42.9)

In the restitution phase the elastic part of internal energy is released

m1(u1 − u) = −Pr (42.10)

m2(u2 − u) = Pr (42.11)

where, Pr ≡∫

τr

0F dt is the restitution impulse and τr is the restitution time. According to

Poissons hypothesis restitution impulse is proportional to compression impulse

Pr = e Pc (42.12)

Restitution impulse e is given by:

e =u2 − u1

v1 − v2

(42.13)

The total impulse is P = Pc + Pr

P = (1 + e)m1m2

m1 + m2

∆v (42.14)



The post impact velocities are given by:

u1 = u − e m2

m1+m2

∆v = v1 −(1 + e)m2

m1 + m2

∆v (42.15)

u2 = u + e m1

m1+m2

∆v = v2 +(1 + e)m1

m1 + m2

∆v (42.16)

where ∆v = v1 − v2. But we are required to determine the pre-collision speed according to

which the safety on the road can be designed. So we will determine v1 and v2 from the given

value of u1 and u2 .

Numerical Example

Two vehicles travelling in the same lane have masses 3000 kg and 2500 kg. The velocity of

rear vehicles after striking the leader vehicle is 25 kmph and the velocity of leader vehicle is 56

kmph. The coefficient of restitution of the two vehicle system is assumed to be 0.6. Determine

the pre-collision speed of the two vehicles.

Solution Given that the: mass of the first vehicle (m1) = 3000 kg, mass of the second vehicle

(m2) = 2500 kg, minal speed of the rear vehicle (u1) = 25 kmph, and minal speed of the leader

vehicle (u2) = 56 kmph. Let initial speed of the rear vehicle be v1, and let initial speed of the

leader vehicle be v2.

Step 1: From equation. 42.15,

25 = v1 −(1.6)2.5(v1 − v2)

(3 + 2.5)5.5v1 − 4v1 + 4v2 = 137.5

4v2 − 1.5v1 = 137.5 (42.17)

Step 2: From equation. 42.16,

56 = v2 +(1.6)3(v1 − v2)

(3 + 2.5)5.5 v2 + 4.8 v1 − 4.8v2 = 308

4.8 v1 − 0.7 v2 = 308 (42.18)

Step 3: Solving equations. 42.17 and 42.18, We get the pre collision speed of two vehicles

as: v1 = 73 kmph, and v2 = 62 kmph.

Step 4: Initial speed of the rear vehicle, v1 = 73 kmph, and the initial speed of leader

vehicle, v2 = 62 kmph. Thus from the result we can infer that the follower vehicle was travelling

at quite high speed which may have resulted in the collision. The solution to the problem may

be speed restriction in that particular stretch of road where accident occurred.



42.4.2 Energy theory

Applying principle of conservation of energy or conservation of momentum also the initial speed

of the vehicle can be computed if the skid marks are known. It is based on the concept that

there is reduction in kinetic energy with the work done against the skid resistance. So if the

vehicle of weight W slow down from speed v1 to v2, then the loss in kinetic energy will be equal

to the work done against skid resistance, where work done is weight of the vehicle multiplied

by the skid distance and the skid resistance coefficient.

W (v21 − v2

2)

2g= W.f.S (42.19)

where, f is the skid resistance coefficient and S is the skid distance. It also follows the law

of conservation of momentum (m1, v1 are the mass and velocity of first vehicle colliding with

another vehicle of mass and velocity m2, v2 respectively)

m1v1 = m2v2 (42.20)

Numerical example

A vehicle of 2000 kg skids a distance of 36 m before colliding with a stationary vehicle of 1500

kg weight. After collision both vehicle skid a distance of 14 m. Assuming coefficient of friction

0.5, determine the initial speed of the vehicle.

Solution: Let the weight of the moving vehicle is WA, let the weight of the stationary

vehicle is WB, skid distance before and after collision is s1 and s2 respectively, initial speed is

v1, speed after applying brakes before collision is v2 and the speed of both the vehicles A and

B after collision is v3, and the final speed v4 is 0. Then:

1. After collision: Loss in kinetic energy of both cars = Work done against skid resistance

(can be obtained from equation mentioned below). Substituting the values we obtain v3.

(WA + WB) × (v23 − v2

4)

2g= (WA + WB).f.s2

(v3)2

2g= 0.5 × 14 = 7

v3 = 11.71m/s



2. At collision: Momentum before impact = momentum after impact (can be obtained from

equation. 42.20)

WA.v2

g=

(WA + WB)v3

g

v2 =(WA + WB)v3

WA

v2 = 20.5m/s

3. Before collision (can be obtained from equation. 42.19): Loss in kinetic energy of moving

vehicle = work done against braking force in reducing the speed

(WA) × (v21 − v2

2)

2g= WA.f.s1

(v21 − v2

2)

2g= 0.5 × 36

v1 = 27.8 m/s = 100 kmph

Ans: The pre-collision speed of the moving vehicle is 100 kmph.

42.4.3 Angular collision

Angular collision occurs when two vehicles coming at right angles collies with each other and

bifurcates in different direction. The direction of the vehicles after collision in this case depends

on the initial speeds of the two vehicles and their weights. One general case is that two vehicles

coming from south and west direction after colliding move in its resultant direction as shown

in Figure 42:7.

The mass of the car 1 is m1 kg and the car 2 is m2 kg and the initial velocity is v1 m/s and v2

m/s respectively. So as the momentum is the product of mass and velocity. The momentum of

the car 1 and car 2 is m1v1 kgm/s and m2v2 kgm/s respectively. By the law of conservation of

momentum the final momentum should be equal to the initial momentum. But as the car are

approaching each other at an angle the final momentum should not be just mere summation of

both the momentum but the resultant of the two, Resultant momentum =√

(m1v1)2 + (m2v2)2

kg m/s. The angle at which they are bifurcated after collision is given by tan−1(h/b) where

h is the hypotenuse and b is the base. Therefore, the cars are inclined at an angle. Inclined

at an angle = tan−1(m2v2/m1v1). Now, since the mass of the two vehicles are same the final

velocity will proportionally be changed. The general schematic diagrams of collision are shown

in Figs. 42:8 to 42:10.



Car 1

Car 2

Car 1

Car 2

Figure 42:7: Angular collision of two vehicles resulting in movement in resultant direction

2

1

1 2

β

α

Figure 42:8: After collision movement of car 1 north of west and car 2 in east of north



2

1

12

αβ

Figure 42:9: After collision movement of car 1 and car 2 in north of east

2

2

1

1

α

β

Figure 42:10: After collision movement of car 1 north of east and car 2 in south of east



Numerical example

Vehicle A is approaching from west and vehicle B from south. After collision A skids 600 north

of east and B skids 300 south of east as shown in Figure 42:10. Skid distance before collision

for A is 18 m and B is 26 m. The skid distances after collision are 30m and 15 m respectively.

Weight of A and B are 4500 and 6000 respectively. Skid resistance of pavement is 0.55 m.

Determine the pre-collision speed.

Solution Let: initial speed is vA1 and vB1, speed after skidding before collision is vA2 and

vB2, speed of both the vehicles A and B after collision is vA3 and vB3, final speed is vA4 and

vB4 is 0, initial skid distance for A and B is sA1 and sB1, final skid distance for A and B is sA2

and sB2, and weight of vehicle A is WA and Weight of vehicle B is WB.

1. After collision: Loss in kinetic energy of each cars= Work done against skid resistance

(can be obtained from equation. 42.19)

WAv2A3

2g= WA f sA2

As vA4 = 0, it is not considered in the above equation

vA3 =√

2gfsA2

vA3 = 18 m/s

Similarly, we calculate vB3 using the similar formula and using sB2

vB3 = 12.7 m/s

2. At collision: Momentum before impact is momentum after impact (resolving along west-

east direction and using equation. 42.20)

WA

g× vA2 + 0 =

WB

gcos BvB3 +

WA

gcos AvA3

vA2 =WB

WA

cos BvB3 + cos AvA3

=6

4.5cos 30 × 12.7 + cos 60 × 18

vA2 = 23.66 m/s.



Resolving the moments along south- north direction

WB

g× vB2 + 0 =

WA

gsin AvA3 −

WB

gsin BvB3

vB2 =WA

WB

sin AvA3 − sin BvB3

=4.5

6× sin 60 × 12.7 − sin 30 × 18

vB2 = 5.34 m/s

3. Before collision: Loss in kinetic energy of each cars= Work done against skid resistance

(can be obtained from equation. 42.19)

WA(v2A1 − v2

A2)

2g= WA.f.sA2

vA1 =√

2gfsA1 + v2A2

= 27.45m/s = 99 km/hr

Similarly, using the same equation and using sB2

vB1 =√

2gfsB1 + v2B2

= 17.57m/s = 63.26 km/hr

Answer: The pre-collision speed of the vehicle A (approaching from west) is vA1 = 99

km/hr and vehicle B (approaching from south) is vB1 = 63.26 km/hr.

42.5 Safety measures

The ultimate goal is to develop certain improvement measures to mitigate the circumstances

leading to the accidents. The measures to decrease the accident rates are generally divided

into three groups engineering, enforcement and education. Some safety measures are described

below:

42.5.1 Safety measures related to engineering

The various measures of engineering that may be useful to prevent accidents are enumerated

below



Visual guidance to driver

There is consecutive change of picture in drivers mind while he is in motion. The number of

factors that the driver can distinguish and clearly fix in his mind is limited. On an average the

perception time for vision is 1/16th, for hearing is 1/20th and for muscular reaction is 1/20th.

The number of factors that can be taken into account by organs of sense of a driver in one

second is given by the formula below.

E = MV/L (42.21)

where, M = No. of factors that can be taken into account by the organ of sense of driver for L

m long, V = speed of vehicle in m/sec. Factors affecting drivers attention when he is on road

can be divided into three groups:

1. Factors relating to the road elements of road that directly affect the driving of a vehicle

are traffic signs, changes in direction of road, three legged intersection and various other

things.

2. Factors connected with traffic Other vehicles, cycles, pedestrians.

3. Factors related indirectly to the vehicle motion Building and structures that strike the

eye, vegetation, landscape, etc.

So using the laws of visual perception certain measures have been suggested:

1. Contrast in visibility of the road should be achieved by provision of elements that differ

from its surrounding by colours, pattern such as shoulder strips, shoulder covered with

grass, edge markings.

2. Providing road side vegetation is an effective means.

3. The visibility of crown of trees from a distant location is also very useful in visual guiding.

4. The provision of guard rails of different contrasting colours also takes drivers attention

and prevent from monotonous driving.

Figure 42:11 and 42:12 is a visual guidance measure. Planting trees along side of roadway

which has a turning angle attracts attention of the driver and signals that a turn is present

ahead. The figure below is another example, when the direction of road has a hazardous at-

grade intersection trees are planted in such a way that it seems that there is dense forest ahead

and driver automatically tends to stop or reduce the speed of the vehicle so that no conflicts

occur at that point. Driver tends to extrapolate the further direction of the road. So it is the

responsibility of the traffic engineer to make the driver psychologically confident while driving

that reduces the probability of error and prevent mental strain.



Local Road

Highway

Figure 42:11: Bifurcation of the highway

Figure 42:12: Road seemed to be stopped by a dense forest



��

��

��

��

��

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��

��

��

��

��

��

��

��

��

��

AfterBefore

NN

Figure 42:13: Diagram of accidents before and after reconstruction

Road reconstruction

The number of vehicles on the road increases from year to year, which introduces complications

into organization of traffic, sharply reduces the operation and transportation characteristic of

roads and lead to the growth of accident rate. This leads to the need of re constructing road.

The places of accidents need to be properly marked so that the reconstruction can be planned

accordingly. The Figure 42:13 shows that there were too many conflict points before which

reduced to a few number after construction of islands at proper places. Reconstruction process

may also include construction of a new road next to the existing road, renewal of pavement

without changing the horizontal alignment or profile of the road, reconstruction a particular

section of road. Few more examples of reconstruction of selected road section to improve

traffic safety are shown in Figure 42:14. The Figure 42:14 (a) shows separation of direction

of main stream of traffic from the secondary ones by shifting place of three-leg intersection,

Figure 42:14(b) shows separation of roads with construction of connection between them and

Figure 42:14(c) shows the construction of additional lane for turning vehicles. The plus sign

indicates the conflict points before the road reconstruction has been carried out. The after

reconstruction figure shows that just by little alteration of a section of road how the conflict

points have been resolved and smooth flow of the vehicles in an organized manner have been

obtained.

Channelization

The channelization of traffic at intersection separates the traffic stream travelling in different

direction, providing them a separate lane that corresponds to their convenient path and spread-

ing as far as possible the points of conflict between crossing traffic streams. The traffic lanes



+ +

+++ +

+++

(a)

(b)

(c)

Before After

L

B

M M

B

L

Figure 42:14: Road reconstruction technique

are separated by marking relevant lines or by constructing slightly elevated islands as shown

in Figure 42:15. Proper channelization reduces confusion. The number of decision required to

be made by the driver at any time is reduced allowing the driver time to make next decision.

The principles of proper channelized intersection are:-

1. The layout of intersection should be visibly clear, simple and understandable by driver.

2. Should ensure superiority to the vehicles using road of higher class.

3. Layout of intersection makes it necessary for a driver running through it to choose at each

moment of time one of not more than two possible direction of travel. This is achieved

by visual guidance, islands and markings.

4. The island provided should separate high speed, through and turning traffic flows.

5. The width of traffic lane should ensure unhampered turning to the big vehicles. Width of

straight section without kerb should be 3.5 m and that of traffic lane near island is 4.5-5

m at entry and 6 m at exit.

6. Pedestrian crossing should be provided



��

��

��

��

��

��

��

��

��

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��

��

��

��

��

��

��

��

��

��

(a)

(b)

b) Fully channelized intersectiona) Partially channelized intersection

Figure 42:15: Channelized Intersection ensuring safety

Road signs

Road signs are integral part of safety as they ensure safety of the driver himself (warning signs)

and safety of the other vehicles and pedestrians on road (regulatory signs). Driver should be

able to read the sign from a distance so that he has enough time to understand and respond. It is

essential that they are installed and have correct shape, colour, size and location. It is required

to maintain them as well, without maintenance in sound condition just their installment would

not be beneficial. According to British investigation height of text in road sign should be

H =(N + 6)v

64+

3

4L

Where, N = No. of words on the sign, v = speed of vehicle (kmph), L = distance from which

inscription should be discernable (m)

Other methods

Various other methods of traffic accident mitigation are described below:

1. Street lighting

Street lightning of appropriate standard contributes to safety in urban area during night

time due to poor visibility. Installation of good lighting results in 21% reduction in all

accidents, 29% reduction in “all casualty” accidents, 21% reduction in “non pedestrian

casualty” accidents, and 57% reduction in “pedestrian casualty” accidents.



2. Improvement in skid resistance

If road is very smooth then skidding of the vehicles may occur or if the pavement is wet

then wet weather crashes occur which account about 20-30%. Thus it is important to

improve the skid resistance of the road. Various ways of increasing the skid resistance of

road are by constructing high-friction overlay or cutting of grooves into the pavement.

3. Road markings

Road markings ensure proper guidance and control to the traffic on a highway. They serve

as supplementary function of road sign. They serve as psychological barrier and delin-

eation of traffic path and its lateral clearance from traffic hazards for the safe movement

of traffic. Thus their purpose is to provide smooth and safe traffic flow.

4. Guide posts with or without reflector

They are provided at the edge of the roadway to prevent the vehicles from being off

tracked from the roadway. Their provision is very essential in hilly road to prevent the

vehicle from sliding from top. Guide posts with reflector guide the movement of vehicle

during night.

5. Guard rail

Guard rail have similar function as of guide post. On high embankments, hilly roads,

road running parallel to the bank of river, shores of lake, near rock protrusion, trees,

bridge, abutments a collision with which is a great hazard for a vehicle. It is required to

retain the vehicle on the roadway which has accidentally left the road because of fault or

improper operation on the part of the driver. Driver who has lost control create a major

problem which can be curbed by this measure.

6. Driver reviver stop

Driver reviver stop are generally in use in countries like U.S.A where driver can stop and

refresh himself with food, recreation and rest. They play a very important part in traffic

safety as they relieve the driver from the mental tension of constant driving. These stops

are required to be provided after every 2 hour travel time.

7. Constructing flyovers and bypass

In areas where local traffic is high bypasses are required to separate through traffic from

local traffic to decrease the accident rate. To minimise conflicts at major intersections

flyovers are required for better safety and less accident rate

8. Regular accident studies

Based on the previous records of accidents the preventive measures are taken and after



that the data related to accidents are again collected to check the efficiency of the measures

and for future implementation of further preventive measures.

42.5.2 Safety measures related to enforcement

The various measures of enforcement that may be useful to prevent accidents at spots prone

to accidents are enumerated below. These rules are revised from time to time to make them

more comprehensive.

Speed control

Checks on spot speed of all vehicles should be done at different locations and timings and legal

actions on those who violate the speed limit should be taken

Training and supervision

The transport authorities should be strict while issuing licence to drivers of public service

vehicles and taxis. Driving licence of the driver may be renewed after specified period, only

after conducting some tests to check whether the driver is fit

Medical check

The drivers should be tested for vision and reaction time at prescribed intervals of time

42.5.3 Safety measures related to education

The various measures of education that may be useful to prevent accidents are enumerated

below.

Education of road users

The passengers and pedestrians should be taught the rules of the road, correct manner of

crossing etc. by introducing necessary instruction in the schools for the children and by the

help of posters exhibiting the serious results due to carelessness of road users.

Safety drive

Imposing traffic safety week when the road users are properly directed by the help of traffic

police as a means of training the public. Training courses and workshops should be organised

for drivers in different parts of the country.



42.5.4 Safety audit

It is the procedure of assessment of the safety measures employed for the road. It has the

advantages like proper planning and decision from beforehand ensures minimization of future

accidents, the long term cost associated with planning is also reduced and enables all kinds of

users to perceive clearly how to use it safely. Safety audit takes place in five stages as suggested

by Wrisberg and Nilsson, 1996. Five Stages of Safety Audit are:

1. Feasibility Stage - The starting point for the design is determined such as number and

type of intersection, relationship of the new scheme to the existing road, the relevant

design standards.

2. Draft Stage - In this stage horizontal and vertical alignment, junction layout are deter-

mined. After the completion of this stage decision about land acquisition is taken.

3. Detailed design stage - Signing, marking, lighting, other roadside equipment and land-

scaping are determined.

4. Pre-opening stage - Before opening a new or modified road should be driven, walked

or cycled. It should be done at different condition like bad weather, darkness.

5. Monitoring of the road in use - Assessment is done at the final stage after the road

has been in operation for few months to determine whether the utilization is obtained as

intended and whether any adjustment to the design are required in the light of the actual

behavior of road users.

An example of safety audit is discussed below.

Road reconstruction safety audit

To estimate the effectiveness of improvement of dangerous section the number of accidents

before and after is compared. To do this Chi Square test is used to check whether the exper-

imental data meet the allowable deviation from the theoretical analysis. In the simplest case

one group of data before and after road reconstruction is considered.

X2 =(n1t2 − n2t1)

2

t1t2(n1 + n2)≥ X2

norm(42.22)

where, t1 and t2 = period of time before and after reconstruction of a stretch of road for

which statistical data of accident is available, n1 and n2 = corresponding numbers of accident,

X2norm

= minimum values of Chi Square at which probability of deviation of laws of accident



Table 42:2: Relationship between P and X2norm

P 10 8 5 3 2 1 0.1

X2norm 1.71 2 2.7 3.6 4.25 5.41 9.6

occurrence after reconstruction P from the laws existing before reconstruction does not exceed

permissible values (usually 5%) The relationship between P and X2norm

is shown in Table. 42:2.

Numerical example

Before reconstruction of an at-grade intersection, there were 20 accidents during 5 years. Af-

ter reconstruction there were 4 accidents during 2 years. Determine the effectiveness of the

reconstruction.

Solution: Using Chi square test, we have (with P = 5 %)

X2 =(20 × 2 − 4 × 5)2

5 × 2(20 + 4)= 1.67 < 2.7

Thus the statistical data available are not yet sufficient for considering with probability of

95 % that the relative reduction in number of accident is due to intersection reconstruction.

Assuming one more accident occurs next year.

X2 =(20 × 3 − 5 × 5)2

5 × 3(20 + 5)= 3.267 > 2.7

Therefore additional analysis confirms that the reduction in accident is due to road reconstruc-

tion.

42.6 Conclusion

This chapter provides an important subject of highway safety and accident studies. Everything

a traffic engineer does, from field studies, planning and design; to control operation is related

to the provision of the safety system for vehicular travel. This chapter gives an insight of how

the analysis of traffic accident can be done from the viewpoint to reduce it by designing proper

safety measure.



42.7 References

1. Road accidents in india, 2009.

2. V F Babkov. Road Condition and traffic safety. MIR Publishers, Moscow, 2019.

3. J Stannard Baker. Traffic Accident Investigation Manual. The traffic Institute North-

western University, 2019.

4. Milan Batista. On the mutual coefficient of restitution in two car collinear collisions,

2006.

5. S K Khanna C E G Justo. Highway Engineering. Nem Chand and Bros, Roorkee, 2001.

6. K W Ogden, S Y Taylor. Traffic Engineering, and Australia. Management. Monash

University. Melbourne. Traffic Engineering and Management. Monash University Mel-

bourne, Australia, 2019.

7. Louis J Pignataro. Traffic Engineering. USA, 2019.


Transportation Systems Engineering 43. Fuel Consumption and Emission Studies

Chapter 43

Fuel Consumption and Emission

Studies

43.1 Overview

This chapter is an attempt to provide a basic knowledge about the fuel consumption and

vehicular emissions. The concepts of air pollution and automobile pollution are also given due

importance. Various types of numerical models related to fuel consumption and air pollution

are discussed briefly. The report aims to identify the necessity of understanding the impact of

vehicular pollution on the environment. In order to bring the fuel consumption and emission

levels to a minimum, various mitigation measures are to be implemented, which are also pointed

out in the report.

43.2 General

Urbanization has paved the way for higher levels of comfort and standard of living. Rapid

urbanization has thus caused an increase in the number of vehicles and this, on the other

hand, is causing another set of problems including lack of space, reduction in natural resources,

environmental pollution, etc. We need to consider the existence of a future generation and plan

the utilization of our environment and resources wisely. The following sections discuss how the

transportation engineering is helpful in bringing about welcome changes in the development of a

sustainable environment. For this, we need to have a basic knowledge about fuel consumption,

emission and resulting air pollution, which are discussed briefly below.

43.2.1 Fuel Efficiency

Fuel efficiency or Fuel Economy is the energy efficiency of a vehicle, expressed as the ratio

of distance traveled per unit of fuel consumed in km/liter. Fuel efficiency depends on many



parameters of a vehicle, including its engine parameters, aerodynamic drag, weight, and rolling

resistance. Higher the value of fuel efficiency, the more economical a vehicle is (i.e., the more

distance it can travel with a certain volume of fuel). Fuel efficiency also affects the emissions

from the vehicles.

43.2.2 Fuel Consumption

Fuel consumption is the reciprocal of Fuel Efficiency. Hence, it may be defined as the amount of

fuel used per unit distance, expressed in liters/100km. Lower is the value of fuel consumption,

more economical is the vehicle. That is less amount of fuel will be used to travel a certain

distance.

43.2.3 Air Pollution

Air Pollution maybe defined as

The disruption caused to the natural atmospheric environment by the introduction

of certain chemical substances, gases or particulate matter, which cause discomfort

and harm to structures and living organisms including plants, animals and humans.

Air pollution has become a major concern in most of the countries of the world. It is responsible

for causing respiratory diseases, cancers and serious other ailments. Besides the health effects,

air pollution also contributes to high economic losses. Poor ambient air quality is a major

concern, mostly in urban areas. Air pollution is also responsible for serious phenomena such as

acid rain and global warming.

The substances causing air pollution are collectively known as air pollutants. They may

be solid, liquid or gaseous in nature. Pollutants are classified as primary and secondary air

pollutants. Primary pollutants are those which are emitted directly to atmosphere, whereas,

secondary pollutants are formed through chemical reactions and various combinations of the

primary pollutants. Some of the major primary and secondary air pollutants are given in

Table. 43:1 and Table. 43:2. The sources of air pollution may be natural or anthropogenic.

The anthropogenic sources of air pollution are those which are caused by human activity. The

major anthropogenic sources include Stationary sources (such as smoke stacks of power plants,

incinerators, and furnaces), Mobile sources (e.g. motor vehicles, aircraft), Agriculture and

industry (e.g. chemicals, dust), Fumes from paint, hair spray, aerosol sprays, Waste deposits

in landfills (which contain methane) and Military (e.g. Nuclear weapons, toxic gases). The

natural sources of air pollution may be Dust from areas of low vegetation, Radon gas from



Table 43:1: Primary Air Pollutants

Sulphur Oxides (SOx) Carbon Monoxide (CO)

Nitrogen Oxides (NOx) Carbon Dioxide (CO2)

Volatile Organic Compounds (V OC) Hydrocarbons (HC)

Ammonia (NH3) Particulate Matter (PM)

Radioactive pollutants Chlorofluorocarbons (CFC)

Toxic Metals like Lead, Cadmium and Copper

Table 43:2: Secondary Air Pollutants

Photochemical smog

Peroxyacetyl Nitrate (PAN)

Ozone (O3)

radioactive decay of Earths crust, Smoke and CO from wildfires, and volcanic activity which

produces sulfur, chlorine and particulates.

43.3 Automobile Pollution

The pollution caused due to the emissions from vehicles is generally referred to as automo-

bile pollution. The transportation sector is the major contributor to air pollution. Vehicular

emissions are of particular concerns, since these are ground level sources and hence have the

maximum impact on the general population. The rapid increase in urban population have re-

sulted in unplanned urban development, increase in consumption patterns and higher demands

for transport and energy sources, which all lead to automobile pollution. The automobile pollu-

tion will be higher in congested urban areas. The vehicle obtains its power by burning the fuel.

The automobile pollution is majorly caused due to this combustion, which form the exhaust

emissions, as well as, due to the evaporation of the fuel itself. The chemical reactions occurring

during ideal combustion stages may be represented as follows:

Fuel (HC) + Air (O2, N2) −→ CO2 + H20 + unaffected Nitrogen (43.1)

Similarly, the typical engine combustion which occurs in vehicles can be represented by the

below chemical equation.

Fuel (HC) + Air (O2, N2) −→ Unburned HC + NOx + CO + CO2 + H2O (43.2)



Evaporative EmissionsRefueling Losses

ExhaustEmissions

Figure 43:1: Losses of fuel in vehicles

43.3.1 Types of Vehicular Emissions

The fuel loss of vehicles may be due to emissions or refuelling. The emissions maybe evaporative

or exhaust emissions. The fuel losses in a vehicle are shown in Fig. 43:1.

1. Exhaust emissions: Exhaust emissions are those which are emitted through the exhaust

pipe when the vehicle is running or is started. Hence, the exhaust emissions maybe of 2

types - start up emissions and running emissions.

(a) Startup emissions: Emissions when the vehicle is started initially. Based on how

long the vehicle had been turned off after use, they may be cold start and hot start.

Cold start refers to when the vehicle is started suddenly after a long gap of use,

whereas, hot start refers to when the vehicle is started without the vehicle getting

enough time to cool off after its previous use.

(b) Running emissions: Emissions during normal running of the vehicle, i.e., when

the vehicle is in a hot stabilized mode.

2. Evaporative emissions: These include running losses and hot soak emissions produced

from fuel evaporation when an engine is still hot at the end of a trip, and diurnal emissions

(daily temperature variations).

43.3.2 Exhaust Pollutants

The pollutants which are emitted from the exhaust pipe of the automobiles are known as

exhaust pollutants. They are formed as a result of combustion of the fuel in the engine. These

pollutants are harmful to the atmosphere and living things in particular. The major types of

exhaust pollutants are discussed in the following sections.



Sulphur Oxides (SOx)

Combustion of petroleum generates Sulfur Dioxide. It is a colorless, pungent and non flammable

gas. It causes respiratory illness, but occurs only in very low concentrations in exhaust gases.

Further oxidation of SOx forms H2SO4 and thus acid rains.

Nitrogen Oxides (NOx)

Combustion under high temperature and pressure emits Nitrogen dioxide. It is reddish brown

gas. Nitrogen oxides contribute to the formation of ground level Ozone and acid rain.

Hydrocarbons and Volatile Organic Compounds (HC and V OC)

Hydrocarbons result from the incomplete combustion of fuels. Their subsequent reaction with

the sunlight causes smog and ground level Ozone formation. V OCs are a special group of

Hydrocarbons. They are divided into 2 types methane and non methane. Prolonged exposure

to some of these compounds (like Benzene, Toluene and Xylene) may also cause Leukemia.

Carbon Dioxide (CO2)

It is an indicator of complete combustion of the fuel. Although it does not directly affect our

health, it is a greenhouse gas which causes global warming.

Carbon Monoxide (CO)

It is a product of the incomplete burning of fuel and is formed when Carbon is partially oxidized.

CO is an odorless, colorless gas, but is toxic in nature. It reaches the blood stream to form

Carboxyhemoglobin, which reduces the flow of Oxygen in blood.

Lead (Pb)

It is a malleable heavy metal. Lead present in the fuel helps in preventing engine knock. Lead

causes harm to the nervous and reproductive systems. It is a neurotoxin which accumulates in

the soft tissues and bones.

Particulate Matter (PM)

These are tiny solid or liquid particles suspended in gas (soot or smoke). Particulate Matter in

higher concentrations may lead to heart diseases and lung cancer.



43.3.3 Factors Affecting Emission Rates

The vehicular emissions are due to a variety of factors. The emissions vary according to the

environment, fuel quality, vehicle, etc. emissions are higher in congested and urban areas.

Fuel adulteration and overloading also cause higher amount of emissions. The emissions from

vehicles depend on the following factors:

1. Travel related factors

2. Highway Network related factors

3. Vehicle related factors

Travel Related Factors

The number of trips, distance travelled and driving mode are the major travel related factors

affecting emissions. As the number of trips increases, the amounts of emissions also increase.

Emissions increase with the distance travelled by the vehicle. The vehicular emissions also

depend on the driving mode. The driving modes may be idling, cruising, acceleration and

deceleration. These modes complete one driving cycle. Other factors affecting the emission

rates are the speed, acceleration and engine load of the vehicle. Low speeds, congested driving

conditions, sharp acceleration, deceleration, etc. result in higher emissions. On the other hand,

intermediate speeds and low density traffic conditions cause lower emissions.

Highway Network Related Factors

These include the geometric design features of the highway such as grade. The emission rate

is very high at steep gradients, as the vehicle needs to put in more effort to maintain its speed.

The highway network facilities such as signalized intersections, freeway ramps, toll booths,

weaving sections, etc. also influence the vehicular emission rates.

Vehicle Related Factors

Vehicle related factors include the engine sizes, horsepower and weight of the vehicle. Vehicles

with large engine sizes emit more pollutants. Since larger sized engines are seen in vehicles with

more horsepower and more weight, these factors also contribute to the emission rates. Another

important factor is the age of the vehicle. Older vehicles have higher emission rates.



Other Factors

1. Ambient Temperature: Evaporative emissions are higher at high temperatures.

2. Type of engine: Two stroke petrol engines emit more amounts of pollutants than the

four stroke diesel engines.

3. Urbanization: Congestion is higher in urban areas, and hence emissions are also higher.

43.3.4 Bharat Stage Emission Standards

Bharat Stage emissions standards are emissions standards instituted by the Government of the

Republic of India that regulate the output of certain major air pollutants (such as nitrogen

oxides (NOx), carbon monoxide (CO), hydrocarbons (HC), particulate matter (PM), sulfur

oxides (SOx)) by vehicles and other equipment using internal combustion engines. They are

comparable to the European emissions standards. India started adopting European emission

and fuel regulations for four-wheeled light-duty and for heavy-dc from the year 2000. For two

and three wheeled vehicles, the Indian emission regulations are applied. As per the current

requirement, all transport vehicles must carry a fitness certificate which is to be renewed each

year after the first two years of new vehicle registration. The National Fuel Policy announced

on October 6, 2003, a phased program for implementing the EU emission standards in India

by 2010. The implementation schedule of EU emission standards in India is summarized in

Table. 43:3. Some of the important emission standards for different vehicle types are given in

the following tables (Table. 43:4 - 43:7).

43.4 Fuel Consumption Models

Fuel consumption models are mathematical functions relating the various factors contributing

to the fuel consumption. The influencing factors may be no. of vehicle trips, distance travelled

by the vehicle, no. of stops, vehicles average speed, etc. The major fuel consumption models

are discussed in the following sections.

43.4.1 Average Speed Model

Average speed models are macroscopic in nature. They are concerned with the traffic network

as a whole, on a large scale. Individual vehicles are not considered. This model relates the fuel

consumption directly with the travel time (or indirectly with vehicle speeds). This model is

not valid for speeds higher than 56 km/hr. as the effects of air resistance become increasingly



Table 43:3: Indian Emission Standards (4-Wheel Vehicles), Source: Emission Norms, SIAM

IndiaStandard Reference Date Region

India 2000 Euro 1 2000 Nationwide

2001 NCR*, Mumbai, Kolkata, Chennai

Bharat Stage II Euro 2 2003.04 NCR*, 13 Cities**

2005.04 Nationwide

Bharat Stage III Euro 3 2005.04 NCR*, 13 Cities**

2010.04 Nationwide

Bharat Stage IV Euro 4 2010.04 NCR*, 13 Cities**

* National Capital Region (Delhi)

** Mumbai, Kolkata, Chennai, Bengaluru, Hyderabad, Ahmedabad,

Pune, Surat, Kanpur, Lucknow, Sholapur, Jamshedpur and Agra

Table 43:4: Emission Standards for Diesel Truck and Bus Engines, g/kWh, Source: Emission

Norms, SIAM India

Year Reference Test CO HC NOx PM

1992 - ECE 17.3- 2.7-3.7 - -

R49 32.6

1996 - ECE 11.2 2.4 14.4 -

R49

2000 Euro I ECE 4.5 1.1 8 0.36*

R49

2005** Euro II ECE 4 1.1 7 0.15

R49

2010** Euro III ESC 2.1 0.66 5 0.1

ETC 5.45 0.78 5 0.16

2010# Euro IV ESC 1.5 0.46 3.5 0.02

ETC 4 0.55 3.5 0.03

* 0.612 for engines below 85 kW

** earlier introduction in selected regions, see Table. 43:1 # only in selected

regions, see Table. 43:1



Table 43:5: Emission Standards for 3-Wheel Wheel Gasoline Vehicles, g/km, Source: Emission

Norms, SIAM India

Year CO HC HC + NOx

1991 Dec- 08- -

30 Dec

1996 6.75 - 5.4

2000 4 - 2

2005 (BS II) 2.25 - 2

2010.04 (BS III) 1.25 - 1.25

Table 43:6: Emission Standards for 2- Wheel Gasoline Vehicles, g/km, Source: Emission Norms,

SIAM IndiaYear CO HC HC + NOx

1991 Dec- 08- -

30 Dec

1996 5.5 - 3.6

2000 2 - 2

2005 (BS II) 1.5 - 1.5

2010.04 (BS III) 1 - 1



Table 43:7: Emission Standards for 4 - Wheel Gasoline Vehicles (GVW 3,500 kg), g/km,

Source: Emission Norms, SIAM India

Year Reference CO HC HC + NOx NOx

1991 - 14.3- 2.0- -

27.1 2.9

1996 - 8.68- -

12.4 3.00-4.36

1998* - 4.34- -

6.20 1.50-2.18

2000 Euro 1 2.72- -

6.90 0.97-1.70

2005** Euro 2 2.2-5.0 - 0.5-0.7

2.3 0.2 0.15

2010** Euro 3 4.17 0.25 - 0.18

5.22 0.29 0.21

1 0.1 0.08

2010# Euro 4 1.81 0.13 - 0.1

2.27 0.16 0.11

* for catalytic converter fitted vehicles

** earlier introduction in selected regions, see Table. 43:1 # only

in selected regions, see Table. 43:1



120110

100

908070

60

5040

30

20

100

0 20 40 60 80 100 120 140 160

PSVsOverall OGV

Speed kph

Lit

res/

100m

Figure 43:2: Fuel consumption as a function of speed

stronger. The fuel consumed is related to the average speed (or travel time) using the relation

below:

F = k1 + k2T (43.3)

F = k1 +k2

v(43.4)

where, F = Fuel consumed per vehicle per unit distance (liters/km), T = Travel time per unit

distance, including stops and speed changes (minutes/km), v = Avg. speed measured over a

distance including stops and speed changes (10 ≤ v ≤ 56kmph), k1 = parameter associated

with fuel consumed to overcome rolling resistance, approximately proportional to vehicle weight

(liters/veh- km), k2 = Parameter approximately proportional to fuel consumption while idling

(liters/hr).Fig. 43:2 gives the relation between fuel and consumption and speed of the vehicle.

It can be inferred from the figure that fuel consumption is high for lower speeds and is the

minimum for intermediate speeds. Fig. 43:3 shows the relation between bus fuel consumption

and number of stops. It is clear from the graph that fuel consumption increases as the number

of stops of the vehicle increases.

Numerical Example 1

A city has a total of 20000 commuters travelling at an average speed of 25kmph, and using an

arterial road of length 15 km. Due to the congestion and parking problems, 35% commuters

form car pools with a car occupancy of 3.0 and 20% arrange for subscription bus service (50

seater). Rest of the commuters choose to travel by private cars. The peak period congestion

was found to be reduced and the speed was increased to 35kmph. Assuming the no. of stops

to be 7, calculate the amount of fuel saved. Take k1 = 0.085liters/km, k2 = 1.5 liters/hr.



Stops per mile

Gal

lon

s p

er b

us

mile

With air conditioning

Without air conditioning

1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Figure 43:3: Bus fuel consumption as a function of stops

Solution: It is required to find the difference in fuel consumption between the two cases. In

the first case, all commuters use private cars (i.e. car occupancy 1) and in the second case,

some of them use public transport services, while others still use private cars.

In the first case, there were a total of 20000 commuters with car occupancy = 1, speed

25kmph and the distance to be travelled is 15 km. from the equation 43.3, we have: Total

fuel consumption, F = k1 + k2/v. Thus for the distance of 15km travelled, the total fuel

consumption is equal to [0.085 * 15] + [(1.5/25) * 15], which is 2.175 liters/vehicle. Thus for a

total of 20000 commuters, the fuel consumption will be 2.175 * 20000 which is equal to 43500

liters.

In the second case, the vehicles move with a new speed of 35kmph, and out of the total

20000 commuters, 35% (0.35 * 20000 = 7000) form carpools with occupancy 3.0. Hence, the

number of carpool vehicles is 7000/3, that is 2333 vehicles. 20% (0.20 * 20000 = 4000) of the

commuters use a 50 seater bus service. Hence the number of buses will be 4000/50, which is

equal to 80 buses. Remaining (20000 - 7000 - 4000 = 9000) are single car drivers. The total

consumption by car will include the consumption of cars of single occupancy and the cars in

the carpool. Hence, the fuel consumption by cars is [0.085 * 15] + [(1.5/35) * 15], that is 1.917

liters/vehicles. So, for all the cars, the total fuel consumption will be 1.917* (9000 + 2333),

which is 21725.36 liters. Similarly, the bus fuel consumption for a bus with 7 stops will be 0.3

*2.35 * 80 * 15 which is 846 liters.

Fuel consumption corresponding to 7 stops is obtained from Fig. 43:3. 2.35 is a conversion

factor to bring the fuel consumption in terms of liters/km instead of gallons/mile. Total fuel

consumption will be the sum of fuel consumptions of bus and car. That is 21725+846 = 22571

liters. The total amount of fuel saved will be the difference of fuel consumptions in both the

cases. Hence the amount of fuel saved is 43500 - 2257, which is equal to 20929 liters.



43.4.2 Drive Mode Elemental Model

Unlike the average speed model, the drive model elemental model is a microscopic fuel con-

sumption model. It considers the movement of a single vehicle. This model is used to obtain

the fuel consumption rates during various vehicle operating conditions or drive mode. The

different drive modes include cruising, idling, accelerating and decelerating, which together

form a driving cycle. The important assumptions used in this model are that the driving mode

elements are independent of each other and the sum of the component consumption equals the

total amount of fuel consumed. The advantages of this model are that the model is simple and

general and there is a direct relationship to existing traffic modelling techniques. The disad-

vantage of this model is that the variation in the behavior of different drivers and behavior of

the same driver under different situations is ignored.The component elements considered here

are various drive modes such as cruising, idling and accelerating. The total fuel consumed for

the drive mode elemental model is given by the relation:

G = f1L + f2D + f3S (43.5)

where, G = fuel consumed per vehicle over a measured distance (total section distance), L

= total section distance traveled, D = stopped delay per vehicle (time spent in idling), S

= number of stops, f1 = fuel consumption rate per unit distance while cruising, f2 = fuel

consumption rate per unit time while idling, f3 = excess fuel used in decelerating to stop and

accelerating back to cruise speed

Numerical example

The total fuel consumption by a vehicle travelling on a stretch of road is 0.0735 liters/veh-km.

The average stopped delay for the vehicle is 6s. The vehicle stops thrice during its journey.

Assume f1 = 0.0045, f2 = 0.0035 and f3 = 0.002. Calculate the length of road considered. If the

vehicle is cruising throughout the stretch of the road, what is the decrease in fuel consumption?

Solution: From the equation. 43.5, the fuel consumed per vehicle over a measured distance

is given by

G = f1L + f2D + f3S

Step 1: It is given that fuel consumed per vehicle is 0.0735 liters/veh-km, average delay is

6s and the number of stops are 3. The values of f1, f2 and f3 are given as 0.0045,0.0035 and

0.002 respectively. It is required to find the length of the road. The length L can be computed



from the above equation as given: 0.0735 = (0.0045 ∗L) + (0.0035 ∗ 6) + (0.002 ∗ 3). Therefore,

Length, L is equal to 10 km.

Step 2: When the vehicle is cruising throughout the length, there will not be any delays or

stops. Therefore, total fuel consumption: G = f1L = 0.0045 ∗ 10 = 0.045liters/veh − km.

Step 3: The decrease in fuel consumption is will be the difference in fuel consumptions as

obtained in steps 1 and 2, which is 0.0735-0.045 = 0.0285 liters/veh-km.

43.4.3 Instantaneous Model

Instantaneous fuel consumption models are derived from a relationship between the fuel con-

sumption rates and the instantaneous vehicle power. Second-by-second vehicle characteristics,

traffic conditions and road conditions are required in order to estimate the expected fuel con-

sumption. Due to the disaggregate characteristic of fuel consumption data, these models are

usually implemented to evaluate individual transportation projects such as single intersections,

toll plazas, sections of highway, etc. In this model the fuel consumption rate is taken as the

function of different variables such as weight of vehicle, drag coefficient, rolling resistance,

frontal area, acceleration and speed, transmission efficiency and grade.

43.5 Air Pollution Models

Air Pollution Models give a causal relationship between emissions, meteorology, atmospheric

concentrations, deposition, and other factors. They explain the consequences of past and future

scenarios and the determination of the effectiveness of abatement strategies. They are also used

to describe the concentration of various pollutants in the air. The major types of air pollution

models are emission models and dispersion models.

43.5.1 Emission Models

Emission models are commonly used to provide traffic emission information for the prediction

and management of air pollution levels near roadways. The model helps in comparing the

actual pollution levels with the emission standards set. Hence, the abatement of pollution can

also be carried out. The basic schematic diagram of an emission model is given in the Fig. 43:4.

Emission models estimate the emission quantity using the emission factor. The emission factor

may be defined as the ratio of average amount of pollutant discharged to the total amount

of the fuel discharged. It is expressed in kg of particulate / metric ton of fuel. The emission



Input Output

Emissionsmodule

Speed

Acceleration

Emissions array

(g)(m/s2)

(km/h)CO,HC,NOx, PM,

CO2, C

Figure 43:4: Basic Schematic Diagram of an Emission model

factors used in the emission models reflect different levels of congestion. The various types of

emission models are briefly discussed in the following paragraphs.

Instantaneous Emission Model

The model is similar to the instantaneous fuel consumption model. It describes the vehicle

emission behavior during any instant of time. The advantages of the model are that the

emission factors can be calculated and generated for any vehicle operating profile, and the

model considers dynamics in driving patterns. The model has some disadvantages also such as:

Detailed and precise information on vehicle operation and location is required and The process

of data collection is expensive.

Emission Factor Model

This model is useful in macro level where detailed information is not required. A single emission

factor is used to represent a particular type of vehicle and general type of driving. Emission is

estimated using the equation:

E = A ∗ EF (43.6)

where, E = emissions, in units of pollutant per unit of time, A = activity rate, in units of weight,

volume, distance or duration per unit of time, EF = emission factor, in units of pollutant per

unit of weight, volume, distance or duration The variation of exhaust emission factors with

speed for the major exhaust pollutants are given in the following figures (Fig. 43:5 to Fig. 43:10).

Cars petrol

HGVs rigid

LGVs diesel

MotorcyclesBusesHGVs articulated

LGVs petrolCars diesel

For Particulate Matter (PM10) and Volatile Organic Compounds, the emissions steadily

decrease with the speed. In case of Nitrogen Oxides, Sulphur Oxides and Carbon Dioxide, the

emission is highest for low speeds, decreases for intermediate speeds and then again increases

with the speed. For Carbon Monoxide, the highest emission levels occur for higher speeds and

minimum emission occurs for intermediate speeds.



0 20 40 60 80 100 1200

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Speed (km/hr)

PM 10

Em

issi

on

fac

tor,

g/k

m

Figure 43:5: Variation of emission factor with Speed for Particulate Matter

0 20 40 60 80 100 1200

2

4

6

8

10

12

14

16

18NOx

Em

issi

on

fac

tor,

g/k

m

Speed (km/hr)

Figure 43:6: Variation of emission factor with Speed for Nitrogen Oxides



0 20 40 60 80 100 1200

1

2

3

4

5

6

7VOC

Em

issi

on

fac

tor,

g/k

m

Speed (km/hr)

Figure 43:7: Variation of emission factor with Speed for Volatile Organic Compounds

0

5

0 20 40 60 80 100 120Speed (km/hr)

Em

issi

on

fac

tor.

g/k

m

CO

10

15

20

25

30

35

40

45

Figure 43:8: Variation of emission factor with Speed for Carbon Monoxide, Source: [5]



0 4020 60 80 100 1200

0.1

0.2

0.3

0.4

0.5

Speed (km/hr)

Em

issi

on

fac

tor,

g/k

m

SO2

Figure 43:9: Variation of emission factor with Speed for Sulphur Dioxide

0 20 40 60 80 100 1200

100

200

300

400

500

600

Em

issi

on

fac

tor,

g/k

m

Speed (km/hr)

CO2

Figure 43:10: Variation of emission factor with Speed for Carbon Dioxide



Numerical example

Using the emission factor model, the amount of CO emitted by a vehicle was estimated as 50

grams per hour. If the vehicle travelled at a velocity of 40kmph, estimate the emission factor

for CO for the vehicle.

Solution It is given that the total emission E is 50g/hr. The activity A here is the amount of

CO emitted by the vehicle, which is 40km/hr. from the eqn. 43.6, we have, the total emissions

is E = A ∗ EF . Therefore, the emission factor will be E/A = 50/40 = 1.25. That is, the

emission factor of CO is 1.25 grams/km.

Average Speed Emission Model

Average Speed Models are used in the measurement of emission rates of a pollutant for a

given vehicle for various speeds during a trip. Average Speed Emission models, along with the

Emission factor models are widely applied in national and regional inventories. The emission

factor in this model (EF ) is measured over a range of driving cycle (which includes driving,

stops, starts, acceleration and deceleration). It is given in g/veh-km. Though these models are

good in measuring congestion, they have certain disadvantages, which are explained below:

1. A single emission factor is used for a value of average speed irrespective of the vehicle

operational characteristics.

2. Average speed is a less reliable indicator of estimation of emissions for the newest gener-

ation of vehicles ( as they have after treatment devices).

3. The shape of an average speed function is not fundamental, but depends, amongst other

factors, on the cycle type used. Even though each cycle used in the development of these

functions represents a real life driving condition, the real distribution of these driving

conditions is not normally taken into account.

4. Average speed models do not allow for detailed spatial resolution in emission predictions.

Modal Emission Model

This model is similar to the drive mode elemental fuel consumption model. Emission rates are

explained as a function of the vehicle operation mode. The model provides accurate emission

estimates at micro level. For each mode, emission rate is fixed for a particular type of vehicle

and pollutant. Instantaneous traffic related data is required to estimate the fuel consumption.



The total emission for a trip on a section of road is given by the product of modal emission

rate and the time spent in the mode.

Major Vehicular Emission Models in Use

Various emission models are available to estimate the contribution of motor vehicle transporta-

tion to air pollution. The major vehicular emission models in use are discussed briefly below:

1. MOBILE: This model was proposed by the Environmental Protection Agency of the

United States. The MOBILE model estimates the emission rates from on-road motor ve-

hicles. The outputs of the MOBILE model are emissions per unit time or distance of a fleet

or vehicle type (i.e. grams/mile or grams/hour) of HC, CO, NOx, CO2, PM, NH3, SO2

and six toxic air contaminants such as lead. MOBILE estimates emissions of both ex-

haust and evaporative emissions, and particulate emissions from brake and tire wear.

MOBILE does not apply the vehicle operation such as distance travelled and number of

starts. The model is designed to be able to predict emission rates from a future fleet to

understand how emissions will change over time. Aggregate driving cycles are considered

in this model. MOBILE 6.2 is the current version of the model.

2. MOVES: MOVES stands for “Motor Vehicle Emission Simulator”. MOVES is also a

product of EPA. This model was proposed as a replacement to their MOBILE model.

The MOVES model contains fine scale information, such as second by second resolution

emissions and driving behaviour that can now be collected with on-board instrumentation.

Any driving pattern can be modelled.

3. EMFAC: The “Emission Factors” model is developed by the California Air Resources

Board. The model is similar to the MOBILE model, except that it is pertained to

California only. The emission standards of California are different from rest of the US.

4. COPERT: This model is developed by the European Environmental Agency. COPERT

stands for “Computer Program to calculate Emissions from Road Transport”. COPERT

4 is the current version of this model. It classifies vehicles into various size and age groups

as well as categories for highway, urban and rural driving situations.

5. CMEM: The “Comprehensive Modal Emissions Model”, or CMEM, was developed at the

University of California, Riverside and is fine-scale emissions predictions model. CMEM

2.0 is the latest version. The model predicts emissions based, not only on the average

speed of the vehicles, but also on the fuel consumption and power of the vehicles.



)Gaussian Plume

(Concentrations vary with and

y

z

CenterlinePlume

x

h

at a rate dependent upon the sigma values,exponentially away from the centerlineplume centerline and decreases

andand are functions of

x, y z

hs

σy

σy

For a given x, the max conc. is at the

σz

σz x

Figure 43:11: Gaussian Dispersion Plume

43.5.2 Gaussian Dispersion Model

This is a simple mathematical model used to estimate the concentration of pollutants at a

point at some distance from the source of emission. This model is used for static as well as

mobile sources of emissions. In this model, the dispersion in the three dimensions is calculated.

Dispersion in the downwind direction is a function of the mean wind speed blowing across the

plume. Air pollution is represented by an idealized plume coming from the top of a stack of

some height and diameter. The major assumption in this model is that over short periods of

time (such as a few hours), steady state conditions exists with regard to air pollutant emissions

and meteorological changes. The prominent limitation of this model is that it is not suitable

for pollutants which undergo chemical transformations in the atmosphere. Also, it depends

largely on steady state meteorological conditions and is short term in nature.

The Fig. 43:11 shows the dispersion of pollutants in a Gaussian plume. Dispersion in

the cross-wind direction and in the vertical direction will be governed by the Gaussian plume

equations of lateral dispersion. Lateral dispersion depends on a value known as the atmospheric

condition, which is a measure of the relative stability of the surrounding air. The model

assumes that dispersion in these two dimensions will take the form of a normal Gaussian

curve, with the maximum concentration in the centre of the plume. The model maybe used to

calculate the Effective Stack Height, Lateral and Vertical Dispersion Coefficients and Ground-

Level Concentrations. The Gaussian plume is used to find out the concentration of pollutants

at any point in space, and is given by:

C(x, y, z) =Q

2πuσyσz

× e−y2

2σ2y ×

(

e

„

−(z−h)2

2σ2z

«

+ e

„

−(z+h)2

2σ2z

«)

(43.7)

where, C = concentration of the emission (micrograms/cubic meter) at any point x meters



downwind of the source, y meters laterally from the centreline of the plume, and z meters

above ground level.Q = quantity or mass of the emission (in grams) per unit of time (seconds),

u = wind speed (in meters per second), h = height of the source above ground level (in meters),

σy and σz are the standard deviations of a statistically normal plume in the lateral and vertical

dimensions, respectively. They are functions of x.

Numerical example

A bus stalled at a signal emits pollutants at the rate of 20000g/s. The exhaust pipe is situated

at height of 0.75 m from the Ground level. What will be the concentration of pollutants inhaled

by a man living on the first floor of a building with storey height 3.5 m? The building is situated

at a lateral distance of 5m from the main road and longitudinal distance of 4m downwind of

the source. Assume a wind velocity of 10 m/s, σy = 375m and σz = 120m.

Solution: The concentration of the emission is given by eqn. 4.2 which is

C(x, y, z) =Q

2πuσyσz

× e−y2

2σ2y ×

(

e

„

−(z−h)2

2σ2z

«

+ e

„

−(z+h)2

2σ2z

«)

Given that, the man lives on the first floor of a building which has a storey height 3.5m. Hence,

the man will inhale the pollutants at a distance of 3.5 * 2 = 7m from the ground level. Also

given that the exhaust pipe is at a height of 0.75m form the ground and the lateral distance′y′ is 5m. The longitudinal distance ′x′ is 4m. σy and σz are functions of x and are given as

375m and 120m respectively. Substituting the values given, we have, The concentration of the

emission,

C(x, y, z) =20000

2π ∗ 10 ∗ 375 ∗ 120∗ exp

−52

2 ∗ 3752∗ (exp(

−(7 − .5)2

2 ∗ 3752) + exp(

−(7 + .5)2

2 ∗ 3752)),

which is equal to 0.0141 micrograms per cubic meters.

43.6 Mitigation Measures

Mitigation measures are measures taken to control, reduce or prevent pollution due to automo-

bile emissions. Some of the measures that may be adopted to reduce fuel consumption and air

pollution are given below.

1. Control at source using catalytic converters: A catalytic converter is a vehicle

emissions control device which converts toxic by-products of combustion in the exhaust



of an internal combustion engine to less toxic substances by way of catalysed chemical

reactions. The specific reactions vary with the type of catalyst installed. Most present-day

vehicles that run on gasoline are fitted with a ”three way” converter, so named because it

converts the three main pollutants in automobile exhaust: an oxidizing reaction converts

carbon monoxide (CO) and unburned hydrocarbons (HC) to CO2 and water vapour, and

a reduction reaction converts oxides of nitrogen (NOx) to produce CO2, nitrogen (N2),

and water (H2O).

2. Modifications in engine - (Exhaust gas recirculation) A system in the engine of a

vehicle that routes a metered amount of exhaust into the intake tract under particular

operating conditions. Exhaust neither burns nor supports combustion, so it dilutes the

air/fuel charge to reduce peak combustion chamber temperatures. This, in turn, reduces

the formation of NOx.

3. Modification or replacement of fuel: Petroleum and diesel are known as fossil-fuels,

during burning the emitted gas is very harmful to living and non-living thing and also to

climate. So, modification or replacement of fuels is a way to reduce emission, by curtailing

the amount of some particular components of fuel, we can modify it, for e.g. As sulphur

is most harmful gas emitted from the vehicles, so we can use low-sulphur fuel. Also we

can replace the fossil fuels by so many available alternatives, for e.g.bio-diesel, methanol,

ethanol battery powered vehicles, LPG, natural gas etc..

4. Setting of standards: by setting stringent emission standard, the amount of emission

from the vehicles can be reduced.

5. Legislative measures: under legislative measures the various factors responsible for

emission from the vehicle can be put under certain restriction, for e.g overloading of

heavy vehicles is a cause of more fuel consumption and emission, so a standard load or

weight can be fixed beyond that load, the vehicles should be considered overloaded and

penalties for the amount of overload can be charged, this measure will discourage the

overloading, other legal measures are deciding the type of engine installed in the different

category of vehicles.

6. Vehicle Pollution Monitoring: vehicles should be monitored regularly at a certain

interval of time for their fuel efficiency, their engines condition , rolling power, etc. this

step will help in keeping the vehicles in proper condition by the vehicle owners and hence

reducing the emission from the vehicle.



7. Check on adulteration: : Adulteration of fuels is one of major causes for excess

emission of pollutants from vehicles. To check adulteration, EPCA proposed setting up

of two independent Fuel Testing Laboratories after consultation with the Ministry of

Petroleum and Natural Gas and the Society for Indian Automobile Manufacturers.

8. Burn less fuel: we should implement the ”burn less fuel” strategy. Burning the less fuel

will lead to lesser emission and consequent the lesser air pollution and its harmful effect.

9. Vent Controls: for reducing the evaporative emission vent control is necessary. By

controlling the vent we can control the leakage of the vapours.

10. Vehicle maintenance: as we know the poor vehicle characteristic is one of the factoer

responsible of higher emission, so proper maintenance of vehicles can be helpful to reduc-

ing the emission specially the old vehicles should be checked and examined for amount of

emission.

11. Enhancing dispersion: once the harmful gases from the vehicles are emitted, they

should not be allowed to concentrate surrounding area, they should be immediately dis-

persed.

12. Using vegetation: we know that plants and trees are a good sink of harmful gases like

CO2 etc. so we should encourage the vegetation on the sides of the roads as much as

possible to reduce the amount of pollutants in ambient air

43.7 Conclusion

Automobiles are large contributer to the environmental pollution. The different fuel consump-

tion and air pollution models discussed in this report help us to estimate how much fuel we are

using and the amount of pollutants we are releasing in the atmosphere. As the population and

number of vehicles are increasing abruptly, more amounts of pollutants are being discharged. If

this trend continues, there will not be any more energy sources left for the future generations.

Also, the world will be so polluted that living organisms may not be able to thrive. Hence, we

need to understand the importance of saving the environment. Alternate sources of fuels for

e.g. renewable sources can be used which also help in reducing the pollution. Our aim must

be to preserve the nature and have the environment, along with a sustainable transportation

system.



43.8 References

1. Society of indian automobile manufacturers:emission norms, 2011.

2. S K Agarwal. Automobile Pollution. Efficient Offset Printers, 1991.

3. Kyoungho Ahn. Microscopic Fuel Consumption and Emission Modeling. 1998.

[1] C Jotin Khisty. Transportation Engineering An Introduction. Printice-Hall, New Jersey

07632, 1990.

4. Tiwary and Colls. Air Pollution. Routledge Group, 2010.

5. S Tolvett and N Davis. Widely used vehicle emission models, 2011.


Transportation Systems Engineering 44. Congestion Studies

Chapter 44

Congestion Studies

44.1 Introduction

Transportation system consists of a group of activities as well as entities interacting with each

other to achieve the goal of transporting people or goods from one place to another. Hence,

the system has to meet the perceived social and economical needs of the users. As these needs

change, the transportation system itself evolves and problems occur as it becomes inadequate

to serve the public interest. One of the negative impacts of any transportation system is

traffic congestion. Traffic congestion occurs wherever demand exceeds the capacity of the

transportation system. This lecture gives an overview of how congestion is generated, how

it can be measured or quantified; and also the various countermeasures to be taken in order

to counteract congestion. Adequate performance measures are needed in order to quantify

congestion in a transportation system. Quality of service measures indicates the degree of

traveller satisfaction with system performance and this is covered under traveller perception.

Several measures have been taken in order to counteract congestion. They are basically classified

into supply and demand measures. An overview of all these aspects of congestion is dealt with

in this lecture.

44.2 Generation of traffic congestion

The flow chart in Fig. 44:1 shows how traffic congestion is generated in a transportation system.

With the evolution of society, economy and technology, the household characteristics as well

as the transportation system gets affected. The change in transport system causes a change in

transport behaviour and locational pattern of the system. The change in household character-

istics, transport behaviour, locational pattern, and other growth effects result in the growth of

traffic. But the change or improvement in road capacity is only as the result of change in the

transportation system and hence finally a situation arises where the traffic demand is greater



Traffic Congestion

Traffic Growth Roadway Capacity

Transport Behavior Location Patterns

Household Characteristics& Norms

Evolution of Society EconomyTechnology

Growth Effects

SystemTransportation

Figure 44:1: Generation of traffic congestion

Traffic Congestion

Traffic Growth

Growth Effects

Household Characteristics

LocationPattern

Roadway Capacity

TransportationSystem

Evolution of Society,Economy and Technology

than the capacity of the roadway. This situation is called traffic congestion.

44.2.1 Effects of congestion

Congestion has a large number of ill effects on drivers, environment, health and the economy

in the following ways.

• Drivers who encounter unexpected traffic may be late for work and other appointments

causing a loss in productivity and their valuable time.

• Since congestion leads to increase in travel time i,e.,vehicles are made to travel for more

time than required which consumes large amount of fuel there by causing fuel loss and

economic loss to the drivers.

• One of the most harmful effects of traffic congestion is its impact on the environment.

Despite the growing number of vehicles ,cars stopped in traffic still produces a large volume



of harmful carbon emissions . Increase in pollutants (because of both the additional fuel

burned and more toxic gases produced while internal combustion engines are in idle or in

stop-and-go traffic)

• Drivers who become impatient may be more likely to drive aggressively and dangerously

and leads to high potential for traffic accidents

• Negative impact on people’s psychological state, which may affect productivity at work

and personal relationships

• Slow and inefficient emergency response and delivery services

• Decrease in road surface lifetime: When a vehicle moves over the surface, the areas of

contact (where the vehicles’ tyres touch the road) are deflected downwards under the

weight of the vehicle and as the vehicle moves forward, the deflection corrects itself to its

original position.

• Vehicle maintenance costs; ’Wear and tear’ on mechanical components of vehicles such as

the clutch and brakes is also considerably increased under stop-start driving conditions

and hence increasing the vehicle maintenance costs.

• One beneficial effect of traffic congestion is its ability to encourage drivers to consider

other transportation options like a subway, light rail or bus service. These options reduce

traffic on the roads ,thereby reducing congestion and environmental pollution.

The summation of all these effects yields a considerable loss for the society and the economy

of an urban area

44.2.2 Traffic congestion

A system is said to be congested when the demand exceeds the capacity of the section. Traffic

congestion can be defined in the following two ways:

1. Congestion is the travel time or delay in excess of that normally incurred under light or

free flow traffic condition.

2. Unacceptable congestion is travel time or delay in excess of agreed norm which may vary

by type of transport facility, travel mode, geographical location, and time of the day.

Fig. 44:2 shows the definition of congestion. The solid line represents the travel speed under

free-flow conditions and the dotted line represents the actual travel speed. During congestion,



Free flowTravel Speed

Amount ofCongestion

ActualTravel Speed

Spe

ed

Distance

Street 4Street 3Street 2Street 1

Figure 44:2: Definition of congestion

the vehicles will be travelling at a speed less than their free flow speed. The shaded area in

between these two lines represents the amount of congestion. Traffic congestion may be of two

types:

1. Recurrent Congestion: Recurrent congestion generally occurs at the same place, at

the same time every weekday or weekend day. This is generally the consequence of factors

that act regularly or periodically on the transportation system such as daily commuting

or weekend trips. Recurrent congestion is predictable and typically occurs during peak

hours. It displays a large degree of randomness in terms of duration and severity.

2. Non-Recurrent congestion: Non-Recurrent congestion is the effect of unexpected ,un-

planned large events( roadwoks, accidents, special events and so on) that affect trans-

portation system more or less randomly and as such,cannot be easily predicted.

44.3 Measurement of congestion

44.3.1 Need and uses of congestion measurement

Congestion has to be measured or quantified in order to suggest suitable counter measures

and their evaluation. Congestion information can be used in a variety of policy, planning

and operational situations. It may be used by public agencies in assessing facility or system

adequacy, identifying problems, calibrating models, developing and assessing improvements,

formulating programs policies and priorities. It may be used by private sector in making

locational or investment decisions. It may be used by general public and media in assessing

traveller’s satisfaction.



44.3.2 System performance measurement

Performance measure of a congested roadway can be done using the following four components:

1. Duration,

2. Extent,

3. Intensity, and

4. Reliability.

44.3.3 Duration

Duration of congestion is the amount of time the congestion affects the travel system. The

peak hour has now extended to peak period in many corridors. Measures that can quantify

congestion include:

• Amount of time during the day that the travel rate indicates congested travel on a system

element or entire system.

• Amount of time during the day that traffic density measurement techniques (detectors,

aerial surveillance, etc.) indicate congested travel.

Duration of congestion is the sum of length of each analysis sub period for which the demand

exceeds capacity. This component measures the performance of a particular road in handling

traffic efficiently i,e.,with the increase in the duration of congestion, poorer will be the perfor-

mance of the transportation system. The maximum duration on any link indicates the amount

of time before congestion is completely cleared from the corridor. Duration of congestion can

be computed for a corridor using the following equation: For corridor analysis,

H = N × T (44.1)

where, H is the duration of congestion (hours), N is the number of analysis sub periods for

which v/c > 1, and T is the duration of analysis sub-period (hours). For area wide analysis,

Hi =T vi

ci

(1 − r)

1 − r(vi

ci

)(44.2)

where, Hi is the duration of congestion for link i (hours), T is the duration of analysis period

(hours), r is the ratio of peak demand to peak demand rate, vi is the vehicle demand on link i

(veh/hr), and ci is the capacity of link i (veh/hr).



Table 44:1: Queue density default values

Subsystem Storage density Spacing

(veh/km/lane) (m)

Free-way 75 13.3

Two lane highway 130 7.5

Urban street 130 7.5

44.3.4 Extent

Extent of congestion is described by estimating the number of people or vehicles affected by

congestion and by the geographic distribution of congestion. These measures include:

1. Number or percentage of trips affected by congestion.

2. Number or percentage of person or vehicle meters affected by congestion.

3. Percentage of the system affected by congestion.

Performance measures of extent of congestion can be computed from sum of length of queuing

on each segment. Segments in which queue overflows the capacity are also identified. This is

useful for ramp metering analysis. To compute queue length, average density of vehicles in a

queue need to be known. The default values suggested by HCM 2000 are given in Table 1.

Queue length can be found out using the equation:

QLi =T (v − c)

N × ds(44.3)

where; QLi is the queue length (meter), v is the segment demand (veh/hour), c is the segment

capacity (veh/hour), N is the number of lanes, ds is the storage density (veh/meter/lane), and

T is the duration of analysis period (hour). If v < c, Qi=0 The equation for queue length is

similar for both corridor and area-wide analysis.

Numerical example

Consider a road segment of 6 lanes with a capacity of 2400 veh/hr/lane. It is observed that

the storage density is 75 veh/meter and the segment demand is found to be 2800 veh/hr/lane.

Given that the duration of analysis sub period is 2 hrs calculate the queue length that is formed

due to congestion.



Solution The queue length of a particular road segment is given by,

QL =T × (v − c)

N × ds(44.4)

It is given that Number of lanes, N=6, Duration of analysis sub period, T= 2 hrs, Segment Ca-

pacity=c=2400 veh/hr/lane, Segment Demand=v=2800 veh/hr/lane, Storage Density=ds=75

veh/meter. Now,the queue length can be calculated by using the above formula as follows:

QL = 2 ∗ (2800 − 2400) ∗ 6/(6 ∗ 75) = 10.667mts Therefore, the extent of congestion in terms

of queue length is 10.667mts

44.3.5 Intensity

Intensity of congestion marks the severity of congestion. It is used to differentiate between levels

of congestion on transport system and to define total amount of congestion. It is measured in

terms of:

• Delay in person hours or vehicle hours;

• Average speed of roadway, corridor, or network;

• Delay per capita or per vehicle travelling in the corridor, or per person or per vehicle

affected by congestion;

• Relative delay rate (relative rate of time lost for vehicles);

Intensity in terms of delay is given by,

DPH = TPH − T 0

PH (44.5)

where, DPH is the person hours of delay, TPH is the person hours of travel under actual

conditions, and T 0

PH is the person hours of travel under free flow conditions. The TPH is given

by:

TPH =OAV × v × l

S(44.6)

where, OAV is the average vehicle occupancy, v is the vehicle demand (veh), l is the length of

link (km), and S is the mean speed of link (km/hr). The TPH is given by:

T 0

PH =OAV × v × l

S0

(44.7)

where, OAV is the average vehicle occupancy, v is the vehicle demand (veh), l is the length of

link (km), and S0 is the free flow speed on the link (km/hr)



Numerical example

On a 2.8 km long link of road, it was found that the demand is 1000 Vehicles/hour mean speed

of the link is 12 km/hr, and the free flow speed is 27 km/hr. Assuming that the average vehi-

cle occupancy is 1.2 person/vehicle, calculate the congestion intensity in terms of total person

hours of delay.

Solution: Given data: Length of the link=l=2.8 km, Vehicle demand=v=1000 veh, Mean

Speed of the link=S=12 km/hr, Free flow speed on the link=So=27 km/hr, and Average Vehicle

Occupancy=AVO=1.2 person/veh. Person hours of delay is given as

DPH = TPH − T 0

PH

Person hours of travel under actual conditions,

TPH =OAV × v × l

S

=1.2 × 1000 × 2.8

12= 280 person hours

Person hours of travel under free flow conditions,

T 0

PH =OAV × v × l

S0

=1.2 × 1000 × 2.8

27= 124.4 person hours

Therefore, person hours of delay can be calculated as follows,,

DPH = = 280 − 124.4

= 155.6 person hours

= 156 person hours (approx).

Hence, the intensity of congestion is determined in terms of person hours of delay as 156 person

hours.

44.3.6 Relationship between duration, extent, and intensity of con-

gestion

The variation in extent and duration of congestion indicates different problems requiring dif-

ferent solutions. Small delay and extent indicates limited problem, small delay for large extent



��

��

Duration

Tim

e

Extent

Distance

Figure 44:3: Intensity of congestion-relation between duration and distance

Ext

ent Congestion

GeneralBroad

ProblemsSystem−Wide

Critical

CorridorsLinks orCritical

ProblemLimited

Duration

Figure 44:4: Intensity of congestion-Relation between extent and duration of delay

indicates general congestion, great delay for small extent indicates critical links and great delay

for large extent indicates critical system-wide problem. Fig. 44:3 also illustrates the relation-

ship between duration, extent and intensity The extent of congestion is seen on the x-axis, the

duration on the y-axis. The intensity is shown in the shading. Based on the extent and dura-

tion the congestion can be classified into four types as shown in Fig.44:4. Fig.44:3 indicates a

time distance graph with the shaded area indicating congestion in individual road segments for

discrete time periods. The figure shows the relationship between duration, extent, and inten-

sity. The product of extent and duration indicates the intensity, or magnitude of the congestion

problem.



44.3.7 Reliability

Reliability is a measure of a drivers ability to accurately predict and plan for a certain travel

time. The more unexpected events that occur on a roadway, the less reliable it is. Non

recurrent congestion has a bigger impact on the reliability of the roadway relative to concurrent

congestion. In other words, Travel-time reliability is defined as the level of consistency in

travel conditions over time and is measured by describing the distribution of travel times that

occur over a substantial period of time. Reliability is an important component of roadway

performance and perhaps more importantly, of motorists perceptions of roadway performance.

The importance of measuring and managing reliability in reducing congestion is explained as

follows.

• Motorists have less tolerance for unexpected delay than for expected delay

• Cost associated with unreliable travel

• Reliability is a valued service in other industries and utilities

Therefore, it is clear that Itreliability is the impact of non-recurrent congestion on transport

system and it can be expressed as average travel rate or speed standard deviation or delay

standard deviation.

44.4 Congestion countermeasures

Fully eradicating roadway congestion is neither an affordable, nor feasible goal in economically

dynamic urban areas. However, much can be done to reduce its occurrence and to lessen its

impacts on roadway users within large cities congestion is a phenomenon that can be better

and more effectively managed. There are many possible measures that can be deployed to treat

or mitigate congestion.

44.4.1 classification

Congestion countermeasures include supply measures and demand measures.,which will be dis-

cussed in detail in the next section. Other than these two measures, an additional longer-term

tool used against traffic problems is land-use planning and policy. It has the potential

• To control the number and growth of major traffic generators along congestion corridors.

• To establish sensible allocations of land for future development given present constraints

and expansion plans for the transportation network and



• To enforce balanced employment and residential development, thus reducing the long

home-to-work trips.

44.4.2 Supply measures:

They add capacity to the system or make the system operate more efficiently. They focus on

the transportation system. All measures in this category supply capacity so that demand is

better satisfied and delays and queuing are lessened. Supply measures include

1. Development of new or expanded infrastructure: This includes civil projects (new free-

ways, transit lines etc), road widening, bridge replacements, permanent freeway lane

conversions, technology conversions(a new rail technology, a modernized bus fleet and

ITS)

2. Small scale capacity and efficiency improvements: This includes signal system upgrade

and coordination, freeway ramp metering, re-location of bus stops, lane management

schemes, bottleneck elimination through channelization and operational improvements.

44.4.3 Demand measures:

Demand measures focuses on motorists and travelers and attempt to modify their trip making

behaviour. All the measures that are employed in this category aim to modify travel habits so

that travel demand is considerably reduced or switch to other modes,other times or other loca-

tions that have more capacity to accommodate it. The demand measures include Congestion

pricing, Parking pricing and Restrictions on vehicle ownership and use. Congestion pricing is

the method in which users are charged on congested roads. This is discussed in detail in the

next section. Parking pricing discourages use of private vehicles to specific areas. It includes

heavy import duties, separate licensing requirement, heavy annual fees, expensive fuel prices,

etc to restrain private vehicle acquisition and use. Heavy annual fees, strict periodic inspections

and expensive fuel prices also restrict use of private vehicles. Intelligent Transportation systems

(ITS) provide tools for implementation of both supply and demand congestion measures. Sup-

ply type ITS tools include early incident detection and resolution, optimized signal operation

based on real time demand, freeway management with ramp metering, accident avoidance with

variable message signs(VMS) warning of upcoming conditions(congestion, fog etc.,) and bus

system coordination. Demand-type ITS include the provision of real-time traffic congestion

information at various places for informed travel decisions.



Cos

t of T

rips

No. of tripsO

R

PS

Q

Figure 44:5: Demand Curve

44.4.4 Congestion pricing

Congestion pricing is a method of road user taxation, charging the users of congested roads ac-

cording to the time spent or distance travelled on those roads. The principle behind congestion

pricing is that those who cause congestion or use road in congested period should be charged,

thus giving the road user the choice to make a journey or not.

Economic principle behind congestion pricing

Journey costs include private journey cost, congestion cost, environmental cost, and road main-

tenance cost. The benefit a road user obtains from the journey is the price he prepared to pay

in order to make the journey. As the price gradually increases, a point will be reached when the

trip maker considers it not worth performing or it is worth performing by other means. This is

known as the critical price. At a cost less than this critical price, he enjoys a net benefit called

as consumer surplus(es) and is given by:

s = x − y (44.8)

where, x is the amount the consumer is prepared to pay, and y is the amount he actually

pays. The basics of congestion pricing involves demand function, private cost function as well

as marginal cost function. These are explained below.

Demand

Fig. 44:5 shows the general form of a demand curve. In the figure, area QOSP indicates the

absolute utility to trip maker and the area SRP indicates the net benefit.



Private cost

Total private cost of a trip, is given by:

c = a +b

v(44.9)

where, a is the component proportional to distance, b is the component proportional to speed,

and v is the speed of the vehicle (km/h). In the congested region, the speed of the vehicle can

be expressed as,

v = d − eq (44.10)

where, q is the flow in veh/hour, d and e are constants.

Marginal cost

Marginal cost is the additional cost of adding one extra vehicle to the traffic stream. It reduces

speed and causes congestion and results in increase in cost of overall journey. The total cost

incurred by all vehicles in one hour(CT ) is given by:

CT = cq (44.11)

Marginal cost is obtained by differentiating the total cost with respect to the flow(q) as shown

in the following equations.

M =d(cq)

dq= c + q

dc

dq(44.12)

dc

dq=

dc

dv×

dv

dq(44.13)

= (−b)/v2×−e (44.14)

= be/v2 (44.15)

d(cq)

dq= c + q

dc

dq(44.16)

= a +b

v+

d − v

e×

be

v2(44.17)

Note that c and q in the above derivation is obtained from Equations 44.9 and 44.10 respectively.

Therefore the marginal cost is given as:

M = a +b

v+

(d − v)b

v2(44.18)

Fig. 44:6 shows the variation of marginal cost per flow as well as private cost per flow. It is seen

that the marginal cost will always be greater than the private cost, the increase representing

the congestion cost.



Marginal Cost / Flow

Private Cost / Flow

Flow(q)

Priv

ate

Cos

t of T

rips

Figure 44:6: Private cost/flow and cost and marginal curve

Equilibrium condition and Optimum condition

Superimposing the demand curve on the private cost/flow and marginal cost/flow curves, the

position as shown in Fig. 44:7 is obtained. The intersection of the demand curve and the private

costs curve at point A represents the equilibrium condition, obtained when travel decisions are

based on private costs only. The intersection of the demand curve and the marginal costs curve

at point B represents the optimum condition. At this point the flow Q0 corresponds to the cost

C0 which is the marginal cost as well as the value of the trip to the trip maker. The net benefit

under the two positions A and B are shown by the areas ACZ and BY CY Z respectively. If

the conditions are shifted from point A to B, the net benefit due to change will be given by

area CCyY X minus AXB. If the area CCyY X is greater than arc AXB, the net benefit will

be positive. The shifting of conditions from point A to B can be brought about by imposing

a road pricing charge BY. Under this scheme, the private vehicles continuing to use the roads

will on an average be worse off in the first place because BY will always exceed the individual

increase in benefits XY.


Vehicles are moving on a road at the rate of 500 vehicle/hour, at a velocity of 15 km/hr. Find

the equation for marginal cost.

Solution: Private cost of the trip is given by,

c =a + b

v

=a + b

15



Marginal Cost / Flow

Z

Optimum Condition

Private Cost / FlowEquilibrium Condition

Flow(q)

Cos

t / B

enifi

t

X

BA

Y

Figure 44:7: Relation between material cost, private cost and demand curves.

It is given that Flow rate, q=500 veh/hr. Speed of the vehicle is given by,

v = d − eq

= d − 500e

Marginal Cost is given by,

M = a +b

v+

(d − v)b

v2

= a +b

15+

(d − 15)b

225

Therefore, the equation of marginal cost for the vehicles moving on the given congested road

is given by M = a + (b/15) + [(d − 15) ∗ b/225]

44.4.6 Uses of congestion pricing

1. Diverts travelers to other modes

2. Causes cancellation of non essential trips during peak hours

3. Collects sufficient fund for major upgrades of highways and other road maintenance works.

4. Cross-subsidizes public transport modes thereby fetching income to the government.



44.4.7 Requirements of a good pricing system

1. Charges should be closely related to the amount of use made of roads

2. Price should be variable at different times of day/week/year or for different classes of

vehicles

3. It should be stable and ascertainable by road users before commencement of journey

4. Method should be simple for road users to understand and police to enforce

5. Should be accepted by public as fair to all

6. Payment in advance should be possible

7. Should be reliable

8. Should be free from fraud or evasion

9. Should be capable of being applied to the whole country

44.5 Conclusion

Causes and effects of congestion along with various performance measures and with many other

counter measures are discussed in detail considering the actual or technical definition of con-

gestion. The congestion performance measures described are generalized measures. There are

several other performance measures and indices. Advanced study on congestion can include

improved measurement schemes and the combined travel demand modeling and route choice

under congested conditions. With the implementation of all the counter measures traffic conges-

tion, the most pronouncing problem of transportation may be reduced or controlled to certain

extent. The principle and process of congestion pricing was also discussed with the help of

certain graphs..

44.6 References

1. Transport research board - quantifying congestion volume 1 final report, nchrp report

398, 1997.






New Delhi, 1987.

4. Sarah B Medley and Michael J Demetsky. Development of congestion performance mea-

sures using its information. Virginia Transportation Research Council, 2019.


Delhi, 1987.


Transportation Systems Engineering 45. Queuing Analysis

Chapter 45

Queuing Analysis

45.1 Introduction

One of the major issues in the analysis of any traffic system is the analysis of delay. Delay is

a more subtle concept. It may be defined as the difference between the actual travel time on a

given segment and some ideal travel time of that segment. This raises the question as to what

is the ideal travel time. In practice, the ideal travel time chosen will depend on the situation;

in general, however, there are two particular travel times that seem best suited as benchmarks

for comparison with the actual performance of the system. These are the travel time under free

flow conditions and travel time at capacity.

Most recent research has found that for highway systems, there is comparatively little

difference between these two speeds. That being the case, the analysis of delay normally focuses

on delay that results when demand exceeds its capacity; such delay is known as queuing delay,

and may be studied by means of queuing theory. This theory involves the analysis of what is

known as a queuing system, which is composed of a server; a stream of customers, who demand

service; and a queue, or line of customers waiting to be served.

45.2 Queuing System

Figure 45:1 shows a schematic diagram illustrating the concept of a queuing system. Various

components are discussed below.

45.2.1 Input parameters

• Mean arrival rate

• Mean service rate

• The number of servers



Service rateArrival rateQueue

discipline

(Customers)Input source

Queue(leaving)costumersServed

Servicefacility

Figure 45:1: Components of a basic queuing system

• Queue discipline

These are explained in the following sections.

Mean Arrival rate (λ)

It is rate at which customers arrive at a service facility. It is expressed in flow (customers/hr or

vehicles/hour in transportation scenario) or time headway (seconds/customer or seconds/vehicle

in transportation scenario). If inter arrival time that is time headway (h) is known, the arrival

rate can be found out from the equation:

λ =3600

h(45.1)

Mean arrival rate can be specified as a deterministic distribution or probabilistic distribution

and sometimes demand or input are substituted for arrival.

Mean arrival rate (µ)

It is the rate at which customers (vehicles in transportation scenario) depart from a transporta-

tion facility. It is expressed in flow (customers/hr or vehicles/hour in transportation scenario)

or time headway (seconds/customer or seconds/vehicle in transportation scenario). If inter

service time that is time headway (h) is known, the service rate can be found out from the

equation:

µ =3600

h(45.2)

Number of servers

The number of servers that are being utilized should be specified and in the manner they work

that is they work as parallel servers or series servers has to be specified.



Queue discipline

Queue discipline is a parameter that explains how the customers arrive at a service facility.

The various types of queue disciplines are

1. First in first out (FIFO)

2. First in last out (FILO)

3. Served in random order (SIRO)

4. Priority scheduling

5. Processor (or Time) Sharing

1. First in first out (FIFO): If the customers are served in the order of their arrival,

then this is known as the first-come, first-served (FCFS) service discipline. Prepaid taxi

queue at airports where a taxi is engaged on a first-come, first-served basis is an example

of this discipline.

2. First in last out (FILO): Sometimes, the customers are serviced in the reverse order

of their entry so that the ones who join the last are served first. For example, assume

that letters to be typed, or order forms to be processed accumulate in a pile, each new

addition being put on the top of them. The typist or the clerk might process these letters

or orders by taking each new task from the top of the pile. Thus, a just arriving task

would be the next to be serviced provided that no fresh task arrives before it is picked

up. Similarly, the people who join an elevator first are the last ones to leave it.

3. Served in random order (SIRO): Under this rule customers are selected for service at

random, irrespective of their arrivals in the service system. In this every customer in the

queue is equally likely to be selected. The time of arrival of the customers is, therefore,

of no relevance in such a case.

4. Priority Service: Under this rule customers are grouped in priority classes on the

basis of some attributes such as service time or urgency or according to some identifiable

characteristic, and FIFO rule is used within each class to provide service. Treatment of

VIPs in preference to other patients in a hospital is an example of priority service.

5. Processor (or Time) Sharing: The server is switched between all the queues for a

predefined slice of time (quantum time) in a round-robin manner. Each queue head is

served for that specific time. It doesn’t matter if the service is complete for a customer or



not. If not then it’ll be served in it’s next turn. This is used to avoid the server time killed

by customer for the external activities (e.g. Preparing for payment or filling half-filled

form ).

45.3 System performance measures

The following notation assumes that the system is in a steady-state condition (At a given time

t):

1. Utilization factor ρ = λµ

2. Pn = probability of exactly n customers in queuing system (waiting + service).

3. L= expected(avg) number of customers in queuing system. [sometimes denoted as Ls]

4. Lq=expected (avg) queue length (excludes customers being served) or no of Customers.

5. W = Expected waiting time in system (includes service time) for each individual customer

or time a customer spends in the system. [sometimes denoted as Ws]

6. Wq = waiting time in queue (excludes service time) for each individual customer or

Expected time a customer spends in a queue

45.3.1 Relationships between L, W, Lq and Wq:

Assume that λn is a constant λ for all n. It has been proved that in a steady-state queuing

process, (λ may be considered as avg):

1. L = λW

2. Lq = λWq

3. W = Wq + 1λ

45.3.2 Queuing Patterns

A variety of queuing patterns can be encountered and a classification of these patterns is

proposed in this section. The classification scheme is based on how the arrival and service

rates vary over time. In the following figures the top two graphs are drawn taking time as

independent variable and volume of vehicles as dependant variable and the bottom two graphs

are drawn taking time as independant variable and cumulative volume of vehicles as dependant

variable.



Sv Sv

m

t t

m

lm

l

q

t

q

t

l

Figure 45:2: Constant arrival and service rates

Σv Σv

q q

t t

tt

µ

λ

λ

λ

µ

λ

µµ

µ’

Figure 45:3: Constant arrival rate and varying service rate

45.3.3 Constant arrival and service rates

In the left hand part of the Fig.45:2 arrival rate is less than service rate so no queuing is

encountered and in the right hand part of the figure the arrival rate is higher than service rate,

the queue has a never ending growth with a queue length equal to the product of time and the

difference between the arrival and service rates.

45.3.4 Constant arrival rate and varying service rate

In the left hand of Fig. 45:3 the arrival rate is constant over time while the service rates vary

over time. It should be noted that the service rate must be less than the arrival rate for some

periods of tim but greater than the arrival rate for other periods of time.

One of the examples of the left hand part of the figure is a signalized intersection and that



Σv Σv

q q

t t

tt

µ

λ

λ λ

µ

µµ

λ

Figure 45:4: Varying arrival rate and constant service rate

Σv Σv

q q

t t

tt

µ

λ

λ λ

µ

µµ

λ

Figure 45:5: Varying arrival and service rates

of the right hand side part of the figure is an incident or an accident on the roads which causes

a reduction in the service rate.

45.3.5 Varying arrival rate and constant service rate

In the left part of Fig. 45:4 the arrival rate vary over time but service rate is constant. Both

the left and right parts are examples of traffic variation over a day on a facility but the left

hand side one is an approximation to make formulations and calculations simpler and the right

hand side one considers all the transition periods during changes in arrival rates.



45.3.6 Varying arrival and service rates

In the Fig.45:5 the arrival rate follows a square wave type and service rate follows inverted

square wave type. The diagrams on the right side are an extension of the first one with

transitional periods during changes in the arrival and service rates. These are more complex to

analyzed using analytical methods so simulation is often employed particularly when sensitivity

parameter is to be investigated.

45.4 Queuing models

There are various kinds of queuing models. These queuing models have a set of defined char-

acteristics like some arrival and service distribution, queue discipline, etc. The queuing models

are represented by using a notation which is discussed in the following section of queue notation.

45.4.1 M/M/1 model

In this model the arrival times and service rates follow markovian distribution or exponential

distribution which are probabilistic distributions, so this is an example of stochastic process.

In this model there is only one server. The important results of this model are:

1. Average number of customers in the system = L = ρ

1−ρ

2. Average number of customers in the system = Lq = ρ2

1−ρ

3. Expected waiting time in the system W = Lλ

= (1/λ) λµ−λ

= 1µ−λ

4. Expected waiting time in the queue Wq = Lq

λ= 1

λ×

λ2

µ(µ−λ)= λ

µ(µ−λ)

Numerical example

Vehicles arrive at a toll booth at an average rate of 300 per hour. Average waiting time at

the toll booth is 10s per vehicle. If both arrivals and departures are exponentially distributed,

what is the average number of vehicles in the system, average queue length, the average delay

per vehicle, the average time a vehicle is in the system?



λ / N

λ / N

λ / N

Arrivals

=arrival

rate

Server 1

Server 1

Server N

Dispatching

discipline

Departures

λ

Figure 45:6: Multi-server model

Solution Mean arrival rate λ = 300 vehicles/hr. Mean service rate µ = 360010

vehicles/hr.

Utilization factor = traffic intensity = ρ = λµ

= 300360

= 0.833. Percent of time the toll booth

will be idle = P(0) = P(X=0) = ρ0(1 − ρ) = (0.833)0(1 − 0.833) = 0.139(60min)=8.34 min.

Average number of vehicles in the system = E[X] = ρ

1−ρ=4.98. Average number of vehicles in

the queue =E[Lq] = ρ2

1−ρ= 4.01. Average a vehicle spend in the system =E[T ] = 1

µ−λ= 0.016 hr

= 0.96 min = 57.6 sec. Average time a vehicle spends in the queue =E[Tq] = λµ(µ−λ)

= 0.013hr

= 0.83 min = 50 sec.

45.4.2 M/M/N model

The difference between the earlier model and this model is the number of servers. This is a

multi -server model with N number of servers whereas the earlier one was single server model.

The assumptions stated in M/M/1 model are also assumed here. Here µ is the average service

rate for N identical service counters in parallel. For x=0

P (0) =

[

N−1∑

x=0

(

ρx

x!+

ρN

(N − 1)!(N − ρ)

)

]

−1

(45.3)

The probability of x number of customers in the system is given by P(x). For 1 ≤ x ≤ N

P (x) =ρx

x!∗ P (0) (45.4)

For x > N

P (x) =ρx

N !Nx−N∗ P (0) (45.5)

The average number of customers in the system is

E[X] = ρ + [ρN+1

(N − 1)!(N − ρ)2]P (0) (45.6)



The average queue length

E[Lq] = [ρN+1

(N − 1)!(N − ρ)2]P (0) (45.7)

The expected time in the system

E[T ] =E[X]

λ(45.8)

The expected time in the queue

E[Tq] =E[Lq]

λ(45.9)


Consider the earlier problem as a multi-server problem with two servers in parallel.

Solution Average arrival rate = λ = 300 vehicles/hr. Average service rate = µ = 360010

vehicles/hr. Utilization factor = traffic intensity = ρ = λµ

= 300360

= 0.833.

P (0) =

[

N−1∑

x=0

(

ρx

x!+

ρN

(N − 1)!(N − ρ)

)

]

−1

= 0.92(60) = 55.2min

Average number of vehicles in the system is = L = E[X] = ρ + [ ρN+1

(N−1)!(N−ρ)2]P (0) = 1.22.

The average number of customers in the queue = Lq = E[Lq] = [ ρN+1

(N−1)!(N−ρ)2]P (0)= 0.387.

Expected time in the system =W = E[X]λ

= 0.004 hr = 14 sec. The expected time in the queue

=Wq = Lq

λ= 0.00129 hr = 4.64 sec.

45.4.4 Multiple single servers’ model

In this model there are N numbers of identical independent parallel servers which receive

customers from a same source but in different parallel queues (Compare to M/M/N model.

It has only one queue) each one receiving customers at a rate of λN

. Fig. 45:7 shows how a

typical multiple single servers’ model looks like.


Consider the problem 1 as a multiple single server’s model with two servers which work inde-

pendently with each one receiving half the arrival rate that is 150 vehicles/hr.



λ / N

λ / N

λ / N

Server 1

Server 1

Server N

Departures

λ

Arrivals

=arrival

rate

Figure 45:7: Multiple single server

M/M/1 model M/M/2 model Multiple single

server model

Idle time of toll 8.34 55.2 35.04

booths(minutes)

Number of vehicles 4.98 1.22 0.712

in the system(units)

Number of vehicles 4.01 0.387 0.296

in the queue(units)

Average waiting time 57.6 14 17.14

in system(seconds)

Average waiting time 50 4.64 8.05

in queue(seconds)

Solution Mean arrival rate = λ = 150 vehicles/hr. Mean service rate =µ = 360010

vehicles/hr.

Utilization factor = traffic intensity = ρ = λµ

= 150360

= 0.416. The percent of time the toll booth

will be idle = P(0) = P(X=0) = (0.416)0(1 − 0.416) = 0.584(60min)=35.04 min. The average

number of vehicles in the system = E[X] = ρ

1−ρ= 0.712. The average number of vehicles in

the queue =Lq = ρ2

1−ρ= 0.296. The average a vehicle spend in the system =E[T ] = W = 1

µ−λ=

0.0047 hr = 0.285 min = 17.14 sec. The average time a vehicle spends in the queue =E[Tq] =

Wq = λµ(µ−λ)

= 0.0022hr = 0.13 min = 8.05 sec



Comparison of the three models

From the Table 1 by providing 2 servers the queue length reduced from 4.01 to 0.387 and the

average waiting time of the vehicles came down from 50 sec to 4.64 sec, but at the expense

of having either one or both of the toll booths idle 92% of the time as compared to 13.9% of

the time for the single-server situation. Thus there exists a trade-off between the customers’

convenience and the cost of running the system.

45.4.6 D/D/N model

In this model the arrival and service rates are deterministic that is the arrival and service times

of each vehicle are known.

Assumptions

1. Customers are assumed to be patient.

2. System is assumed to have unlimited capacity.

3. Users arrive from an unlimited source.

4. The queue discipline is assumed to be first in first out.


Morning peak traffic upstream of a toll booth is given in the table 2. The toll plaza consists of

three booths, each of which can handle an average of one vehicle every 8 seconds. Determine

the maximum queue, the longest delay to an individual vehicle.

Time period 10 min volume

7.00-7.10 200

7.10-7.20 400

7.20-7.30 500

7.30-7.40 250

7.40-7.50 200

7.50-8.00 150



Time 10 min Cum. Service Cumulative Queue Delay

period flow (3) rate(4) service(5) =(3)-(4) (6)

7.00-7.10 200 200 200 200 0 0

7.10-7.20 400 600 225 425 175 7.78

7.20-7.30 500 1100 225 650 450 20.00

7.30-7.40 250 1350 225 875 475 21.11

7.40-7.50 200 1550 225 1100 450 20.00

7.50-8.00 150 1700 225 1325 375 16.67

Solution The arrival volume is given in the table. Service rate is given as 8 seconds per

vehicle. This implies for 10 min, 75 vehicles can be served by each server. It is given there are

3 servers. Hence 225 vehicles can be served by 3 servers in 10 min. In the first 10 min only 200

vehicles arrive which are served so the service rate for rest 50 min is 225 veh/10 min as there is

a queue for the rest period. The solution to the problem is showed in the table 3 following. The

cumulative arrivals and services are calculated in columns 3 and 5. Queue length at the end

of any 10 min interval is got by simply subtracting column 5 from column 3 and is recorded in

column 6. Maximum of the column 6 is maximum queue length for the study period which is

300 vehicles. The service rate has been found out as 225 vehicles per hour. From proportioning

we get the time required for each queue length to be served and as 475 vehicles is the max

queue length, the max delay is corresponding to this queue. Therefore max delay is 21.11 min.

45.5 Conclusions

The queuing models often assume infinite numbers of customers, infinite queue capacity, or

no bounds on inter-arrival or service times, when it is quite apparent that these bounds must

exist in reality. Often, although the bounds do exist, they can be safely ignored because the

differences between the real-world and theory is not statistically significant, as the probability

that such boundary situations might occur is remote compared to the expected normal situation.

Furthermore, several studies show the robustness of queuing models outside their assumptions.

In other cases the theoretical solution may either prove intractable or insufficiently informative

to be useful. Alternative means of analysis have thus been devised in order to provide some

insight into problems that do not fall under the scope of queuing theory, although they are

often scenario-specific because they generally consist of computer simulations or analysis of

experimental data.



45.6 References


2. Frederick S. Hillier and Gerald J. Lieberman. Operations Research. CBS publishers,

2019.



4. C S Papacostas. Transportation engineering and planning by Papacostas. C. S, 3rd

edition, Prentice-Hall of India in 2001. Prentice-Hall of India, 2001.


Transportation Systems Engineering 47. Pedestrian Studies

Chapter 47

Pedestrian Studies

47.1 Introduction

People walk for many reasons: to go to a neighbour’s house, to run errands, for school, or

to get to a business meeting. People also walk for recreation and health benefits or for the

enjoyment of being outside. Some pedestrians must walk to transit or other destinations if

they wish to travel independently. It is a public responsibility to provide a safe, secure, and

comfortable system for all people who walk. In this lecture we will discuss about the pedestrian

problems, pedestrian survey (data collection), characteristics, different level of services, and

design principles of pedestrian facilities. There are many problems related to safety security of

pedestrians. These are discussed below in brief.

47.1.1 Pedestrian Problems

Accidents Circumstances - Pedestrian accidents occurs in a variety of ways; the most common

type involves pedestrian crossing or entering the street at or between intersections.

1. Darting: It is used to indicate the sudden appearance of a pedestrian from behind a

vehicle or other sight obstruction.

2. Dashing: It refers to the running pedestrians.

Special Problems

1. Age: Children under 15 years of age from the largest group of pedestrian victims and have

the highest injury rate per population in their age group, the elderly have the highest

fatality rate because of the lower probability of their recovery from injuries.

2. Intoxication and Drug effects: Alcohol and drugs impair the behavior of pedestrians to

the extent that they may be a primary cause of accident.



3. Dusk and Darkness: Special pedestrian safety problems arise during the hours of dusk

and darkness, when it is most difficult for motorists to see pedestrians.

47.1.2 Definition of a Pedestrian

Any person afoot is the definition of Uniform Vehicle Code of pedestrian. However expand this

definition to explicitly include people with disabilities, such as who use wheelchairs or other

mobility devices. At the beginning and end of every motorist’s trip, he or she is pedestrian.

The driver and/or passenger walks to the vehicle, which is parked, drives to a destination, parks

the vehicle again, and walks to the final destination. In urban centers, pedestrian flows can

be significant, and they must be accommodated in planning and design of traffic facilities and

controls. Pedestrian safety is also a major issue, as the pedestrian is at a visible disadvantage

where potential pedestrian-vehicle conflict exist, such as at the intersections.

It is important to recognize the forces influencing the demand for provision of more and

better pedestrian facilities. Undoubtedly one important factor has been the increased awareness

of the environmental problems created by the rapid national and worldwide growth in vehicle

travel, but of equal important has been the recognition by many people of need for physical

fitness and the role that play in achieving this.

47.1.3 Factors affecting pedestrian demand

The demand for pedestrian facilities is influenced by a number of factors of which some of the

most important are

1. The nature of the local community- Walking is more likely to occur in a community

that has a high proportion of young people.

2. Car ownership -The availability of the private car reduces the amount of walking, even

for short journey.

3. Local land use activities- Walking is primarily used for short distance trips. Conse-

quently the distance between local origins and destinations (e.g. homes and school, homes

and shops) is an important factor influencing the level of demand, particularly for the

young and elderly.

4. Quality of provision- If good quality pedestrian facilities are provided, then demand

will tend to increase.



5. Safety and security- It is important that pedestrians perceive the facilities to be safe

and secure. For pedestrians this means freedom from conflict with motor vehicle, as well

as a minimal threat from personal attack and the risk of tripping on uneven surfaces.

47.1.4 Terminology

1. Pedestrian speed is the average pedestrian walking speed, generally expressed in units of

meters per second.

2. Pedestrian flow rate is the number of pedestrians passing a point per unit of time, ex-

pressed as pedestrians per 15 min or pedestrians per minute. Point refers to a line of

sight across the width of a walkway perpendicular to the pedestrian path.

3. Pedestrian flow per unit of width is the average flow of pedestrians per unit of effective

walkway width, expressed as pedestrians per minute per meter (p/min/m). Pedestrian

density is the average number of pedestrians per unit of area within a walkway or queuing

area, expressed as pedestrians per square meter (p/m2).

4. Pedestrian space is the average area provided for each pedestrian in a walkway or queuing

area, expressed in terms of square meters per pedestrian. This is the inverse of density,

and is often a more practical unit for analysing pedestrian facilities.

5. Platoon refers to a number of pedestrians walking together in a group, usually involun-

tarily, as a result of signal control and other factors.

47.1.5 Data collection

Before deciding on the appropriate extent and standard of pedestrian facilities, it is important

to assess the potential demand. The possible methods of obtaining such estimates are manual

count, video survey, and attitude survey described as follows.

Manual counts

Count the flow of pedestrian through a junction, across a road, or along a road section/footway

manually using manual clicker and tally marking sheet. Manual counts need to satisfy the

following conditions.

1. The time period(s) in the day over which the counts are undertaken must coincide with

the peak times of the activity of study.



2. The day(s) of the week and month(s) of the year when observations are made must be

representative of the demand. School holidays, early closing, and special events should

be avoided since they can result in non-typical conditions.

3. The survey locations need to be carefully selected in order to ensure that the total existing

demand is observed.

Advantages of this manual counting are that these are simple to set up and carry out, and

flexible to response observed changes in demand on site and disadvantages are that these are

labour intensive also simple information can be achieved and not detailed information.

Video survey

Cameras are setup at the selected sites and video recording taken of the pedestrians during the

selected observation periods. A suitable vantage point for the camera is important. Such survey

produces a permanent record of pedestrian movement and their interaction with vehicles. In it

the record of behavior pattern is also obtained which helps in analyzing the crossing difficulties.

Attitude survey

Detailed questionnaire requires enabling complete information about pedestrian’s origins and

destination points, also can gather information on what new facilities, or improvements to ex-

isting facilities, need to be provided to divert trips to walking, or increase the current pedestrian

activities.

47.2 Pedestrian Flow characteristic

In many ways pedestrian flow are similar to those used for vehicular flow because it can be

described in terms of familiar variables such as speed, volume, rate of flow and density. Other

measures related specifically to pedestrian flow include the ability to cross a pedestrian traffic

stream, to walk in the reverse direction of a major pedestrian flow, to manoeuvre generally

without conflicts and changes in walking speed, and the delay experienced by pedestrians at

signalized and unsignalized intersections. It is dissimilar to the vehicular flow in that pedestrian

flow may be unidirectional, bidirectional, or multidirectional. Pedestrian do not always travel

in clear ”lanes” although they may do sometimes under heavy flow.



90

60

120

Students

Commuters

Shoppers

0.3 0.6 0.9 1.2

30

Figure 47:1: Relationship between pedestrian speed and density

Pedestrian Speed-Density Relationships

The fundamental relationship between speed, density, and volume for pedestrian flow is analo-

gous to vehicular flow. As volume and density increase, pedestrian speed declines. As density

increases and pedestrian space decreases, the degree of mobility afforded to the individual

pedestrian declines, as does the average speed of the pedestrian stream, it is shown in Fig. 47:1.

Flow-Density Relationships

The relationship among density, speed, and flow for pedestrians is similar to that for vehicular

traffic streams, and is expressed in equation.

Qped = Sped ∗ Dped (47.1)

where, Qped= unit flow rate (p/min/m), Sped= pedestrian speed (m/min), and Dped= pedestrian

density (p/m2). Pedestrian density is an awkward variable in that it has fractional values in

pedestrian per square meter. This relationship often expressed in terms of Space module(M)

which is the inverse of pedestrian density. The inverse of density is more practical unit for

analysing pedestrian facilities ,so expression becomes

Qed =Sped

M(47.2)

where M in(m2/ped). The basic relationship between flow and space, recorded by several

researchers, is illustrated in the Fig. 47:2. The conditions at maximum flow represent the



Space (m /p)2

125

150

75

100

50

25

0

Flo

w (

p/m

in/m

)

1 2 3 54 6 7 8 9 100

Figure 47:2: Relationship between pedestrian space & flow

capacity of the walkway facility. From Fig. 47:2, it is apparent that all observations of maximum

unit flow fall within a narrow range of density, with the average space per pedestrian varying

between 0.4 and 0.9 m2/p. Even the outer range of these observations indicates that maximum

flow occurs at this density, although the actual flow in this study is considerably higher than

in the others. As space is reduced to less than 0.4 m2/p, the flow rate declines precipitously.

All movement effectively stops at the minimum space allocation of 0.2 to 0.3 m2/p.

Speed-Flow Relationships

The following Fig. 47:3 illustrates the relationship between pedestrian speed and flow. These

curves, similar to vehicle flow curves, show that when there are few pedestrians on a walkway

(i.e., low flow levels), there is space available to choose higher walking speeds. As flow in-

creases, speeds decline because of closer interactions among pedestrians. When a critical level

of crowding occurs, movement becomes more difficult, and both flow and speed decline. The

Fig. 47:4 confirms the relationships of walking speed and available space, and suggests some

points of demarcation for developing LOS criteria. The outer range of observations indicates

that at an average space of less than 1.5 m2/p, even the slowest pedestrians cannot achieve

their desired walking speeds. Faster pedestrians, who walk at speeds of up to 1.8 m/s, are not

able to achieve that speed unless average space is 4.0 m2/p or more.

Pedestrian Space Requirements

Pedestrian facility designers use body depth and shoulder breadth for minimum space standards,

at least implicitly. A simplified body ellipse of 0.50 m * 0.60 m, with total area of 0.30 m2 is

used as the basic space for a single pedestrian, as shown in Fig. 47:5 this represents the practical



2.5

2.0

1.5

1.0

0.5

0

Sp

eed

(m

/s)

Flow (p/min/m)

25 50 100 125 1500

Figure 47:3: Relationships between Pedestrian Speed and Flow

Space (m /p)2

2.5

2.0

1.5

1.0

0.5

0

Sp

eed

(m

/s)

1 2 3 4 6 7 8 9 100 5

Figure 47:4: Relationships between Pedestrian Speed and Space



0.5 m

body

depth

0.60 m shoulder breadth

Figure 47:5: Pedestrian body ellipse

Pacing ZoneForward Space

Sensory Zone or

Figure 47:6: Pedestrian walking space requirement

minimum for standing pedestrians. In evaluating a pedestrian facility, an area of 0.75 m2 is

used as the buffer zone for each pedestrian. A walking pedestrian requires a certain amount of

forward space. This forward space is a critical dimension, since it determines the speed of the

trip and the number of pedestrians that are able to pass a point in a given time period. The

forward space in the Fig 47:6 is categorized into a pacing zone and a sensory zone.

Pedestrian Walking Speed

Pedestrian walking speed is highly dependent on the proportion of elderly pedestrians (65 years

old or more) in the walking population. If 0 to 20 per cent of pedestrians are elderly, the average

walking speed is 1.2 m/s on walkways. If elderly people constitute more than 20 per cent of

the total pedestrians, the average walking speed decreases to 1.0 m/s. In addition, a walkway

upgrade of 10 per cent or more reduces walking speed by 0.1 m/s. On sidewalks, the free-flow

speed of pedestrians is approximately 1.5 m/s. There are several other conditions that could

reduce average pedestrian speed, such as a high percentage of slow-walking children in the

pedestrian flow.



Figure 47:7: LOS A

Pedestrian Start-Up Time and Capacity

A pedestrian start-up time of 3 s is a reasonable midrange value for evaluating crosswalks at

traffic signals. A capacity of 75p/min/m or 4,500p/h/m is a reasonable value for a pedestrian

facility if local data are not available. At capacity, a walking speed of 0.8 m/s is considered a

reasonable value.

47.3 Level of Services

The HCM uses pedestrian space as primary measure of effectiveness, with mean speed and

flow rate as secondary measures. Provision of adequate space for both moving and queuing

pedestrian flow is necessary to ensure a good LOS. Alternatively LOS considered as pedestrian

comfort, convenience, perception of safety and security. Alternative LOS measurements con-

sider specific constraints to pedestrian flow such as stairway and wait time to cross roadways.

We are going to discuss LOS of walkways, LOS of queuing and LOS at signalised intersection

below.

47.3.1 Pedestrian Walkway LOS

LOS A

Pedestrian Space > 5.6 m2/p Flow Rate ≤ 16 p/min/m. At a walkway LOS A, pedestrians move

in desired paths without altering their movements in response to other pedestrians. Walking

speeds are freely selected, and conflicts between pedestrians are unlikely. It is shown in Fig. 47:7.



Figure 47:8: LOS B

Figure 47:9: LOS C

LOS B

Pedestrian Space > 3.7−5.6 m2/p Flow Rate > 16−23 p/min/m. At LOS B, there is sufficient

area for pedestrians to select walking speeds freely, to bypass other pedestrians, and to avoid

crossing conflicts. At this level, pedestrians begin to be aware of other pedestrians, and to

respond to their presence when selecting a walking path. It is shown in Fig. 47:8.

LOS C

Pedestrian Space > 2.2−3.7 m2/p Flow Rate > 23−33 p/min/m. At LOS C, space is sufficient

for normal walking speeds, and for bypassing other pedestrians in primarily unidirectional

streams. Reverse-direction or crossing movements can cause minor conflicts, and speeds and

flow rate are somewhat lower. It is shown in Fig. 47:9.

LOS D

Pedestrian Space > 1.4−2.2 m2/p Flow Rate > 33−49 p/min/m. At LOS D, freedom to select

individual walking speed and to bypass other pedestrians is restricted. Crossing or reverse flow

movements face a high probability of conflict, requiring frequent changes in speed and position.



Figure 47:10: LOS D

Figure 47:11: LOS E

The LOS provides reasonably fluid flow, but friction and interaction between pedestrians is

likely. It is shown in Fig. 47:10.

LOS E

Pedestrian Space > 0.75 − 1.4 m2/p Flow Rate > 49 − 75 p/min/m. At LOS E, virtually

all pedestrians restrict their normal walking speed, frequently adjusting their gait. At the

lower range, forward movement is possible only by shuffling. Space is not sufficient for passing

slower pedestrians. Cross- or reverse-flow movements are possible only with extreme difficulties.

Design volumes approach the limit of walkway capacity, with stoppages and interruptions to

flow. It is shown in Fig. 47:11.

LOS F

Pedestrian Space ≤ 0.75 m2/p Flow Rate varies p/min/m. At LOS F, all walking speeds

are severely restricted, and forward progress is made only by shuffling. There is frequent,

unavoidable contact with other pedestrians. Cross- and reverse-flow movements are virtually

impossible. Flow is sporadic and unstable. Space is more characteristic of queued pedestrians

than of moving pedestrian streams. It is shown in Fig. 47:12.



Figure 47:12: LOS F

47.3.2 Pedestrian Queuing LOS

LOS A

Average Pedestrian Space > 1.2 m2/p. Standing and free circulation through the queuing area

is possible without disturbing others within the queue.

LOS B

Average Pedestrian Space > 0.9 − 1.2 m2/ p. Standing and partially restricted circulation to

avoid disturbing others in the queue is possible.

LOS C

Average Pedestrian Space > 0.6 − 0.9 m2/p. Standing and restricted circulation through the

queuing area by disturbing others in the queue is possible; this density is within the range of

personal comfort.

LOS D

Average Pedestrian Space > 0.3− 0.6 m2/p. Standing without touching is possible; circulation

is severely restricted within the queue and forward movement is only possible as a group;

long-term waiting at this density is uncomfortable.

LOS E

Average Pedestrian Space > 0.2 − 0.3 m2/p. Standing in physical contact with others is un-

avoidable; circulation in the queue is not possible; queuing can only be sustained for a short

period without serious discomfort.



Table 47:1: Los Criteria For Pedestrians At Signalized Intersections

LOS Pedestrian Delay(s/p) Likelihood of

Noncompliance

A < 10 Low

B ≥ 10 − 20

C > 20 − 30 Moderate

D > 30 − 40

E > 40 − 60 High

F > 60 Very high

LOS F

Average Pedestrian Space ≤ 0.2 m2/p. Virtually all persons within the queue are standing in

direct physical contact with others; this density is extremely uncomfortable; no movement is

possible in the queue; there is potential for panic in large crowds at this density.

LOS at signalised intersection

The signalized intersection crossing is more complicated to analyse than a midblock crossing,

because it involves intersecting sidewalk flows, pedestrians crossing the street, and others queued

waiting for the signal to change. The service measure is the average delay experienced by a

pedestrian. Research indicates that the average delay of pedestrians at signalized intersection

crossings is not constrained by capacity, even when pedestrian flow rates reach 5,000 p/h. The

average delay per pedestrian for a crosswalk is given by Equation:

dp =0.5(C − g)2

C(47.3)

Where, dp= average pedestrian delay (s), g = effective green time (for pedestrians) (s), and C=

cycle length (s).

Numerical example

Calculate time delay of pedestrian crossing at a signalized intersection operating on a two phase,

80.0-s cycle length, with 4.0-s change interval, and no pedestrian signals. Major street: Phase

green time, Gd = 44.0 s; Crosswalk length, Ld = 14.0 m; Minor street: Crosswalk length, Lc

= 8.5 m; Phase green time, Gc = 28.0 s;



Table 47:2: Minimum pedestrian clear area (excluding sidewalk obstructions)

Pedestrian Flow rate LOS A LOS B LOS C LOS D LOS E

(pedestrian/hour)

< 600 1.5 m 1.2 m 1.2 m 1.2 m 1.2 m

600-1200 3.1 m 1.2 m 1.2 m 1.2 m 1.2 m

1200-2400 6.1m 1.8 m 1.5 m 1.2 m 1.2 m

2400-3600 2.8 m 1.8 m 1.5 m 1.2 m

3600-4800 3.7 m 2.5 m 1.8 m 1.2 m

4800-6000 4.6 m 3.1 m 2.1 m 1.2 m

6000-7200 Not 5.5 m 3.7 m 2.5 m 1.5 m

7200-8400 recommended 6.1 m 4.3 m 3.1 m 1.8 m

8400-9600 7.1 m 4.9 m 3.4 m 2.1 m

9600-10800 8.1 m 5.5 m 3.7 m 2.5 m

10800-12000 8.9 m 6.1 m 4.3 m 2.5 m

Solution dp =(c−g)2/2c, dp (major) = (80.0 - 28.0)* (80.0 - 28.0)/2(80), = 16.9 s (i.e. LOS

B using above table), dp (minor) = (80.0 - 44.0)* (80.0 - 44.0)/2(80) = 8.1 s (i.e. LOS A using

above table).

47.4 Design principle of pedestrian facilities

In the design facilities we will discuss the design criteria of sidewalk, street corner, crosswalk,

traffic island, overpass and underpass and other facilities like as pedestrian signals and signage.

47.4.1 Side walk

Sidewalks are pedestrian lanes that provide people with space to travel within the public right-

of-way that is separated from roadway vehicles. They also provide places for children to walk,

run, skate, ride bikes, and play. Sidewalks are associated with significant reductions in pedes-

trian collisions with motor vehicles.

1. Width: The minimum clear width of a pedestrian access route shall be 1220 mm

exclusive of the width of curb. It varies according to pedestrian flow rate and different

LOS. It is shown in following Table.

2. Cross slope: The cross slope of the pedestrian access route shall be maximum 1:48.



Solid Standard Continental Dashed Zebra Ladder

Figure 47:13: Cross walk marking pattern

3. Surfaces: Surface should be firm, stable, slip resistance and prohibit openings & avoid

service elements i.e. manholes etc.

A buffer zone of 1.2 to 1.8 m (4 to 6 ft) is desirable and should be provided to separate

pedestrians from the street. The buffer zone will vary according to the street type. In downtown

or commercial districts, a street furniture zone is usually appropriate.

47.4.2 Cross Walk

Marked crosswalks indicate optimal or preferred locations for pedestrians to cross and help

designate right-of-way for motorists to yield to pedestrians. Crosswalks are often installed at

signalized intersections and other selected locations.

1. It should be located at all open legs of signalized intersection.

2. It should be perpendicular to roadway.

3. The parallel line should be 0.2-0.6 m in width and min. length 1.8 m (standard 3m).

4. Marking may be of different type to increase visibility like as solid, standard, continental,

dashed, zebra, ladder. It is shown in Fig. 47:13.

47.4.3 Traffic Islands

Traffic islands to reduce the length of the crossing should be considered for the safety of all

road users. It is used to permit safe crossing when insufficient gap in two directions traffic &

helps elderly, children and disabled.

1. It works best when refuse area median is greater than cross walk width or 3.6 m, have

a surface area of at least 4.6 sq.m, are free of obstructions, have adequate drainage, and

provide a flat, street level surface to provide accessibility to people with disabilities.



Figure 47:14: Ladder pattern at intersection

2. The Refuge area width should be at least 1.2 m wide and depend upon traffic speed.

It should be 1.5m wide on streets with speeds between 40-48 kmph, 1.8 m wide(48-56

kmph), and 2.4 m (56-72 kmph).

47.4.4 Pedestrian Overpass and Underpass

Pedestrian facilities at-grade and as directly as possible are always preferred. However, where

grade separation is indicated, paths that are attractive, convenient and direct can become

well-used and highly valued parts of a city’s pedestrian infrastructure.

1. These are expensive method but eliminate all or most conflicts. These may be warranted

for critical locations such as schools factory gates, sports arenas, and major downtown

intersections (specially in conjunction with transit stations).

2. Overpasses are less expensive than underpass. However , vertical rise and fall to be

negotiated by pedestrians is usually greater for an overpass, and it may be aesthetically

inferior.

3. Minimum width is required 1.22 m, although 1.83 is preferred.

4. Ramps slopes not greater than 1:12 (8.33%) are preferable to flights of stairs to accom-

modate wheelchair, strollers, and bicycles and to comply with ADA.



Ld

Wa

VdiVdo

Sidewalk B Major street

lineBuilding Wb

Sid

ewal

k A

Vco Vci Area = 0.215R2

Cro

ssw

alk

D

Wd

Figure 47:15: Intersection Corner Geometry

47.4.5 Street Corner

Available Time-Space: The total time-space available for circulation and queuing in the inter-

section corner during an analysis period is the product of the net corner area and the length

of the analysis period. For street corners, the analysis period is one signal cycle and therefore

is equal to the cycle length. The following equation is used to compute time-space available at

an intersection corner. Intersection Corner Geometry is shown in Fig. 47:15.

TS = C(Wa ∗ Wb − 0.215R2) (47.4)

where, TS =available time-space (m2-s), Wa = effective width of Sidewalk a (m), Wb = effective

width of Sidewalk b (m), R = radius of corner curb (m), and C = cycle length (s).

47.4.6 Pedestrian signals

Pedestrian signals are designed basically considering minimum time gap required for crossing

the pedestrians. This minimum time gap can be calculated by using following gap equation.

Gs =W

Sped

+ tc(N − 1) + ts (47.5)

where, Gs=min time gap in sec, W= width of crossing section, ts= startup time, tc=consecutive

time between two pedestrian, N=no of rows, and Sped =pedestrian speed.


Calculate time gap for a platoon of 27 school children 5 in a row, consecutive time 2 sec width

of crossing section is 7.5 m and walking speed of children .9 m/s start up time 3 sec. Solution



Figure 47:16: In-Pavement Raised Markers with Amber LED Strobe Lighting and LED Signs

Given w=7.5m; tc= 3 sec Sped= 0.9m/s Find out N N=27/5 i.e. 6 row (5 containing 5 & 6th

containing 2) Time gap

Gs =W

Sped

+ tc(N − 1) + ts

= [(7.5/0.9) + 2(6 − 1) + 3]

= 21.33sec

47.4.8 Traffic signage

There are many signage used for pedestrian facilities like as in-pavement flashers, overhead

signs, animated pedestrian indications and school zone symbol. These are shown below.

1. In-Pavement Flashers (Fig. 47:16)

2. Overhead Signs (Fig. 47:17)

3. Animated Pedestrian Indications (Fig. 47:18)

4. School Zone Symbol (Fig. 47:19)

47.5 Conclusion

This lectures covers pedestrian problems, their characteristics, different level of services and de-

sign principles of pedestrian facilities. Pedestrian as the most basic unit / component for street

and public space design. Pedestrian includes vulnerable road users - elderly, disabled, children,



Figure 47:17: Overhead Pedestrian Signs

Figure 47:18: Animated Pedestrian Signals

Figure 47:19: School Zone Symbol



people with luggage etc. Safety of pedestrians to be on top priority (to be never compro-

mised by design / policy). Effective integration of technical innovations, policies, institutional

mechanisms for pedestrian safety.

47.6 References

1. Pedestrians Research Problem Statements. Transportation Research Circular E-C084,

Transportation Research Board, 2005.

2. C A O Flaherty. Transport Planning and Traffic Engineering. Elsevier, 2006.




New Delhi, 1987.






Transportation Systems Engineering 48. Intelligent Transportation System - I

Chapter 48

Intelligent Transportation System - I

48.1 Overview

Intelligent Transportation Systems (ITS) is the application of computer, electronics, and com-

munication technologies and management strategies in an integrated manner to provide traveler

information to increase the safety and efficiency of the road transportation systems. This pa-

per mainly describes ITS user services, ITS architecture and ITS planning. The various user

services offered by ITS have been divided in eight groups have been briefly described. The

ITS architecture which provides a common framework for planning, defining, and integrating

intelligent transportation systems is briefly described emphasizing logical and physical architec-

ture. Integration of ITS in transportation planning process which follows a systems engineering

approach to develop a transportation plan is also briefly described in this paper.

48.2 Introduction

Intelligent Transportation Systems (ITS) is the application of computer, electronics, and com-

munication technologies and management strategies in an integrated manner to provide traveler

information to increase the safety and efficiency of the surface transportation systems. These

systems involve vehicles, drivers, passengers, road operators, and managers all interacting with

each other and the environment, and linking with the complex infrastructure systems to improve

the safety and capacity of road systems.

As reported by Commission for Global Road Safety(June 2006) , the global road deaths were

between 750,000 to 880,000 in the year 1999 and estimated about 1.25 million deaths per year

and the toll is increasing further. World health organization report (1999), showed that in the

year 1990 road accidents as a cause of death or disability were the ninth most significant cause of

death or disability and predicted that by 2020 this will move to sixth place. Without significant

changes to the road transport systems these dreadful figures are likely to increase significantly.



Traditional driver training, infrastructure and safety improvements, may contribute to certain

extent to reduce the number of accidents but not enough to combat this menace. Intelligent

Transport Systems are the best solution to the problem. Safety is one of the principal driving

forces behind the evolution, development, standardization, and implementation of ITS systems.

ITS improves transportation safety and mobility and enhances global connectivity by means

of productivity improvements achieved through the integration of advanced communications

technologies into the transportation infrastructure and in vehicles. Intelligent transportation

systems encompass a broad range of wireless and wire line communication based information

and electronics technologies to better manage traffic and maximize the utilization of the exist-

ing transportation infrastructure. It improves driving experience, safety and capacity of road

systems, reduces risks in transportation, relieves traffic congestion, improves transportation

efficiency and reduces pollution.

48.3 ITS user services

In order to deploy ITS, a framework is developed highlighting various services the ITS can

offer to the users. A list of 33 user services has been provided in the National ITS Program

Plan. The number of user services, keep changing over time when a new service is added. All

the above services are divided in eight groups. The division of these services is based on the

perspective of the organization and sharing of common technical functions. Some of the user

services offered by ITS are shown in Fig. 48:1. The eight groups are described as follows:

1. Travel and traffic management

2. Public transportation operations

3. Electronic payment

4. Commercial vehicle operations

5. Advance vehicle control and safety systems

6. Emergency management

7. Information management

8. Maintenance and construction management



Electronic Road ParkingIncident Detection

Travel Time Prediction

Intelligent Parking

Transit Priority

Signal Control Systems

Road MaintananceScheduling and Monitoring

Bus SchedulingAssistance

Figure 48:1: ITS user services

48.3.1 Travel and traffic management

The main objective of this group of services is to use real time information on the status of the

transportation system to improve its efficiency and productivity and to mitigate the adverse

environmental impacts of the system. This group of user service is further divided in 10 user

services. Most of these services share information with one another in a highly integrated

manner for the overall benefit of the road transportation system. These services are described

as below:

Pre trip information

This user service provides information to the travelers about the transportation system before

they begin their trips so that they can make more informed decisions regarding their time of

departure, the mode to use and route to take to their destinations. The travelers can access

this information through computer or telephone systems at home or work and at major public

places. Pre travel information can be accessed through mobile phones as shown in Fig. 48:2.

Different routes and respective travel time durations indicated on VMS are shown in Fig. 48:3.

The information include real time flow condition, real incidents and suggested alternate routes,

scheduled road construction and maintenance tasks, transit routes, schedules, fares, transfers,

and parking facilities.

En-route driver information

This user service provides travel related information to the travelers en route after they start

their trips through variable message signs (VMS), car radio, or portable communication devices.

Fig. 48:4 shows the various congested and non congested routes shown on display screen. VMS



START :ABCD: 396: 12:21

END : XYZ

: 13:05

Figure 48:2: Pre trip information

3 mins

6 mins

7 mins

9 mins

City Transit

DUEROUTE

69

98

408

535

Figure 48:3: VMS showing routes



SatelliteMap HybridTraffic

Figure 48:4: Showing congested routes

11 MIN19 MIN

LYNNWOODS. EVERETT

Figure 48:5: VMS showing routes and travel times

indicating different routes and travel time is shown in Fig. 48:5. This helps the travelers to

better utilize the existing facility by changing routes etc to avoid congestion. This also provides

warning messages for roadway signs such as stop signs, sharp curves, reduced speed advisories,

wet road condition flashed with in vehicle displays to the travelers to improve the safety of

operating a vehicle. The information can be presented as voice output also.

Route guidance

This service provides information to the travellers with a suggested route to reach a specified

destination, along with simple instructions on upcoming turns and other manoeuvres. This

also provides travellers of all modes the real-time information about the transportation system,

including traffic conditions, road closures, and the status and schedule of transit systems. The

benefits of this service are reduced delay and drivers stress levels particularly in an unfamiliar

area.

Ride matching and reservation

This user service provide real-time ride matching information to travellers in their homes, offices

or other locations, and assists transportation providers with vehicle assignments and scheduling.



��

��

1

3

2 4

Access roadLoop detectors

Detect,Verify and Respond

Accident Occurs

Figure 48:6: Incident management

Travellers give information to the service center and get number of ride sharing options from

which they can choose the best.

Traveler Services Information

This service provides a business directory of information on travel-related services and facilities

like the location, operating hours, and availability of food, lodging, parking, auto repair, hos-

pitals, gas stations and police facilities. This also makes reservations for many of these traveler

services. The traveler services information are accessible in the home, office or other public

locations to help plan trips. These services are available en-route also.

Traffic Control

This service collects the real time data from the transportation system, processes it into usable

information, and uses it to determine the optimum assignment of right-of-way to vehicles and

pedestrians. This helps in improving the flow of traffic by giving preference to transit and other

high occupancy vehicles or by adjusting the signal timing to current traffic conditions. The

information collected by the Traffic Control service is also disseminated for use by many other

user services.

Incident Management

This service aims to improve the incident management and response capabilities of transporta-

tion and public safety officials, the towing and recovery industry, and others involved in incident

response. Advanced sensors (close circuit TV cameras), data processors and communication

technologies are used to identify incidents quickly and accurately and to implement response



which minimizes traffic congestion and the effects of these incidents on the environment and

the movement of people and goods. Fig. 48:6 shows the occurrence of incident and its detection

by the center and decision implemented responding to the incident on a highway pertaining to

incident management.

Travel Demand Management

This user service develop and implement strategies to reduce the number of single occupancy

vehicles while encouraging the use of high occupancy vehicles and the use of more efficient

travel mode. The strategies adopted are:

1. Congestion pricing

2. Parking management and control

3. Mode change support

4. Telecommuting and alternate work schedule.

Emissions Testing and Mitigation

The main objective of this service is to monitor and implement strategies to divert traffic away

from sensitive air quality areas, or control access to such areas using advanced sensors. This

also used to identify vehicles emitting pollutants exceeding the standard values and to inform

drivers to enable them to take corrective action. This helps in facilitating implementation and

evaluation of various pollution control strategies by authorities.

Highway Rail Intersection

This service is to provide improved control of highway and train traffic to avoid or decrease

the severity of collisions between trains and vehicles at highway-rail intersections. This also

monitors the condition of various HRI equipments.

48.3.2 Public transportation operations

This group of service is concerned with improving the public transportation systems and en-

couraging their use. Fig. 48:7 shows different public transportation facilities. This group is

divided in four services which are described as below:



Bus Systems

Enviornment of Urban

Improving the

Operational

Facilitating the

Development of

Urban Bus Systems

Systems

Quality of Rapid Transit

Enhancing the Service

Mass Rapid Transit Systems

Operational Environment ofProviding a Healthy

Systemsof Metropolitan Rapid TransitConstruction and Development

Implementing the

Figure 48:7: Different public transportation systems

Public Transportation Management

This user service collects data through advanced communications and information systems to

improve the operations of vehicles and facilities and to automate the planning and management

functions of public transit systems. This offers three tasks:

1. To provide real-time computer analysis of vehicles and facilities to improve transit op-

erations and maintenance by monitoring the location of transit vehicles, by identifying

deviations from the schedule, and offering potential solutions to dispatchers and operators.

2. To maintain transportation schedules and to assure transfer connections from vehicle to

vehicle and between modes to facilitate quick response to service delays .

3. To enhance security of transit personnel by providing access management of transit ve-

hicles.

En-Route Transit Information

This service is intended to provide information on expected arrival times of t vehicles, transfers,

and connections to travellers after they begin their trips using public transportation. This also

provide real-time, accurate transit service information on-board the vehicle, at transit stations

and bus stops to assist travellers in making decisions and modify their trips underway.



Personalized Public Transit

The aim of this service is to offer public transport facility to travellers by assigning or scheduling

vehicles by

1. diverting flexibly routed transit vehicles.

2. assigning privately operated vehicles on demand which include small buses, taxicabs, or

other small, shared-ride vehicles.

Under this service, travellers provide information of their trip origin and destination to service

station. The center then assigns the closest vehicle to service the request and to inform the

travellers regarding arrival of such vehicles well in advance to reduce their anxiety.

Public Travel Security

This user service creates a secure environment for public transportation operators and support

staff and monitors the environment in transit facilities, transit stations, parking lots, bus stops

and on-board transit vehicles and generates alarms (either automatically or manually) when

necessary. It also provides security to the systems that monitor key infrastructure of transit

(rail track, bridges, tunnels, bus guide ways, etc.).

48.3.3 Electronic payment

This user service allows travellers to pay for transportation services with a common electronic

payment medium for different transportation modes and functions. Toll collection, transit fare

payment, and parking payment are linked through a multimodal multi-use electronic system.

With an integrated payment system a traveller driving on a toll road, using parking lot would

be able to use the same electronic device to pay toll, parking price and the transit fare. Fig. 48:8

shows the electronic payment facility by radio car tag.

48.3.4 Commercial Vehicle operations

The aim is to improve the efficiency and safety of commercial vehicle operations. This involves

following services:

1. CV electronic clearance

2. Automated road side safety inspection

3. Onboard safety monitoring administrative process



5MPH

trafficmonitoring camera

tag reader

E−Z Pass tag

traffic gate

trafficInformation display

REDUCESPEEDPASS

The E−Z Pass Process

��

��

Figure 48:8: Electronic payment facility

4. Hazardous material incident response

5. Freight Mobility

Commercial Vehicle Electronic Clearance

This service allows enforcement personnel to electronically check safety status, vehicle’s creden-

tials, and size and weight data for the commercial vehicles before they reach an inspection site.

The authorities send the illegal or potentially unsafe vehicles only for inspection and bypass

safe and legal carriers to travel without stopping for compliance checks at weigh stations and

other inspection sites.

Automated Roadside Safety Inspection

At inspection station the safety requirements are checked more quickly and more accurately

during a safety inspection using automated inspection capabilities. Advanced equipments are

used to check brake, steering and suspension performance and also the driver’s performance

pertaining to driver alertness and fitness for duty.

On-board Safety Monitoring

This service monitors the driver, vehicle, and cargo and notify the driver, carrier, and, also

to the enforcement personnel, if an unsafe situation arises during operation of the vehicle.

This is user service also assures freight container, trailer, and commercial vehicle integrity by

monitoring on-board sensors for a breach or tamper event.



Commercial Vehicle Administrative Processes

This service allows carriers to purchase credentials such as fuel use taxes, trip permits, over-

weight permit, or hazardous material permits automatically. The mileage and fuel reporting

and auditing components are provided to the carriers automatically which reduce significant

amount of time and paperwork.

Hazardous Materials Incident Response

This user service provides immediate information regarding the types and quantities of haz-

ardous materials present at incident location to the emergency personnel in order to facilitate

a quick and appropriate response. The emergency personnel are informed regarding shipment

of any sensitive hazardous materials so that timely action could be taken in case of accidents.

Freight Mobility

This service provides information to the drivers, dispatchers, and intermodal transportation

providers, enabling carriers to take advantage of real-time traffic information, as well as vehicle

and load location information, to increase productivity.

48.3.5 Advanced vehicle control and safety systems

This user service aims to improve the safety of the transportation system by supplementing

drivers’ abilities to maintain vigilance and control of the vehicle by enhancing the crash avoid-

ance capabilities of vehicles. Following user services are included in this group:

Longitudinal Collision Avoidance

This user service provides assistance to vehicle operators in avoiding longitudinal collisions

to the front and/or rear of the vehicle. This is achieved by implementing rear-end collision

warning and control, Adaptive Cruise Control (ACC), head-on collision warning and control,

and backing collision warning to the drivers.

Lateral Collision Avoidance

This helps drivers in avoiding accidents that result when a vehicle leaves its own lane of travel,

by warning drivers and by assuming temporary control of the vehicle. This service provides

to the drivers the lane change/blind spot situation display, collision warning control and lane

departure warning and control.



Intersection Collision Avoidance

This user service is specifically aimed at providing vehicle operators with assistance in avoiding

collisions at intersections. The system tracks the position of vehicles within the intersection

area through the use of vehicle-to-vehicle communications or vehicle to infrastructure commu-

nications.

Vision Enhancement for Crash Avoidance

This service helps in reducing the number of vehicle crashes that occur during periods of

poor visibility by in vehicle sensors capable of capturing an image of driving environment and

providing a graphical display of the image to the drivers.

Safety Readiness

This helps to provide drivers with warnings regarding their own driving performance, the con-

dition of the vehicle, and the condition of the roadway as sensed from the vehicle.

Pre-Crash Restraint Deployment

This service helps in reducing the number and severity of injuries caused by vehicle collisions

by anticipating an imminent collision and by activating passenger safety systems prior to the

actual impact.

Automated Vehicle Operations (AVO)

This service provides a fully automated vehicle-highway system in which instrumented vehicles

operate on instrumented roadways without operator intervention.

48.3.6 Emergency management

This service has two functions:

1. Emergency notification and personal security - This is to provide travellers the ability to

notify appropriate emergency response personnel regarding the need for assistance due

to emergency or non-emergency situations either by manually or automatically from the

vehicle on the occurrence of an accident.

2. Emergency vehicle management - This user service is to reduce the time from the receipt

of an emergency notification to the arrival of the emergency vehicles at incident location

thereby reducing the severity of accident injuries.



48.3.7 Information management

This service is aimed to provide the functionality needed to store and archive the huge amounts

of data being collected on a continuous basis by different ITS technologies.

48.3.8 Maintenance and construction management

This user service is aimed to provide the functionality needed for managing the fleets of mainte-

nance vehicles, managing the roadway with regards to construction and maintenance and safe

roadway operations.

48.4 ITS Architecture

The ITS Architecture provides a common framework for planning, defining, and integrating

intelligent transportation systems. It specifies how the different ITS components would inter-

act with each other to help solving transportation problems. It provides the transportation

professionals to address their needs with wide variety of options. It identifies and describes

various functions and assigns responsibilities to various stakeholders of ITS. The ITS architec-

ture should be common and of specified standards throughout the state or region so that it can

address solution to several problems while interacting with various agencies.

1. Interoperability - The ITS architecture should be such that the information collected,

function implemented or any equipment installed be interoperable by various agencies in

different state and regions.

2. Capable of sharing and exchanging information - The information by traffic operations

may be useful to the emergency services.

3. Resource sharing - regional communication towers constructed by various private agencies

are required to be shared by ITS operations.

48.4.1 National ITS architecture

This is developed by US Department of Transportation to provide guidance and co-ordinate all

regions in deploying ITS. It documents all information available and keep updating continuously.

The national architecture contains the following components:



Table 48:1: User service requirements for Traffic Control user service

Traffic Control provides the capability to efficiently manage the movement of traffic

on streets and highways. Four functions are provided which are

(1) Traffic Flow Optimization,

(2) Traffic Surveillance,

(3) Control, and

(4) Provide Information.

This will also include control of network signal systems with integration of freeway

control. The specified User service requirements

(1) TC shall include a Traffic Flow Optimization function to provide the capability

to optimize traffic flow.

(1.1) Traffic Flow Optimization shall employ control strategies that seek to maximize

traffic-movement efficiency.

(1.2) Traffic Flow Optimization shall include a wide area optimization capability, to

include several jurisdictions.

(1.2.1) Wide area optimization shall integrate the control of network signal systems

with the control of freeways.

(1.2.2) Wide area optimization shall include features that provide preferential

treatment for transit vehicles.

(2) TC shall include a Traffic Surveillance function.

48.4.2 User services and their requirements

A number of functions are needed to accomplish the user services. These functional statements

are called user services requirements. For all the user services the requirements have been

specified. If any new function is added, new requirements are to be defined. Table. 48:1 shows

an illustration of user service requirements for traffic control user service.

48.4.3 Logical architecture

To accomplish user service requirements many functions or processes are needed. The logical

architecture defines a set of functions (or processes) and information flows (or data flows) that

respond to the user service requirements. It describes the lower end interaction of different

components of ITS. Processes and data flows are grouped to form a particular functions. These

are represented graphically by data flow diagrams (DFDs). Fig. 48:9 shows the interaction

of Manage Traffic process with other processes. Each process is broken down into more sub



andMonitoring

VehicleProvide

Control

ProvideElectronicPaymentServices

ProvideDriver andTravellerServices

EmergencyServices

Manage ManageCommercial

Vehicles ManageArchived

Data

ManageTransit

TrafficManage

andConstruction

ManageMaintenance

Figure 48:9: High level ITS logical architecture

Figure 48:10: Decomposition of process into P-specs

processes. The sub process is further broken into sub process which are called process specifica-

tions (P-specs) lowest level. These p specs are required to be performed to fulfill user services

requirements. Fig. 48:10 shows process decomposition into process specifications.

48.4.4 Physical architecture

The functions from logical architecture that serve the same need are grouped into sub systems.

With these subsystems a physical entity is developed to deliver functions. The data flow of

logical architecture are also combined to define interface between subsystems. Fig. 48:11 shows

the functions A and B of logical architecture assigned to subsystem A in physical architecture.

Both the architecture forms the core of ITS. The physical architecture of ITS defines the physical

subsystems and architectural flows based on the logical architecture. The 22 subsystems are

broadly classified in four groups as centers, field, vehicle, and travelers. Fig. 48:12 shows

the subsystems and communications that comprise the national physical architecture. The

subsystem represent aggregation of functions that serve the same transportation need and

closely correspond to physical elements of transportation management system.



Logical ArchitectureWhat has to be done

(functions orprocesses)

Physical Architecture(Group functions

together)

A C

D

Architectureflow

Subsystem HSubsystem A

data flows

Function

B

Function Function

Function

Figure 48:11: Assigning function from logical to the physical architecture

EmergencyManagementManagement

Traffic

CentersTravelers

Vehicles Field

Emergency

Vehicle

Vehicle

VehicleTransit

CommercialVehicle

Maintenance &

VehicleConstruction

Roadway

SecurityMonitoring

CollectionToll

ManagementParking

CheckVehicle

Commercial

TravelerRemote

Support

InformationAccess

Personal

AdministrationToll Commercial

VehicleAdministration Management

ConstructionMaintenance &

Information

ProviderService Management

Emissions TransitManagement Management

FreightFleet and

ManagementData

Archived

Fixed Point − Fixed CommunicationsWide Area Wireless Communications

Veh

icle

− V

ehic

le C

omm

unic

atio

ns

Fie

ld −

Veh

icle

Com

mun

icat

ions

Figure 48:12: National ITS physical architecture showing subsystems and communications

Vehicle group consists of five different types of vehicles. The traveler group represents

different ways a traveler can access information on the status of the transportation system.

There are four different types of communication systems.

1. Fixed point to fixed point

2. Wide area wireless

3. Vehicle - vehicle communication

4. Field - vehicle communication

Through the communication systems all the subsystems are interconnected and transfer the

required data. Fig. 48:13 shows the communication between traffic management subsystem

and the roadway subsystem. Traffic management subsystem is connected to communications



CommunicationsCentral Computer System

Traffic management center

Roadway Subsystem

Surveillance

Controller Cabinet

Signal Control

ManagementFleet and Freight

AdministrationCommercialVehicle Construction

Maintenance and

Archived DataManagement

TrafficManagement Management Management

ManagementManagement

Emergency Payment

Emissions TransitService

Information

Provider

Remote TravelerSupport

Information AccessPersonal

CentersTravelers

Wide Area Wireless(Mobile)Communications Fixed Point − fixed Point Communications

Vehicle Roadway

EmergencyVehicle SecurityMonitoring

RoadwayPavement

ParkingManagement

Commercial VehicleCheck

CommercialVehicle

TransitVehicle

Maintanance andConstructionVehicle F

ield

− V

ehic

le C

omm

unic

atio

ns

Veh

icle

− V

ehic

le C

omm

unic

atio

ns

Vehicles Field

Figure 48:13: Communications between subsystems of physical architecture

Table 48:2: TMC Signal control equipment package

TMC Equipment package provides the capability for traffic managers to monitor

and manage the traffic flow at signalized intersections. It analyzes and reduces the

collected data from traffic surveillance equipment and implements control plans

for signalized intersections.

TMC signal control equipment package contains five P- specs:

(i) Traffic operation personnel traffic interface

(ii) Process traffic data

(iii) Select strategy

(iv) Determine indicator state for road management

(v) Output control data for roads

which gets real time information of the transportation system through roadway subsystem

which comprise of signal control, detectors, camera, VMS etc.

48.4.5 Equipment packages

In order to provide more deployment oriented perspective to the ITS architecture an equipment

package is developed. In this similar functions of a particular subsystem are grouped together

and implemented by a package of hardware and software facilities. As an example Table. 48:2

shows the TMC signal control equipment package and its functional requirements.



Traffic OperationsPersonnel

ManagementTraffic

Collect TrafficSurveillance

TrafficMaintenance

TMC SignalControl

traffic operatorinputs

datatraffic operator

Roadway

Pedestrians

Traffic

Driver

OtherRoadway

information

coordinationequipment

roadway

call

characteristics

driver

crossing

crossingpermission

traffic

datasignal control

signal controlstatus

traffic imagestraffic flow +

control +traffic sensor

video surveillancecontrol

request forright−of−way

RoadwayBasic

Surveillance

Roadway

CoordinationEquipment

Roadway

ControlsSignal

ATMS03 − Surface Street Control

Figure 48:14: Surface street control market package

48.4.6 Market package

The market package defines a set of equipment packages that are required to work together

to provide a given transportation service. Most market packages are made up of equipment

packages from two or more subsystems. These are designed to address specific transportation

problems and needs. Fig. 48:14 shows surface street control market package. This package

provide the central control and monitoring equipment, communication links and the signal

control equipment that support local street control or arterial traffic management. The various

signal control systems dynamically adjusted control plans and strategies based on current traffic

conditions and priority requests.

48.5 ITS Planning

ITS planning is to integrate ITS into the transportation planning process.

48.5.1 Transportation planning and ITS

Transportation planning helps in shaping a well balanced transportation system that can meet

future demands. Transportation planning is an iterative process which include problem identi-

fication, solution generation, analysis, evaluation and implementation. This can be integrated

with ITS using computers, communication systems and software. As planning is normally made

for long period, installing ITS facilities needs to be updated and one should ensure that the

equipments and technologies are compatible for future improvement and expansion. The steps



in traditional transportation planning are as follows:

1. Establish goals and objectives

2. Inventory existing conditions

3. Analyze existing conditions

4. Long range/ short range element

5. Forecast land use, population/employment

6. Forecast future travel/trips

7. Develop and evaluate alternative transportation plans

8. Prepare recommended plans and programs

ITS transportation planning process differs from the traditional transportation planning pro-

cess. ITS has the unique capability to integrate different modes of transportation such as

public auto, transit, and infrastructural elements through communications and control. The

multimodal integration potential provides a great opportunity for planning across modes. The

comparison between ITS approach and conventional approach for solving various transportation

problems are shown for few problems are shown in table. 48:3.

48.5.2 Planning and ITS architecture

ITS architecture is a useful tool for integrating ITS technique into planning process. The ITS

architecture defines the comprehensive set of data that should be shared by various agencies of

transportation network. With the knowledge of what data must be exchanged, these agencies

develop a common interest in cooperating planning efforts between all transportation projects.

48.5.3 Planning for ITS

ITS planning process follows a systems engineering approach to develop a deployment plan in

descending order vision, goal, objectives, and functions. Table. 48:4 shows the ITS approach

for achieving goal “enhance public safety”.



Table 48:3: Relationship between problems, conventional approach and ITS approach

Problem Possible solutions Conventional approach ITS approach

Lack of Provide user Expand fixed route Multimodal pre trip and

mobility friendly access to transit and Para en-route traveler

and quality transit service information

accessibility transportation

services Radio and TV Personalize public

traffic reports transportation

Enhance fare card

Traffic Increase roadway New roads Advanced traffic

congestion capacity control, advanced

Car pooling vehicle systems

Reduce demand

Flex-time program Real time ride matching

Personalized public

transport

Telecommuting

transportation pricing

Traffic Improve safety Improve roadway Fully automated vehicle

accidents geometry, sight control system

distance, traffic

signal Automated warning

system

Grade separated

intersection Driver condition on

monitoring

Driver training

Automated detection of

Street lighting adverse weather

Emergency notification



Table 48:4: ITS approach for the goal enhance public safety

Vision Improvement of travelers safety by providing advance warning by

implementing crash counter measures and by controlling to the security

of the transportation facilities

Goal Enhance public safety

Objectives Promote safety of transportation Reduce crashes on freeways

facility and streets

Functions # Monitoring of rest areas # Implement crash counter

measures at high accident

# Provide public safety at park locations

and ride lots

# Implement work zone safety

# Coordinate emergency response measures

using appropriate agency

# Install traffic signs signals and

road marking

# Remove obstruction from the

incident scene



48.5.4 Integrating ITS into Transportation planning

Integrating ITS into transportation planning process require overcoming some obstacles and

some changes in the business practices of many institutions. The major challenges in main-

streaming ITS into everyday operations of transportation agencies are:

• Institutional coordination and cooperation for sharing information and data

• Technical compatibility among ITS projects

• Human resource needs and training

• Financial constraints and opportunities to involve the private sector

Most public agencies are aware of the challenges in mainstreaming ITS into transportation

planning process where ITS projects are part of traditional transportation programs on local

or state level to achieve the best output from transportation investments.

48.6 Summary

This lecture introduces three important intelligent transportation system concepts such as:

user services architecture planning. ITS user services includes concept on Travel and traffic

management, Public transportation operations, Electronic payment, Commercial Vehicle op-

erations, Advanced vehicle control and safety systems, Emergency management, Information

management, and Maintenance and construction management A general ITS architecture and

its national representation is then covered. The ITS planning discusses how to integrate ITS

into transportation planning

48.7 References

1. M A Chowdhary and A Sadek. Fundamentals of Intelligent Transportation systems

planning. Artech House Inc., US, 2003.

2. Bob Williams. Intelligent transportation systems standards. Artech House, London,

2008.


Transportation Systems Engineering 49. Intelligent Transportation System - II

Chapter 49

Intelligent Transportation System - II

49.1 Standards

Standards provide some norms and regulations to be followed. Just as the standards are

provided by IRC for the signs to be used similar standards are there for ITS. They bring

oneness in the system. They help in generalizing any system. Also they bring homogeneity in

the design. The standards help the non-transportation designers to adhere to some guidelines

so that the system is sound technically.

49.1.1 Need of ITS standards

The need of ITS standards can be explained by five aspects:

• Product behavior.

• Interface.

• Performance.

• Co-ordination and interaction.

• Benefits to vendors, manufacturers and government.

Product behavior

The standards prescribe ways the product should behave. The behavior everywhere should be

uniform. It should not happen that the product behaves differently in some different scenarios.

It ensures uniform product responses. It also helps in easy understanding of a device. It

provides consistency in the output. Confusion to the users is also avoided. Just as a STOP or

GO sign is used it everywhere and every time means the same. Standards do the same thing

in ITS.



Interface

Many devices are to be connected with each other. Connection of components to system must

be universal. More ‘plug and play’ type devices should be used. By having a standard the

device will get connected using a standard interface. For ex, many traffic signals should be

connectable to same controller. If universal interface is not there, then many devices will not

work everywhere, which is not desirable.

Performance

Check on performance of a device is essential. Standards should be set to have at-least minimum

performances. The standards will help the manufacturers to develop quality and less expensive

products. It will set the minimum quality threshold accepted for the product. Detection of

under-performance of a device is essential to keep an overall check on the system.

Co-ordination and interaction

Data transfer is an important aspect in the ITS and the data flows from one agency to other.

Thus the co-ordination and interaction between various agencies must take place effectively.

The data must be in stored or transferred in standard format. Data sharing must be possible.

Standard data dictionary and message sets are required for this purpose. The data for each

organization should mean the same. Thus the data dictionary is essential.

Benefits to vendors, manufacturers and government

It helps the government in enforcing some rules which are otherwise difficult to implement. It

also helps the vendors to choose the manufacturer best from the lot which will also be best for

the users. It provides manufacturer with a guide to produce efficient device. If some standards

are made by the government then the manufacturer has to follow the rules. So the uniformity is

achieved in the product and its output. As all the devices are made by following same standards

it provides same platform for vendors to judge a product. Thus a best product is selected by

the vendor which will also be good for the user.

49.1.2 Case study

In US there are many types of toll collection systems implemented to collect the toll. Each

system requires its own tags and receiver devices. This gives rise to many types of tags and

receiver devices. Such variance in devices is undesirable and difficult to handle. Thus some

standard platform was thought to be required to generalise the system. Standardization of



ETC was thus started with this issue in mind. Standardization will provide uniform platform.

Still the process of standardization is ongoing and a single standard is in the making. It is

expected to reduce the problems of toll collection in US. Thus from this case study it can be

seen that the standards are helping the engineers to simplify the system and help in reducing

complexities.

49.2 Classification of standards

Just like ITS services are classified into user services the standard are to be classified in some

five groups depending upon the interface it is made for. These classifications are termed as

application areas. The various application area in ITS standards are:

• Centre - roadside interface

• Centre - center interface

• Centre - vehicle interface

• Roadside - vehicle interface

• Roadside - roadside interface

Each of the class has some sub classes or sub-groups. For each sub-group some set of standards

are to be used. Each sub-group may have more than one standard to follow. This takes care

for the standard to be effective in all aspects.

49.2.1 Centre - roadside interface

Standards are made for the interface that exists between a center device and a roadside de-

vice. These are standards for communications between transportation management center and

roadway equipment. Majority of the ITS services can be grouped under this. Various fields

included are:

• Data collection and monitoring

• Dynamic message system

• Ramp metering

• Traffic signal

• Vehicle sensors



Data collection and monitoring

This application area includes the interface between a traffic management center or a data

archive and roadside equipment. Primarily the interface is between traffic management sub-

system and roadway sub-system. By this standard we can effectively control, monitor and

collect data from the equipment on or at the roadside. The roadside equipment collects and

processes signals from the sensors as vehicles are detected to generate information. The roadside

equipment sends the information to the center. The standards included are:

• Object definitions for video switches.

• Data dictionary for closed circuit television

• Object definitions for environmental sensor station and roadside weather information

system.

• Transportation system sensor objects.

• Data collection and monitoring devices.

The 1st, 2nd and 4th standards are used for video data collection. The 3rd is used when some

environmental data collection is to be done. The last is the common standard to be followed

while data collection is done.

Dynamic message signing

It is an interface between traffic management and roadway system. It gives real time information

such as traffic conditions, weather conditions or any other advisory to user. It has one primary

and several secondary standards. The primary standard is listed below. The standard included

is

• Object definitions for dynamic message signs.

The standard is discussed below in detail.

Ramp metering

This application area provides an interface between traffic management and roadway system.

The roadway sub-system includes a ramp meter which controls traffic in freeway lanes. One

primary standard is included for this application. The standard included is

• Ramp meter controller objects.



Traffic signal

It is an interface that is used for local signal controllers. It is also used for master controller.

The roadway sub-system includes a local-signal controller or on-street master controller. Based

on the traffic data appropriate signal timing is decided and then interface provides information

to controller about the signal timings. 2 major standards for this are:

The standards used are:

• Objects for signal system master.

• Object definitions for actuated traffic signal controller.

Vehicle sensors

This application area includes the interface between a traffic management and roadway system

and a roadway and archived data management subsystem. The roadway subsystem includes

roadway sensors that identify different characteristics and communicates it to main center.

There are 4 primary standards for this application. The standards are:

• Object definitions for video switches.

• Data dictionary for CCTV.

• Transportation system sensor objects.

• Data collection and monitoring devices.

49.2.2 Center - center interface

It is an interface that is used to make standards for communication between management

centers. This interface is important from planning point of view. The standards help in

tackling the diversities. Effective communication takes place between various centers because

of these group of standards. The archived data transfer is efficient and also the real time data

transfer is possible. Various fields in centre - centre interface are:

• Data archival

• Traffic management

• Traveller information



Data archival

This application area includes an interface between the archived data management subsystem

and the sources and the users of archived data. The data archive collects data for off-line

analysis purposes such as planning and research. Data sources for the archive include traffic

management centers, emergency management centers and commercial vehicle administration

system. Effectively it is the data transfer between centers for planning and research. There are

two primary standards for this. Standards used are:

• Archival data management system(ADMS) guidelines

• ADMS data dictionary specifications

Traffic management

It provides an interface between a traffic management center and other centers like transit

management center, emergency management, toll operation, event promoter, media and other

management centers. It enables transfer of real time traffic data and control over emergency-

maintenance operations. Three standards are used for this. Standards used are:

• Message set for external TMC communications.

• Standard for functional level traffic management data dictionary.

• Message set for weather reports.

Traveller information

This application area includes the interface between information service provider and traveler

information collector/disseminator. These interfaces support the roles of an ISP that may

include information collection, integration of collected data and dissemination of aggregated

data. Four standards are included in this. Standards used are:

• Data dictionary for advanced traveler information system (ATIS).

• Message system for ATIS.

• Messages for handling strings and look-up tables in ATIS standards

• Message set for weather reports



49.2.3 Center - vehicle interfaces

It provides standards for communication between management center and vehicle. The number

of application area in this interface may be less but they assume high importance in ITS services.

There effective implementation helps in overall effective use of ITS. Fields included are:

• Mayday

• Transit vehicle communications

MAYDAY

This application area includes interface between driver and emergency management center. The

interface enables the driver or traveler to either request emergency assistance or have such a

request automatically sent after a crash. One standard is included for this type of application.

Standards used is

• On-board land vehicle Mayday reporting interface

Transit vehicle communications

This application area includes interface between transit vehicle and transit management center.

Transit vehicles send information on location, passenger count, maintenance and so on to the

transit management center. Similarly the transit management center provides information

regarding dispatch, routing and other information. Standards used are:

• TCIP-control center business area standard.

• TCIP-common public business area standard.

• TCIP-fare collection business area standard.

• TCIP-onboard business area standard.

The TCIP stands for Transit Communications Interface Profiles. This is body forms under

NTCIP. It is responsible to formation of standards regarding the transit management.

49.2.4 Roadside - vehicle interfaces

This interface provides standards for wireless communication between roadside and vehicles.

These are implemented to increase the service of any system and their by increasing its quality.

Communication takes place between a vehicle and roadside equipment by automatic means.

Fields included are:



• Toll/fee collection

• Signal priority

Toll/Fee collection

This application area includes interface between toll or parking management facility and vehicles

that would pay the toll or fee. This interface supports reading vehicle and processing electronic

identification and associated account information. 5 primary standards are included in this.

Standards used are:

• Standard specification for 5.9 GHZ data link layer.

• Standard specification for 5.9 GHZ physical layer.

• Standard for message set for vehicle /roadside communications.

• Specification for Dedicated Short Range Communication (DSRC) medium access and

logical link control

• Specification for Dedicated Short Range Communication (DSRC) physical layer using

microwave in 902-928 MHz.

Signal priority

This application area includes interface between traffic controllers and transit or emergency

vehicles. The interface supports providing priority to the transit vehicles or preempting emer-

gency vehicles, depending on the detection of the vehicle type or request from vehicle. This

application area has 5 standards associated with it. Out of these 5 standards 4 are same as for

toll collection. Standards used are:

• Standard specification for 5.9GHZ data link layer.

• Standard specification for 5.9GHZ physical layer.

• Objects for signal control priority.

• Specification for Dedicated Short Range Communication (DSRC) medium access and

logical link control

• Specification for Dedicated Short Range Communication (DSRC) physical layer using

microwave in 902-928 MHz.



49.2.5 Roadside - roadside interfaces

This area involves standards for communications between roadside and railroad wayside equip-

ment. The most important of it is the interaction between the road and rail equipment.

Highway Rail Interface

This application area includes interface between railway and roadside equipment. The interface

support co-ordinated operations of the railway and roadway-side equipment to improve the

operations and safety for both rail transit and highway vehicles. This includes one standard

between two systems. Standard used is:

• Standard for interface between railway subsystem and highway sub-system at intersection

49.2.6 Dynamic Message Sign Standard

Dynamic message sign standard is a standard employed to have certain set of rules and reg-

ulations for dynamic message signs. All the devices used should comply with the standard

so that the device can be used on any platform. All the functioning of the device should be

universal. It defines the data elements required for DMS. Data elements are like font, font size,

the height of font, the spacing between characters, the type of message etc. It also defines

the conformity-performance of a DMS device. That is it defines how the DMS system should

work in any scenario. The performance of the system is thus checked. It contains mandatory,

optional and conditional clauses which are needed to be followed.

There are many actions that are required to be done in a DMS system. All such actions can

be done using some syntax. The standard provides these syntaxes that are to be used while

working with the DMS devices. All devices should work with this syntax.

Sign configuration

All the parameters regarding the sign boards are included in this feature. Whenever a message

has to be displayed some standard data of the sign board is required for proper display of

message. To access this parameter some syntax is to be followed to get the information. 2

important parameters are:

• Height/Width of sign board- it gives the height and width of the board.

• Horizontal/vertical border parameter- it gives the border available on the board.



Font configuration

All data regarding the type of font, the size is described by the font configuration. It is a

read-write parameter where we can access the data and also overwrite it if required. Height

may be expressed in pixels. The important parameters are:

• Font name parameter - it gives the type of font to be used as default which can be changed.

• Font size parameter - gives the size of font.

Sign control objects

These provide some codes that are used for controlling any sign. The activity on a sign is

governed by these parameters. Some important parameters are:

• Activate message parameter - provides a code - when to activate a certain parameter.

• Message display time remaining parameter - states the display time remaining for a par-

ticular message.

Message parameters

All the data regarding the various types of messages their characteristics are controlled by these

parameters. The changing of any message or the status of any message can be assessed by these

parameters. Some important parameters are discussed below:

• Max. no. of changeable message parameter - it specifies the maximum number of change-

able messages that can be stored or used at a time.

• Message run time priority parameter - it gives the run time priority of the message and

thus is helps in decision making.

• Message status parameter - it gives the status of the message i.e. whether it has been

displayed or not; whether it is edited; whether it is being edited, etc.

Illumination objects

This gives the parameters related to the illumination of the sign boards. The status of present

illumination, the source of illumination can be assessed. Some important parameters of it are:

• Illumination control parameter - it gives the source of the illumination of the sign board.

The source can be assessed and also can be changed. Thus it is a read-write parameter.



• Illumination brightness level parameter - it gives the brightness around the sign board.

Some sensors are used to know the current brightness level.

Status objects

They help in finding the status as is specified initially. Some important parameters are:

• Current speed parameter - it gives the current speed of the vehicle. It is an read-only

parameter.

• Current speed limit parameter - it denotes the current speed limit of the corridor. It is a

read-write parameter.

Power status objects

It gives the power status of a vehicle. This type of DMS service is inside the vehicle. It gives

information to the driver. Some important parameters of this field are discussed below:

• Low fuel parameter.

• Engine RPM parameter.

• Power source parameter.

49.2.7 Standards testing

Just as testing is required for any new thing which is made, the standards are also needed to

be tested. It is like an evaluation of a system. It helps in judging whether the standard made is

effective or not. Also the practicality of standard is needed to be judged. So testing is essential

for any standard. It can be done in 3 ways.

Validation testing

Standards are continually tested during development process. It ensures that it satisfies all

requirements. The standards are validated in this step.

Verification testing

This examines the practicality and economic viability to build system based on standards.

This is mainly done by vendors and users. It can be performed by reviewing and analyzing the

standards documents or developing software for the same.



Experienced based testing

This type of testing is done by experience. It includes real world experience with the system.

As it is subjective mostly it is not followed.

49.3 Evaluation

Just like testing is done for standards the whole ITS system is also needed to be evaluated in

stages. It helps in judging any project and its deployment. It minimizes the risk of project

failure. It helps in identification of current performance of system.

49.3.1 Types of evaluation

The various types of evaluation stages are:

• Planning level evaluation

• Deployment tracking

• Impact assessment

• RP and SP survey

Planning level evaluation

Evaluation is done before the project is implemented. During the planning stage this type of

evaluation can be done. Previous data can be used for doing this. Two methods of this are:

• Benefit cost analysis- the benefits of the project need to be evaluated. The cost of the

project is also to be found out. Then depending upon the ratio the evaluation is done.

• Relative ranking- it is a weight based method. Weight given to criteria and the value of

each alternative is calculated.

S = ΣK × V (49.1)

where, S is the value of alternative, V is the value of one criterion, and K is the weight of that

criterion.

Here, S is the total value of the alternative. More the value of alternative, more prospects

of that alternative to be selected. Each alternative can be evaluated by different criteria. The

value of that criteria is denoted by V . Study is to be conducted to calculate the value of the



criteria. K denotes the importance of that criteria to the alternative. It is a global entity and

does not change with the value of the criteria. For example, consider a case of providing the

signal priority system on a certain link. For evaluating this system an important criteria is the

travel time on a corridor. The value of the travel time will be the V value. Also the weightage

to this parameter will be K.

Deployment tracking

This evaluation is done when the project is being implemented. It gives the idea regarding the

difference in the goals and actual work undertaken. We can determine the current progress rate

of the work. The future directions needed to to be taken can also be assessed. Effective way of

knowing this is the amount of data transfer between various agencies.

Impact assessment

After an ITS system is deployed it is allowed to collect data over a period of time. The data

collected is regarding the parameters from which assessment can be done. The criteria and the

measure of effectiveness is mentioned in table. 49:1.

RP and SP survey

Many times benefits cannot be expressed in terms of monetary units as is required for benefits

cost analysis. In such cases RP and SP surveys are conducted. RP survey is the revealed

preference survey. In this assessment of present system is done. In this survey the questionnaire

is asked regarding the present facilities. The respondents grade the parameters set in the survey.

Based on this grading the evaluation is done. SP survey is stated preference survey. This

survey is done for future projects. In this type of survey the future project is explained to the

respondents. They are given alternatives regarding this project. The respondents rate each

alternative and thus total evaluation is done.

49.3.2 Evaluation tools

Some tools are used which help in evaluation of the ITS technologies. They are just the means

of evaluation. The basic principle of evaluation remains the same. It can be done in 2 ways.

Traffic simulation models

This is a model based technique. In this method, models such as ‘INTEGRATION’, ‘DYNAS-

MART’, ‘DYNAMIT’ are used for evaluation. It is a cost effective way of analysis. In these



Table 49:1: The criteria and measure of effectivenessPerformance Criteria Measure of Effectiveness

Crashes

Safety Injuries

Fatalities

Travel time/delays for selected O-D

Travel time survey

Network travel time

Throughput Vehicles / persons using the facility

Customer satisfaction Ratings of travel experience

CO

NO2

Air Quality V OC

HC

Ozone

Fuel consumption Reduction or not

models simulation is done considering the future ITS installment in the facility. The facility is

reproduced in the software. The future changes to be made in the facility are added. Then it

is simulated to show the desired results in terms of some traffic parameters. Also simulation is

done without the introduction of the new facility. The parameters are again calculated. These

two analysis gives the difference in the facility that may arise in the facility. This gives instant

evaluation of the facility of ITS. Also it is cost effective as less personnel are required and the

data collection is not a major issue. Evaluation can be done before the implementation of any

facility. Thus cost savings in selection of alternative facilities is also observed. If the present

technology used is not found satisfactory then some improved technology can be procured to

fulfill our requirements.

ITS deployment analysis system

In this type of technique the traditional way of benefit-cost analysis is done. There are some

softwares that directly compute cost and benefit. Some softwares use parameters like travel

time, speed, delay to compute cost and benefit. But the basic idea remains the same. IDAS

model of US DOT is an example of such software.

The basic principle in IDAS model is to calculate the benefit cost ratio. It helps in providing



INPUTSCOST

ALTERNATIVE

MODULECOMPARISON MODULE

BENEFITS

COST MODULE

ALTERNATIVESGENERATOR

INPUT/OUTPUT INTERFACE

TRAVEL DEMAND MODEL

Figure 49:1: IDAS model

a step wise approach for calculate it. Initially input is to be given from a travel demand

model. It will evaluate the input and output parameters from the system. Depending upon

the parameters various parameters will be generated. Then the control goes to cost and benefit

module where the benefits and cost of alternatives are calculated. Last step is comparison of

these calculated cost and benefits. Depending upon the comparison is done. At all the steps

cost input is given. This cost may not always be in monetary terms but can be expressed in

some discomfort. The IDAS model is shown in Fig. 49:1.

Sample Question 1

Describe the Dynamic Message Sign Standard with 3 features?

Answer Dynamic message sign standard is a standard employed to have certain set of rules

and regulations for dynamic message signs. All the devices used should comply with the

standard so that the device can be used on any platform. All the functioning of the device

should be universal. It defines the data elements required for DMS. Data elements are like

font, font size, the height of font, the spacings between characters, the type of message etc.

It also defines the conformity-performance of a DMS device. That is it defines how the DMS

system should work in any scenario. The performance of the system is thus checked. It contains

mandatory, optional and conditional clauses which are needed to be followed.

There are many actions that are required to be done in a DMS system. All such actions can

be done using some syntax. The standard provides these syntaxes that are to be used while

working with the DMS devices. All devices should work with these syntax.



Features:

1. Sign configuration: All the parameters regarding the sign boards are included in this

feature. Whenever a message has to be displayed some standard data of the sign board

is required for proper display of message. To access this parameter some syntax is to be

followed to get the information. Two important parameters are:

• Height/Widht of sign board- it gives the height and width of the board.

• Horizontal/vertical border parameter- it gives the border available on the board.

2. Font configuration: All data regarding the type of font, the size is described by the

font configuration. It is a read-write parameter where we can access the data and also

overwrite it if required. Height may be expressed in pixels. The important parameters

are:

• Font name parameter which gives the type of font to be used as default which can

be changed.

• Font size parameter which gives the size of font.

3. Sign control objects: These provide some codes that are used for controlling any sign.

The activity on a sign is governed by these parameters. Some important parameters are:

• Activate message parameter which provides a code stating when to activate a certain

parameter.

• Message display time remaining parameter indicating states the display time remain-

ing for a particular message.

Sample Question 2

Describe the methods of evaluation of ITS technologies.

Answer ITS evaluation can be done in four different ways as given below:

(a) Planning level evaluation: evaluation is done before the the project is imple-

mented. During the planning stage this type of evaluation can be done. Previous

data can be used for doing this. Two methods of this are:

• Benefit cost analysis- the benefits of the project need to be evaluated. The

cost of the project is also to be found out. Then depending upon the ratio the

evaluation is done.



Performance criteria Parameters

Crashes

Safety Injuries

Fatalities

Travel time/delays for selected O-D

Travel time or mode.

Network travel time

Throughput Vehicles / persons using the facility

Customer satisfaction Ratings of travel experience

• Relative ranking- it is a weight based method. Weight given to criteria and the

value of each alternative is calculated as S = ΣK × V , where S is the value of

alternative, V is the value of one criterion, and K is the weight of that criterion.

(b) Deployment tracking: this evaluation is done when the project is being imple-

mented. It gives the idea regarding the difference in the goals and actual work

undertaken. We can determine the current progress rate of the work. The future

directions needed to to be taken can also be assessed. Effective way of knowing this

is the amount of data transfer between various agencies.

(c) Impact assessment: after an ITS system is deployed it is allowed to collect data

over a period of time. The data collected is regarding the parameters from which

assessment can be done(Table. 3c).

(d) RP and SP survey: many times benefits cannot be expressed in terms of monetary

units as is required for benefits cost analysis. In such cases RP and SP surveys are

conducted. RP survey is the revealed preference survey. In this assessment of present

system is done. SP survey is stated preference survey. This survey is done for future

projects.

Sample Question 3

Describe how IDAS model can be used for ITS evaluation.

Answer The basic principle in IDAS model is to calculate the benefit cost ratio. It

helps in providing a step wise approach for calculate it. Initially input is to be given

from a travel demand model. It will evaluate the input and output parameters from the



system. Depending upon the parameters various parameters will be generated. Then

the control goes to cost and benefit module where the benefits and cost of alternatives

are calculated. Last step is comparison of these calculated cost and benefits. Depending

upon the comparison is done. At all the steps cost input is given. This cost may not

always be in monetary terms but can be expressed in some discomfort.

49.4 Summary

This lecture give in detail ITS standards, its use and classification followed by various ways of

evaluation ITS deployment. Some of the important ways of evaluation include: planning level

evaluation, deployment tracking, impact assessment, and RP and SP survey.

49.5 References

1. M A Chowdhary and A Sadek. Fundamentals of Intelligent Transportation systems

planning. Artech House Inc., US, 2003.



3. Yokota Toshiyuki and Weiland Richard. Its standards for developing countries. (3),

2004.


Transportation Systems Engineering 50. Advanced ITS

Chapter 50

Advanced ITS

50.1 Introduction

Some new features in the ITS sector are covered in this section. The first basic concept in any

ITS implementation is SMART CAR. It is the car with all modern features. The SMART CAR

has to be complimented by a SMART ROAD. The developments in the ITS field started with

the infrastructure to infrastructure communications. They formed the basis of further devel-

opment of ITS. Then the I2I communications were upgraded with the vehicle to infrastructure

communications. They are called V2I communications. The latest development is the vehicle

to vehicle communications, i.e. V2V communications.

50.2 Smart car

As mentioned earlier the car is equipped with all the new electronic gadgets. It helps the user

to use service efficiently. Some of the features of SMART CAR are:

• GPS and on-board communications

• Anti-collision sensors

A smart car must be able to sense, analyse, predict and react to the road environment, which

is the key feature of smart cars. The car works with a central component that monitors

the roadway and the driver. It also evaluates of the potential safety benefits. It addresses

navigation, obstacle avoidance and platooning problems. The car aims at expanding the time

horizon for acquiring safety relevant information and improving precision, reliability and quality

of driving. There are some preventive safety technologies and in-vehicle systems, which sense

the potential danger. The Adaptive Integrated Driver-vehicle Interface (AIDE) project tries

to maximize the efficiency and safety of advanced driver assistance systems, while minimizing

the workload and distraction imposed by in-vehicle information systems. Almost 95% of the



accidents are due to human factors and in almost three-quarters of the cases human behaviour

is solely to blame. Smart cars present promising potentials to assist drivers in improving their

situational awareness and reducing errors. With cameras monitoring the driver’s gaze and

activity, smart cars attempt to keep the driver’s attention on the road ahead. Physiological

sensors can detect whether the driver is in good condition. The actuators will execute specified

control on the car without the driver’s commands. The smart car will adopt active measures

such as stopping the car in case that the driver is unable to act properly, or applying passive

protection to reduce possible harm in abrupt accidents, for example, popping up airbags.

50.3 Smart road

As mentioned earlier SMART CAR alone cannot operate in a system. Thus along with the

SMART CAR, the infrastructure should also be improved. The infrastructure also should be

well prepared for taking care of smart car. The road equipment will communicate with the

vehicle and provide real time assistance to the user. Provision of Smart road along with Smart

car will complete the Smart features of any facility. It may be possible that the highway forms

a high density platoon of vehicles moving bumper to bumper and this platoon will move at

a speed of 70 kmph or so. That road will be equipped with some sensors may be along the

pavements and the decisions are left to the central unit. The road itself will show some messages

which can be easily read.

50.4 Infrastructure to Infrastructure Communications

This type of communication is a initial stage in formation of present ITS system. Communica-

tion takes place between infrastructures. Evolution of I2I services led to more advanced vehicle

communications. They are the easy means of communications. But handling them on a large is

an area of concern. Fig. 50:1 and 50:2 show the I2I communications in case of ramp metering.

50.5 Vehicle to infrastructure communications

These involve advanced vehicle to infrastructure interface. The communication takes place

between a vehicular device and a infrastructure equipment. It is an improvement over I2I

services. Large communication is possible with this type of communication. Some examples of

V2I communication are:

• Blind merge warning



Ramp signals Vehicles enteringthe motorway

One vehicle perlane per greenVehicles on

the motorway phase

Figure 50:1: On-ramp meterting-1

ONE VEHICLE PEREACH LANE

STOPWERE ONRED

Figure 50:2: On-ramp meterting-1



• Curve speed warning

• Weather warning

• Intelligent on-ramp metering

• eCALL

50.6 Vehicle to vehicle communications

Each vehicle communicates with other vehicles and assess the required data. It is the most

advanced technique implemented in ITS. It requires very less communication with the centre or

infrastructure. All vehicles will communicate with each other and decisions will be made by the

vehicle device only. For ex, the ramp meter will work all by itself and no infrastructure device

will be required. Some real time services cannot be provided by infrastructure. In these cases

such type of communication will be helpful. Fig. 50:3 shows the collision warning principle.

Some examples are:

• Approaching vehicle warning

• Blind spot warning

• Co-operative cruise control

• Collision warning

• Lane change assistant

50.7 Summary

This chapter briefly covers some pointers to future directions of ITS developments. This inlcude

smart cars and smart road and a communcation system between them resulting in complete

automation of the taffic system.

50.8 References


New Delhi, 1987.



BrakeSupport

CollisionWarning

Figure 50:3: Collision Warning


Problems

Lecture notes in Traffic Engineering And Management

August 14, 2013

Introduction to Transportation Systems Analysis

Select a current transportation issue for modeling and do the following.

(i) Identify the transportation system components, (ii) Activity system that is interest to the transportaion issue, (iii) What

could be a suitable service function, (iv) What could be a suitable demand function, (v) Visualize how the activity system

may change, (vi) Propose some transport improvement options, (vii) Illustrate flow predictions.

1.

An airline company has set a base price of Rs 2500 on a particular route. However, depending upon demand they increase

the price of a seat by Rs 50 per user. The maximum number of people travel on this route is 4000. However, people will

drop out of travel at a rate of one person for every Rs 10 rise.

From next year airliner is planning to change fare structure, the new base price of a route is Rs 3000. However, they

increase the price of a seat by Rs 52 per user. The maximum number of people that travel from next year is 5000.

However, people will drop out of travel at a rate of 2 persons for every Rs 10 rise. What is the revenue generated by

airliner this year as well as next year? (8)

2.

A highway connecting two small cities has the following characteristics. The time to travel on a certain stretch of a

highway is =12+0.01 , where is the flow of vehicles (veh/hr). The demand function is =4800+0.01 .

(a) Estimate the equilibrium flow and travel time

(b)The traffic department wants to close the existing highway and replace it with a better highway with a supply function

of =12+0.006 , with the same demand function. How much additional traffic will will be induced by this new highway?

(c) Citizens currently using the existing highway want to continue using it, and in addition, demand the new highway as

well. What will be the equilibrium flow and travel time for this scenario, assuming the demand for travel time remains

3.

Problems http://www.civil.iitb.ac.in/tvm/1111_nptel/800_Problems/plain/

1 of 33 06-02-2014 12:42

unchanged (Wardrop's principle applies)?

(d)If the new road is built with a supply function =10+0.005 , and the existing highway is uased as well, what would

be the equilibrium flow and travel time?


the price of a seat by Rs 50 per user. The maximum number of people that may travel on this route is 4000. However,

people will drop out of travel at a rate of one person for every Rs 10 of the actual price. From next year airliner is

planning to change fare structure, the new base price of a route is Rs 3000. However, they increase the price of a seat by

Rs 45 per user. The maximum number of people that travel from next year is 5000. However, people will drop out of

travel at a rate of two persons for every Rs 10 of the actual price. What is the revenue generated by airliner this year as

well as next year?

4.

State and illustrate the three relationships between transportation, activity, and flow system5.

Illustrate with a sketch a demand function, service function and how they are used to predict flow and the associated

impact

6.

Fundamenal Parameters of Traffic Flow

Fundamenal Relations of Traffic Flow

The following travel times in seconds were measured for vehicles as they traversed a 3 km segmeny of a highway.

Compute the time mean speed and space mean speed for this data. Why space mean speed is always lower than time

mean speed, explain with a derivation.

1.

A moving vehicle experiment was conducted on a 2.5 km section of a highway. Two trials were conducted in the direction

of dominant traffic flow. In the first trial, number of vehicles that had overtaken the test vehicle is 30, number of vehicles

overtaken by the test vehicle is 6, and test vehicle speed is 30 kmph. In the second trial, number of vehicles that had

2.


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overtaken the test vehicle is 20, number of vehicles overtaken by the test vehicle 26, and test vehicle speed is 35 kmph.

Calculate the fundamental parameters of traffic flow and the average headway and spacing.

Derive the equation for flow ( ) from the moving observer method.3.

Calculate the time mean speed and the space mean speed of the following spot speed data:

Speed Range Volume

(m/sec) (veh/hr)

10-12 12

12-14 18

14-16 24

16-18 20

18-20 14

4.

(a) Derive the relationship between time mean speed and space mean speed. (b) Write the probability density function for

normal distribution and Parson type III distribution and its special cases with various notations used.

5.

A 6 km undivided four lane highway on level terrain has free flow speed of 75 kmph. The lane width is 3.5m with peak

hour volume of 1600 veh/hr and 12% trucks and buses, 2% Recreational vehicles. Find the capacity and level of service.

Assume peak hour factor 0.9.

6.

Two friends were traveling from Mumbai to Pune and have decided to count the vehicles on a short stretch of 5 km. The

first one sat on the left side and counted vehicles passed by him. The second sat on the right side and counted vehicles

overtaken him. They counted 20 and 60 respectively while traveling at 30 kmph. They did the same exercise on the next

day about same time and counted 25 and 40 respectively and were traveling at 35 kmph. Assuming same traffic

conditions on both days, compute the density, mean speed, and flow on that stretch.

7.

Derive the relationship between fundamental parameters of traffic with a detailed illustration of fundamental diagrams of

traffic flow.

8.

Determine the time mean speed and space mean speed from the following data. Verify the relationship between them.

Speed m/s Frequency

1-5 2

6-10 5

11-15 7

9.


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16-20 9

As a traffic engineer, discuss various traffic management measures that you will recommend to IITB authorities for our

campus (Make brief and specific points, with simple sketches).

10.

(a) Derive the expression for flow across a section of road by moving car method. (b) Prove that this formulae actually

estimates the stream flow.

11.

Determine the time mean speed, space mean speed, and percentile speed from the following data.

Speed m/s Frequency

1- 5 9

6-10 16

11-15 32

16-20 48

21-25 23

26-30 9

12.

A student riding his bicycle from campus on a one-way street takes 50 min to get home, of which 10 min was taken

talking to the driver of a stalled vehicle. He counted 42 vehicles while he rode his bicycle and 35 vehicles while he

stopped. What are the travel time and flow of the vehicle stream? (6)

13.

Derive expression for the fundamental parameters of traffic flow by moving observer method (10)14.

On a 2.8km long link of road, it was found that the vehicle demand was 1000, mean speed of the link 12 km/hr, and free

flow speed 27 km/hr. Assuming the Average vehicle occupancy as 1.2 person/vehicle, calculate congestion intensity in

terms of total person hours of delay.

15.

A person walking from office on a one-way street takes 60 min to get home, of which 12 min was taken talking to the

driver of a stalled vehicle. He counted 52 vehicles while he was walking and 25 vehicles while he stopped. What are the

travel time and flow of the vehicle stream? (7)

16.

The observations from a moving car method are given below. Assuming linear speed-density relation, what is the

maximum flow, speed, and density the following following stretch can take. Show the details of the calculation

Overtaken

by the

test

Overtaking

the test

vehicle

Moving

against

traffic

Travel

time

with

Travel

time

against

17.


4 of 33 06-02-2014 12:42

vehicle stream the

traffic

(s)

the

traffic

(s)

5 119 618 422 268

26 12 389 213 188

24 9 401 226 396

2 55 410 274 255

26 9 374 226 396

Traffic Stream Models

A study of flow at a particular location resulted in a calibrated speed-density relationship as follows. .

For this relationship, determine free flow speed, jam density, maximum flow, speed-flow relationship, and flow-density

relationship. (Illustrate with a sketch)

1.

Explain with neat sketch the need and examples of multi-regime stream models.2.

In a traffic study, the observed densities were 150, 120, 50, 70 and 20 veh/km and the corresponding speeds were 10,

25, 45, 40 and 32km/h. Find the jam density according to Greenberg's logarithmic traffic stream model. (Hint: Linearize

the expression)

3.

Sketch the three fundamental diagrams of traffic flow. Derive the relation between maximum flow ( ), jam density (

), and free flow speed ( ). Assume liner speed flow relation: .

4.

Sketch the three fundamental diagrams of traffic flow. Derive the relation between maximum flow, jam density, and free

flow speed. Assume Greenshields' speed-flow relation.

5.

For the following data on speed and concentration, determine the parameters of Greenshields' model. Find the

concentration corresponding to a speed of 40 kmph. Find also the maximum flow.

Concentration(veh/km) Speed(kmph)

180 4

140 20

30 50

75 35

6.


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A study of flow at a particular location resulted in a calibrated speed-density relationship as follows.

. For this relationship, determine free flow speed, jam density, maximum flow, and the relationship between fundamental

parameters of traffic. (Illustrate with a sketch)

7.

Determine the parameters of Greenshields model for the following data. Find the maximum flow and density for a speed

of 45 kmph.

Speed (kmph) Density (veh/km)

5 150

20 120

30 100

40 70

8.

In a traffic study experiment, density values are obtained as 160, 120, 40, and 72 veh/km corresponding to speed values

of 3, 18, 55, 32 respectively. Determine the parameters of Greenshields' model. Find the density corresponding to a

speed of 40 kmph. Find also the maximum flow.

9.

A study of flow at a particular location resulted in a calibrated speed-density relationship as follows.

For this relationship, determine free flow speed, jam density, maximum flow, speed-flow relationship, and flow-density

relationship. (Illustrate with a sketch)

10.

The following speed and density is observed from a road section. If we assume the speed decreases linearly with respect

to density, then: (a) what will be the density at a speed of 10 kmph, and (b) what will be the maximum flow across the

section


5 120

20 90

30 40

40 10

11.

The speed and density observed from a road is given below. What is the density and flow corresponding to a speed of 25

kmph. State the assumptions/model used in the computation.


12.


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10 200

20 170

30 120

40 100

Illustrate neatly on a single graph the speed-density relation by Greenberg, Greenshield, Underwood, Pipe(n=0.5,2), two

regime, and three regime models, along with typical field observations

13.

The speed and density observed from a road is given below. What will be the maximum flow in this stretch? State the

assumptions/model used in the computation.


10 200

20 170

30 120

40 100

14.

Moving Observer Method

In a traffic stream, 30% of the vehicles travel at a constant speed of 60km/h, 30% at a constant speed of 80km/h, and

the remaining vehicles at a constant speed of 100km/h. An observer travelling at a constant speed of 70km/h with the

stream over a length of 5km is overtaken by 17 vehicles more than what he has overtaken. The observer met 303

vehicles while traveling against the stream at the same speed and over the same length of highway. What is the mean

speed and flow of the traffic stream?

1.

Calculate the time mean speed and the space mean speed of the following observation.

Speed Range Volume

(m/sec) (veh/hr)

10-12 12

12-14 18

14-16 24

16-18 20

18-20 14

2.


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Parking

Calculate the length required to park N number of vehicles in the case of on-street parking facility with the help of

neat diagrams. Assume the dimensions of vehicle as 5.5m X 2.5m.

1.

Illustrate with a sketch on-street parking facility and derive the length required to park N number of vehicles with the

help of neat diagrams. Assume the dimensions of vehicle as 5.5m X 2.5m.

2.

From an in-out survey consiting of 50 bays, the initial count was 18. The number of vehicles coming in and out of the

parking lot for a time interval of 5 minutes is shown below. Find the accumulation, total parking load, average occupancy,

and efficiency of parking lot.

Time 5 10 15 20 25 30

In 7 6 3 3 7 4

Out 2 4 5 2 8 3

3.

Headway Modeling

An observation of headways for 800 samples is given below. Mean headway and standard deviation observed are 2.76

and 1.79. Fit Pearson type III distribution if the shift parameter is 0.5.

t Observed Proportion

0.0 1.0 191

1.0 2.0 131

2.0 3.0 170

3.0 4.0 98

4.0 5.0 82

5.0 6.0 81

6.0 7.0 44

7.0 2

1.

The number of vehicles arriving on a single lane highway from one direction in successive 10 seconds intervals is shown

below. Fit a poisson distribution to this data and comment on the results. Plot the observed and modeled values in a

graph sheet.

2.


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Vehicle arriving 0 1 2 3 4 5 6

in 20s interval

Frequency 17 31 12 24 10 6 0

The headway distribution from 1200 observation ( 1.5 sec and 0.8 sec) is given below. (a) Fit a negative exponential

distribution and show the results in a tabular form. (b) What is the probability of headway between 1.8 and 2.1 seconds.

(c) How many vehicles arrived (both actual and modeled) with headway greater than 1.5 sec and less than 2.5 sec.

h h+dh prob(obs)

0.0 0.5 0.086

0.5 1.0 0.283

1.0 1.5 0.297

1.5 2.0 0.153

2.0 2.5 0.086

2.5 3.0 0.077

3.0 0.018

3.

Using the following random numbers generate vehicle arrival for a period of 20 sec. Assume headways to follow

exponential distribution with mean time headway 6 sec.

4.

Vehicles arrive at a toll booth at an average rate of 300 per hour. Average waiting time at the toll booth is 10 s per

vehicle. If both arrival and departures are markovian events, what is the average number of vehicles in the system,

average queue length, average delay per vehicle, average time in the system?

5.

Given the headways observed from a survey is given below. Fit an exponential distribution and compare the actual and

computed mean and standard deviation. 5.15, 1.22, 2.65, 2.35, 0.47, 2.8, 7.67, 4.74, 2.42, 4.87, 5.94, 8.58, 9.74, 0.56,

0.66, 6.72, 7.41, 6.94, 2.42, 5.61

6.

A headway survey gave a mean of 3.76 and standard deviation of 1.17. Fit a Pearson type III distribution and find

probability that the headway is between 2 and 4 seconds. Assume a shift parameter of 0.5 and an interval of 0.5 for

calculations.

7.

If the flow rate at a given section of road is 1600 and if we assume the inter arrival time of vehicles follow an exponential

distribution, then:

the probability of headways greater than 1.8 second1.

8.


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the probability of headway between 1.2 and 2.4 seconds2.

the probability of headways less than the mean headway3.

Shockwave Theory

Explain the shock-wave phenomenon and derive the expression for speed of a shock wave with the help of neat diagrams.1.

Write a brief note on the shockwave phenomenon and illustrate with neat sketches.2.

Markings & Signs

Discuss any five road markings with the help of neat sketches.1.

(a) Any two longitudinal and transverse road markings. (b) A diamond interchange with movement of all flows. (c)

Elements involved in the design of a rotary. (d) Zone and zoning principles. (e) Show all the relevant dimensions of a

angle parking for a car.

2.

(a) Describe the main categories of traffic signs with two examples for each category alongwith neat sketches.

(b) Describe any two longitudinal markings with the help of neat diagrams.

3.

Draw a neat sketch of the time-space diagram of an overtaking operation of a two-lane two directional flow and mark the

important parameters(like etc.).

4.

Illustrate with neat sketches: (i) A diamond interchange showing the movement of all the flows. (ii) Road markings on a

two lane bi-directional horizontal curve when the sight distance is less than the length of the curve. (iii) The concept of

flow prediction in a transportation system when the supply is improved.

5.

Draw a neat sketch of a fully clover leaf intersection and mark all the traffic movements.6.

What is the difference between a stop sign and give way sign? Under what circumstances are they required? Illustrate

with neat sketches.

7.

With a neat sketch describe the signs and marking required for a three legged intersection.8.

With the help of neat diagrams show the traffic signs and road markings for

Ramp from an urban arterial joining the freeway,1.

Rotary,2.

Uncontrolled intersection joining a minor and major road,3.

9.


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Signalised intersection.4.

A road has four lanes. A bridge goes over the road, which has a pile at the middle of road. Illustrate with neat sketch the

road markings that are to be provided.

10.

Discuss various traffic control measures at a typical 4 legged intersection in an urban area. Illustrate them with the help

of neat sketches. Explore all the options other than rotary, signal and grade separation.

11.

Give two examples for each of the following categories of traffic signs: [A] Right of way series, [B] Movement series, [C]

Informatory signs, and [D] Warning signs

12.

Illustrate with neat sketch various road markings at a signalized intersection13.

(a) Illustrate with a neat sketch what traffic signs and road markings you propose at the IITB main gate? (b) Illustrate

with a neat sketch no passing zone markings at a horizontal curve when the stopping sight distance is less than the radius

of the curve (Assume the road is two lane bidirectional).

14.

Channelize the intersection given in the Figure [*] with the help of a neat sketch. Show the paths of movements by short

arrows. All the roads are bidirectional.

Figure: Intersection

layout

[width=6cm]1903.eps

15.

i) How do you channelize a three legged intersection for a high volume traffic in an urban area? ii) At an uncontrolled

intersection the cumulative number of gaps accepted and rejected have been tabulated as shown below. Determine

critical gap using Raff's method.

Gap (sec) Accepted gaps Rejected gaps 0.0

16.

Simulation

A line of vehicles are in car following mode and all vehicles are travelling at 15 m/s with distance headway of 25 m. After

1 second, the lead vehicle suddenly decelerates at a rate of until it stops completely. Simulate the behaviour of

first following vehicle using the GM fifth car following model for the first 3 seconds. Tabulate the results. Assume headway

exponent 1.0, speed exponent 1.5, sensitivity coefficient 0.5, reaction time 0.5 seconds, and scan interval 0.25 seconds.

1.

Explain with the help of an example vehicle-vehicle interaction models for a straight multi-lane link.2.


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1.2 seconds, the lead vehicle suddenly decelerates at a rate of 1.2 until it stops completely. simulate the behaviour

of first following vehicle using the GM fifth car following model for the first 2.5 seconds. Tabulate the results. Assume

headway exponent 1.2, speed exponent 1.6, sensitivity coefficient 0.8, reaction time 0.6 seconds, and scan interval 0.3

seconds.

3.

A car is travelling with a speed of 16 m/sec at time t=0. Another car follows the first at a distance of 28 m with same

velocity. If the first car accelerated by 1 m/sec from t=1 to 2 and decelerate by 1 m/sec from t=2 to 3, find the speed,

acceleration and spacing of the follower at time t=3.0 sec. Assume the reaction time is 1 sec, vehicle dynamics are

updated every 0.5 seconds, and the car following model is given by Eq. [*]. (Use of a tabular form is encouraged).

(1)

4.

Simulate the following vehicle behaviour for the following data using Widemann 74 model. (a) For the case of stand still

distance 3.5m, additive part of safety distance 1.5, and multiplicative part of safety distance 0.8. (b) For the case of stand

still distance 3.5m, additive part of safety distance 1.5, and multiplicative part of safety distance 0.8. Comment on the

following vehicle behaviour for the above two cases.

5.

In a simulation experiment on a single lane road, one vehicle is travelling at 18 . After 1.5 seconds, the vehicle

suddenly accelerates at a rate of for the next 1.8 seconds. Simulate the behaviour of subsequent vehicle with an

initial speed of 16 m/s using GM fifth car following model for the first 3 seconds if the initial distance headway is 20 .

Tabulate the results. Assume headway exponent 1.2, speed exponent 1.5, sensitivity coefficient 0.8, reaction time 0.6

seconds, and update interval of 0.3 seconds.

6.

Discuss the concepts and model formulations of Generalised GM model, Gipps' model, and Wiedemann 74 car-following

models.

7.


1.2 seconds, the lead vehicle suddenly decelerates at a rate of 1.2 until it stops completely. simulate the behaviour

of first following vehicle using the GM fifth car following model for the first 2.5 seconds. Tabulate the results. Assume

8.


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headway exponent 1.2, speed exponent 1.6, sensitivity coefficient 0.6, reaction time 0.6 seconds, and scan interval 0.3

seconds.



initial speed of 16 m/s using GM fifth car following model for the first 2.1 seconds if the initial distance headway is 25 .



9.

Discuss the concepts and model formulations of Generalised GM model.10.



initial speed of 16 using GM fifth car following model for the first 3 seconds if the initial distance headway is 20 .



11.

Traffic Signals

The phase plan and flows of a signalised intersection are given in Fig. [*]. Design the cycle length using HCM method (

=0.9) and green time for each phase. Compute also the average delay per vehicle using Webster's model. Show these in

a phase-time diagram. Assume lost time and amber time as 3 and 4 sec respectively for each phase. Ignore pedestrian

requirements.


flows and phase plan

[width=6cm]1000.eps

1.

A North-South corridor has three junctions namely A, B, and C. Junction A is on the south end of the corridor and junction

C is on the north end. These junctions are coordinated in the north direction. All the junctions are having two phase

signals with a cycle of 80 sec. The juctions A, B, and C have green times of 40, 50, and 30 sec respectively in the

coordinated direction. The distance between A and B is 600 meters and B and C is 900 meters. The junctions are

coordinated considering a speed of 15 m/sec. (a) What will be the resulting band width? (b) While the corridor is

2.


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operating under the above control conditions, if the vechiles could travel only at a speed of 12 m/sec, what bandwidth will

be achieved?

The phase plan and flows of a signalised intersection are given in Fig. [*]. Design the cycle length using HCM method (

=0.9) and green time for each phase. Compute also the average delay per vehicle using Webster's model. Show these in

a phase-time diagram. Assume lost time and amber time as 3 and 4 sec respectively for each phase. Ignore pedestrian

requirements.


flows and phase plan

[width=6cm]1405.eps

3.

A major road with four lane running E-W direction meets a minor road having two lane running in N-S direction. The E-W

flow is 1670, W-E flow is 1550, N-S flow is 720, and S-N flow is 680 vehicles per hour. The intersection of the two road is

controlled by a traffic signal with a cycle time of 60 seconds. Assume for all the phases the yellow time is 3 seconds, the

lost time is 4 seconds, and saturation headway is 2.1 seconds. Ignore turning movements and pedestrian traffic. Compute

the green time for each phase and total delay experienced by all vehicles in the intersection for one hour duration.

4.

A major road with four lane running E-W direction meets a minor road having two lane running in N-S direction. The E-W

flow is 1670, W-E flow is 1550, N-S flow is 720, and S-N flow is 680 vehicles per hour. The intersection of the two road is

controlled by a traffic signal with a cycle time of 60 seconds. Assume for all the phases the yellow time is 3 seconds, the

lost time is 4 seconds, and saturation headway is 2.1 seconds. Ignore turning movements and pedestrian traffic. Compute

the green time for each phase and total delay experienced by all vehicles in the intersection for one hour duration.

5.

Calculate the delay and level of service using HCM method for a signalised intersection in South bound direction. Follow

the terminology as per HCM 2000 and the intersection geometry is as shown in Figure [*].


Geometry

[width=8cm]1422.eps

The intersection is located in CBD area and the traffic volume in each direction in vehicles/hour is given as

East West North South

bound bound bound bound

Left turn 65 30 30 40

Through 620 700 370 510

6.


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Right turn 35 20 20 50

Pedestrian volume = 100 pedestrains/hour,

Percentage of heavy vehicles = 5% in East and West approaches and 8% in North and South approaches,

Base saturation flow rate = 1900 veh/h/lane,

Peak hour factor= 0.9,

Cross walk width = 3.0 m,

Two phase signal with cycle time 70 seconds and North bound-South bound green time=36 s,

East bound-West bound green time =26 s,

Amber time= 4 s and Movement lost time =4 s,

Arrival type 4 and Analysis duration = 15 min,

Assume 0% grade with no parking maneuvers and no buses stopping.

Consider Lane utilisation adjustment factor in North and South approaches= 1.00, East and West approaches = 0.95.

Left turn pedestrian/bicycle adjustment factor= 0.999(N), 0.998(S), 0.997(E), 0.998(W),

Right turn pedestrian/bicycle adjustment factor= 0.996(N), 0.994(S), 0.992(E), 0.995(W),

Passenger car equivalent for heavy vehicle = 2.0,

Left turn adjustment factor is 0.937(N), 0.951(S), 0.716(E), 0.901(W).

Incremental delay factor= 0.5 and Initial queue delay= 0 s/veh.

Progression adjustment factor = 1.000.

The distance between two intersections is 0.75 km and the average vehicle speed in the northbound direction is 50 kmph

and south bound direction is 54 kmph. If the cycle time is 100 seconds and north bound and south bound traffic volume is

950 vehicles/hour. (a) Compute the offset if south bound direction is ignored. (b) Compute the offset if both directions are

considered. Illustrate the result using time-space diagram.

7.

Describe the levels of intersection control.8.

The traffic flow and phase plan for a four-legged intersection is as shown in fig1. The E-W flow is 1420(Through 710, Left

284, Right 426), W-E flow is 1150(Through 575, Left 230, Right 345), N-S flow is 640(Through 320, Left 128, Right 192)

and S-N flow is 580(Through 290, Left 116, Right 174) vehicles per hour. Assume for all the phases the yellow time is 3

seconds, the lost time is 4 seconds, saturation headway is 1.2 seconds and degree of saturation is 0.9. Assume left turn

adjustment factor 1.2 and right turn adjustment factor 1.3. Compute the cycle length and green time for each phase.

9.


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Figure:

Intersection

Geometry

[width=6cm]1506


and south bound direction is 50 kmph. If the cycle time is 90 seconds, split is 50 percent, and north bound and south

bound traffic volume is 900 vehicles/hour, compute offset and band width, if: (a) only north bound traffic is considered,

and (b) both directions are considered. Illustrate the result using time-space diagram.

10.

The intersection of Third Avenue (NB/SB) and Main Street (EB/WB) is located in the central business district (CBD) of a

small urban area. Intersection geometry and flow characteristics are shown on the input worksheet. Facts/Data

/Assumptions: (a) EB and WB HV = 5 percent, (b) NB and SB HV = 8 percemnt (c) PHF = 0.9, (d) Two-phase signal,

(e) 70 sec cycle length, (f) NB-SB green = 36 s, (g) EB-WB green = 26 s, (h) Yellow =4 s, (i) Third avenue has two lanes,

one in each direction, (j) Main street has four lanes, two in each direction, (k) No parking at intersection, (l) Pedestrian

volume = 100 p/h, all approaches, (m) Bicycle volume = 20 bicycles/h, all approaches, (n) Movement lost time = 4s, (o)

Level terrain, (p) Assume crosswalk width = 3.0 m for all approaches, (q) Assume base saturation flow rate = 1900

pc/h/lane, (r) Assume , (s) No buses, (t) Left turn correction factor = 0.937, (u) Pedestrian-Bicycle effects on

turning , and (v) Lane utilization factor Compute the the delay and peak-hour LOS of the

NB approach using HCM 2000 guidelines? Fill the relevant cells of the Exhibit 16-20,21, and 22.

11.



/Assumptions: (a) EB and WB HV = 6 percent, (b) NB and SB HV = 9 percent (c) PHF = 0.85, (d) Two-phase signal, (e)

76 sec cycle length, (f) NB-SB green = 40 s, (g) EB-WB green = 28 s, (h) Yellow =4 s, (i) Third avenue has two lanes,



Level terrain, (p) Assume cross walk width = 3.0 m for all approaches, (q) Assume base saturation flow rate = 1900

pc/h/lane, (r) Assume , (s) No buses, (t) Left turn correction factor , (u) Pedestrian-Bicycle effects on

turning , and (v) Vehicle arrival type (AT) is 4 (w) Type of control is pre-timed (P) (x) East bound

flow is 750 ( Left 70, Through 640, and Right 40) Compute the the delay and peak-hour LOS of the EB approach using

12.


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HCM 2000 guidelines? Fill the relevant cells of the Exhibit 16-20,21, and 22.

Derive an expression for webster's uniform delay.13.

What are the various building blocks of area traffic control system SCOOT.14.

An urban arterial with 2 signalized intersections 400 m apart is to be coordinated in both directions with a design speed of

20 m/s and a cycle of 60 seconds. Determine the optimal offset at the second intersection with respect to both directions.

15.

A person standing at a stop line of signalized intersection found that the vehicles arrive at 3.7, 6.9, 9.7, 12, 14.1, 16,

17.9, and 19.8 seconds after the start of the green. The signal turns red at 20th second. Find the lost time, saturation

flow and lane capacity. (Assume cycle is 60 second, amber is 3 s)

16.

A person standing at a stop line of signalized intersection found that the vehicles arrive at 3.7, 6.9, 9.7, 12, 14.1, 16,

17.9, and 19.8 seconds after the start of the green. Find the lost time and saturation headway.

17.

In the above problem, If the actual green time allotted for phase 1,2,3 and 4 is 30, 35, 8, and 9 respectively, compute

the stopped delay for East-West movement (Assume uniform vehicle arrival).

18.

(a) Derive an expression for cycle length calculation for a signalized intersection. (b) Write briefly on Webster's stopped

delay calculations

19.

Highlight the broad principle of SCOOT system and its implementation issues for Indian cities.20.


and south bound direction is 60 kmph. If the cycle time is 120 seconds, split is 50 percent, and north bound traffic is 1000

vph and south bound traffic is 800 vph, compute offset and band width, if: (i) only north bound traffic is considered, and

(ii) both directions are considered. Illustrate the result using time-space diagram.

21.



/Assumptions: (a) EB and WB HV = 6 percent, (b) NB and SB HV = 9 percent (c) PHF = 0.85, (d) Two-phase signal, (e)

76 sec cycle length, (f) NB-SB green = 40 s, (g) EB-WB green = 28 s, (h) Yellow =4 s, (i) Third avenue has two lanes,



Level terrain, (p) Assume cross walk width = 3.0 m for all approaches, (q) Assume base saturation flow rate = 1900

pc/h/lane, (r) Assume , (s) No buses, (t) Left turn correction factor , (u) Pedestrian-Bicycle effects on

turning , and (v) Vehicle arrival type (AT) is 4 (w) Type of control is pre-timed (P). The north

22.


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bound flow is 420 ( Left 30, Through 370, and Right 20) Compute the saturation flow of the NB approach using HCM 2000

guidelines?

i) Illustrate the concept of control delay and oversaturate delay using appropriate sketches. ii) Derive an expression for

the stopped delay if you assume that vehicle arrival is uniform.

23.

Discuss briefly how the performance of a corridor is evaluated in HCM 2000.24.

Rotary

The entry and exit width of a rotary intersection are 9m and 11m respectively. The width of approaches at the

intersection is 15m. The traffic from the four approaches traversing the intersection is given below. If the traffic

composition is 50% car, 40% two-wheelers and 10% trucks and the passenger car units of two-wheelers and trucks are

0.5 and 3 respectively, find the capacity of the rotary using TRL formulae.

Approach Left turn Straight Right turn

North 500 800 300

South 400 350 450

East 250 400 500

West 300 450 500

1.


intersection is 15m. The traffic from the four approaches traversing the intersection is given below. Find the capacity of

the rotary.


North 500 800 300

South 400 350 450

East 250 400 500

West 300 450 500

2.


intersection is 14 m. The traffic from the four approaches traversing the intersection is given below. Find the capacity of

3.


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the rotary using TRL formulae.


North 550 750 340

South 450 390 450

East 280 400 520

West 350 480 500

The entry and exit width of a rotary intersection are 8 m and 10 m respectively. Assume the length of the weaving section

is four times the weaving width. The traffic from the four approaches traversing the intersection is given below. Find the

capacity of the rotary using TRL formulae.


North 550 750 340

South 450 390 440

East 280 400 520

West 350 480 500

4.

The entry and exit width of a rotary intersection are 10m each. The width of approaches at the intersection is 15m. The

traffic from the four approaches traversing the intersection is given below. Find the capacity of the rotary using TRL

formulae


North 415 643 350

South 549 358 424

East 408 450 402

West 450 423 493

5.

Transportation Systems Analysis

Select a current transportation issue for modeling and do the following.

(i) Identify the transportation system components, (ii) Activity system that is interest to the transportaion issue, (iii) What

could be a suitable service function, (iv) What could be a suitable demand function, (v) Visualize how the activity system

may change, (vi) Propose some transport improvement options, (vii) Illustrate flow predictions.

1.

Briefly discuss the principles of road classification and the classification of roads by Nagpur and Lucknow congress.2.


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Explain various vehicle factors affecting transportation.3.

Discuss the principles of classification of roads and the practice followed in India.4.

Explain terminal functions for airport terminal. Explain the status of knowledge about various types of transport terminals.

OR

Explain LP model formulation for the traffic assignment.

5.

Sketch various vehicle performance characteristics1.

List the technological and operational characteristics of mass transit modes2.

6.

Explain the use of production functions for a freight transport company.7.

Explain shadow pricing in economic analysis. Compare IRR method with NPV and B/C methods for their advantages and

limitations.

8.

Define the goals/objectives/problems relationship in the context of transportation system9.

Explain by any model, the transportation system components and their interactions/relationships.10.

Differentiate between financial and economic analysis.11.

Trace various vehicle performance chracteristics. (4)12.

Explain with examples, the production functions and their use.13.

Explain the status of knowledge about various types of terminals.14.

Explain transportation system-environment ensemble.15.

Explain the concept and importance of transportation systems problems.16.

List major challenges in the analysis of transportation systems analysis.17.

Explain the economic and political roles of transportation in society.18.

Differentiate between traffic management / transport management / transportation planning.19.

Bring out the importantance of criteria for differentiating MOC and MOE. OR

Explain the allocation to and performance of different major modes of transportation.

20.

Explain the concept of transportation system demand-supply equilibrium with the help of neat sketches.21.


the price of a seat by Rs 50 per user. The maximum number of people travel on this route is 4000. However, people will

drop out of travel at a rate of one person for every Rs 10 rise.

From next year airliner is planning to change fare structure, the new base price of a route is Rs 3000. However, they

22.


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increase the price of a seat by Rs 52 per user. The maximum number of people that travel from next year is 5000.

However, people will drop out of travel at a rate of 2 persons for every Rs 10 rise. What is the revenue generated by

airliner this year as well as next year? (8)

Define ramp meter and explain various objectives of ramp metering23.

In a case study, the average travel time for a particular stretch was found out to be 22.8 seconds, standard deviation is

5.951 and model time step duration is 10 sec. Find out the Robertson’s model parameters and also the flow at

downstream at different time steps where the upstream flows are as follows

24.

Calculate time gap for a platoon of 27 school children 5 in a row, consecutive time 2 sec width of crossing section is 7.5 m

and walking speed of children 0.9 m/s start up time 3 sec.

25.

Describe how traffic flow can be predicted using the concepts of system and by using

service and demand functions.

26.

State and illustrate the three relationships between transportation, activity, and flow system27.

Illustrate with a sketch a demand function, service function and how they are used to predict flow and the associated

impact

28.


the price of a seat by Rs 50 per user. The maximum number of people that may travel on this route is 4000. However,

people will drop out of travel at a rate of one person for every Rs 10 of the actual price. From next year airliner is

planning to change fare structure, the new base price of a route is Rs 3000. However, they increase the price of a seat by

Rs 45 per user. The maximum number of people that travel from next year is 5000. However, people will drop out of

travel at a rate of two persons for every Rs 10 of the actual price. What is the revenue generated by airliner this year as

well as next year?

29.

A highway connecting two small cities has the following characteristics. The time to travel on a certain stretch of a

highway is =12+0.01 , where is the flow of vehicles (veh/hr). The demand function is =4800+0.01 .

(a) Estimate the equilibrium flow and travel time

30.


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(b)The traffic department wants to close the existing highway and replace it with a better highway with a supply function

of =12+0.006 , with the same demand function. How much additional traffic will will be induced by this new highway?

(c) Citizens currently using the existing highway want to continue using it, and in addition, demand the new highway as

well. What will be the equilibrium flow and travel time for this scenario, assuming the demand for travel time remains

unchanged (Wardrop's principle applies)?

(d)If the new road is built with a supply function =10+0.005 , and the existing highway is uased as well, what would

be the equilibrium flow and travel time?

Capacity & LOS

A major arterial is meeting a minor arteial and is located in the central business district (CBD) of a small urban area.

Compute the delay and peak-hour LOS for west bound direction. Main Street has four lanes of 3.3 width, two in each

direction and minor street has two lanes of 4.5m width, one in each direction. Heavy vehicle percentage is 5 % in east

and west bound direction and 8 % in north and south bound. Assume no parking at intersection and no buses. Peak hour

factor is 0.90. Pedestrian volume is 100 p/h in all approaches, Bicycle volume is 20 bicycles/h for all approaches,

Movement lost time is 4 s, yellow time is 4 s and terrain is level. Assume base saturation flow rate ,

crosswalk width of 3.0 m, and heavy vehicle adjustment factor 2.0. Left turn adjustment factor in east bound direction is

0.716 and west bound direction is 0.901. Left turn pedestrian/bike adjustment factor is 0.998 and right turn

pedestrian/bike adjustment factor is 0.995 for all approaches. The traffic volume is given in the input worksheet. Report

the results in the capacity and LOS worksheet and submit alongwith the answer sheet

1.

How do you measure operational performance of a given urban arterial? Explain the HCM method of assessment2.

A segment of undivided four-lane highway on level terrain has field-measured FFS 74.0-km/h, lane width 3.4-m,

peak-hour volume 1,900-veh/h, 13 percent trucks and buses, 2 percent RVs, and 0.90 PHF. What is the peak-hour speed,

and density for the level terrain portion of the highway? ( and )

3.

Consider an existing four lane free-way in rural area, having very restricted geometry with rolling terrain. Peak hour

volume is 2000 veh/h with 5% trucks. The traffic is commuter type with peak hour factor 0.92 and interchange density as

4.


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0.6 interchanges per kilometer. Free-way consists of two lanes in each direction of 3.3 m width with lateral clearance of

0.6 m. Find the LOS of free-way during peak hour.

Discuss in detail (i) the concept of capacity and LOS in HCM 2000 and (ii) how it is used in the analysis of ramp metering.5.

ITS

Show a typical ITS architecture and write briefly on the communications involved.1.

Describe how RP & SP surveys can be used for ITS evaluation.2.

Discuss briefly any three services offered and their respective implementation challenges for each of the following ITS

user service components (i) travel and traffic management, and (ii) public transport operations.

3.

Advanced Topics

Assume a single lane road stretch divided into 9 cells and vehicles are present in the first ,fourth , seventh and eight cells

with 3, 2 , 2, 1 as their velocities respectively. Apply the rules of CA and update the position of the vehicles in the next

second.

1.

Vehicle A is approaching from west and vehicle B from south. After collision A skids north of east and B skids

south of east. Skid distance before collision for A is 18 m and B is 26 m. The skid distances after collision are 30m and 15

m respectively. Weight of A and B are 4500 and 6000 respectively. Skid resistance of pavement is 0.55 m. Determine the

pre-collision speed.

2.

A bus stalled at a signal emits pollutants at the rate of 20000 g/s. The exhaust pipe is situated at height of 0.75 m from

the Ground level. What will be the concentration of pollutants inhaled by a man living on the first floor of a building with

storey height 3.5 m? The building is situated at a lateral distance of 5 m from the main road and longitudinal distance of

4 m downwind of the source. Assume a wind velocity of 10 m/s, = 375 m and = 120 m. The concentration of the

emission is given by

3.

What is the total fuel consumption of a vehicle travelling on a 10 km stretch of road if the average stopped delay is 6 s

and it stops thrice during its journey. Assume that the fuel consumption rate per unit distance while cruising is 0.0045,

the fuel consumption rate per unit time while idling is 0.0035, and the excess fuel used in decelerating to stop and

accelerating back to cruise speed is 0.002. If the vehicle is cruising throughout the stretch of the road, what is the

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decrease in fuel consumption?

Illustrate with a numerical example of your choice how energy theory is used in the accident reconstruction of a collinear

impact.

5.

Describe the working principle and various control parameters of a vehicle actuated controller and its limitations.6.

Trip Generation

The trip rate ( ) and the corresponding household sizes ( ) from a sample are shown in table below. Compute the trip

rate if the average household size is 3.25 (Hint: use regression method).

Household size(x)

1 2 3 4

Trips 1 3 4 5

per 3 4 5 8

day(y) 3 5 7 8

1.

A study area has four zones and it is observed that they generate 65, 84, 115, 105 trips per day. The average income is

respectively 1400, 2400, 3400, and 2700 and the population is 3000, 2500, 3500, and 4000. Government proposes two

major policy changes in zone 2. First proposal will result in an increase of income by 40 % and the second will increase

the population by 50 %. Compute the trips that will be generated as a result of these policy changes.

2.

A study area has four zones and it is observed that they generate 70, 89, 120, 110 trips per day. The average income is

respectively 1500, 2500, 3500, and 2800 and the population is 3100, 2600, 3600, and 4100. Government proposes two

major policy changes in zone 2. First proposal will result in an increase of income by 40 % and the second will increase

the population by 50 %. Which proposal will generate more trips?.

3.

Trip Distribution

The trip productions from zones 1, 2 and 3 are 110, 122 and 114 respectively and the trip attractions to these zones are

120,134 and 118 respectively. The cost matrix is given below. The function

1.


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Compute the trip matrix using doubly constrained gravity model. Provide one complete iteration.

The base year trip matrix for a study area consisting of three zones is given below. The productions from the zones 1,2

and 3 for the horizon year is expected to increase to 95, 102, and 98 respectively. The attractions for the zones 1 and 2

are expected to increase to 85 and 115 respectively. Compute the trip matrix for the horizon year.

1 2 3

1 25 33 27

2 28 38 14

3 22 19 24

2.

Derive expressions for the distribution factors of a doubly constrained gravity model.3.

The trips originating from zones 1, 2 and 3 are 110, 122 and 114 respectively and the trips ending at these zones are

120, 108 and 118 respectively. Assume distance within the zones is of 1 km while it is 1.2 km from 1 to 2, 1.8 km from 1

to 3 and 1.5 km from 2 to 3. If we also assume the deterance to travel is inverse to the square of the distance, then how

many trips will be taking place from each zone to the other zone.

4.

Mode Choice

The total number of trips from zone to zone is 4200. Currently all trips are made by car. Government has two

alternatives- to introduce a train or a bus. The travel characteristics and respective coeffcients are given in table. Decide

the best alternative in terms of trips carried.

coefficient 0.05 0.04 0.07 0.2 0.2

car 25 - - 22 6

bus 35 8 6 8 -

train 17 14 5 6 -

1.

The total number of trips from zone to zone is 4000. Currently all trips are made by car. Government plans to

introduce a train and a bus. The travel characteristics and respective coeffcients are given in table. Compute the trips

2.


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carried by each mode and also the fare collected by bus and train.

coefficient 0.04 0.05 0.06 0.1 0.1

car 20 - - 25 6

bus 40 10 5 10 -

train 15 15 5 5 -

A person is currently using his car to go to office which takes about 15 minutes and costs about Rs. 33 for fuel and

parking. One of his friends suggested to use a bus instead which takes about 30 minutes but costs only Rs. 20. However,

another friend suggested him to use a metro which takes only 20 minutes but costs Rs. 15. Assuming that the weightages

given to travel time and travel cost by the person are 0.7 and 0.5 respectively, (a) What is the probability that the person

will stop using car? (b) Given that the person stops using car, what is the probability that he will use metro?

3.

Total number of trips (people) from zone A to zone B is 1000. Some travel by car which takes 20 minutes and they have

to spend Rs. 30 for fuel and Rs. 10 for parking. Some travel by train which takes 30 minutes with a fare of Rs. 10 and

incurs a waiting time of 10 minutes. Suppose a new taxi company starts a service which takes the same travel time as

that of a car and the charge is Rs. 15 per person. But the person has to wait about 17 minutes to get a taxi. How many

people will travel by the newly introduced taxi service. How many people will shift from car to the new taxi service.

Assume that the people of the city give a weightage of 0.7 for their time and 0.5 for their money.

4.

A roadway has 3 lanes. A vehicle is travelling in the middle lane (i.e., 2nd ) and has the options of either travelling in the

same lane or changing either to the 1st or 3rd lanes. These decisions are governed by the utlities of the lanes ( ) and

gaps ( ) . If the vehicle has decided to leave the current lane, the decisions of choosing among the other two lanes are

governed by the utilities of gaps ( ) in those lanes. On which lane would the vehicle like to travel probably?

Lane

No.

Relative

speed

(m/s)

Front

gap

(m)

Lead

gap

(m)

Lag

gap

(m)

1 5 8 5 3

5.


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2 3 - - -

3 8 - 9 6

Trip Assignment

Calculate the system travel time and link flows by doing user equilibrium assignment for the network in the given figure.

Verify that the flows are at user equilibrium.

[width=6cm]1007.eps

1.

Using shortest path algorithm and given O-D and t-t matrix, assign the travel demand to the given four node network.2.

Explain step by step, the computational procedure for the shortest path algorithm.3.

Calculate the system travel time and link flows by doing user equilibrium assignment for the network in the given

figure [*]. Verify that the flows are at user equilibrium.

Figure: Example

network

[height=1.8cm]1122.eps

4.


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Calculate the system travel time and link flows by all or nothing, user equilibrium, and system optimum assignment for a

network with two nodes having two paths as links. The travel time functions are and . The total flow on

the two links is limited to 14.

5.

A network has two nodes with two paths as links. The travel time functions are given as 18+4 and 12+2 . The total

flow on the two links is limited to 16. What will be the system travel time and link flows if we ignore the effects of

congestion and at the same time assuming user equilibrium conditions.

6.

A transport network is shown below along with the free flow link travel time. Given , , ,

, , where is the demand (trips) from node to . Compute the total system travel time and average

travel time if we assume that each link has infinite capacity. Show also the path flows and link flows.

[width=6cm]1128.eps

7.

Calculate the system travel time and link flows by the following cases for a network with two nodes having two paths as

links by All or nothing, User equilibrium, and System optimum assignment methods. The travel time functions are

and and total flow on the two links is limited to 12.

8.

Calculate the system travel time and link flows by system optimum assignment using Frank Wolfe algorithm for a network

with two nodes having two paths as links. The travel time functions are and . The total flow on the two

links is limited to 14.

[width=4 cm]1713

9.

Calculate the system travel time and link flows for the network in the given figureAssume that the drivers are forced to

take path that will result in an overall minimum travel time. Given that the total flow is 14.

[width=3cm]1007j.eps

10.

A transport network is shown below along with the free flow link travel time. Given , , ,

, , where is the demand (trips) from node to . Compute the total system travel time and average

travel time if we assume that each link has infinite capacity. Show also the path flows and link flows.

[width=4.5cm]1128j

11.

Systems Planning


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Explain the procedure for urban transportation planning.1.

Write the formulation of a network capacity exapansion problem.2.

Discuss briefly with the help of a block diagram how four step (stage) travel demand modeling is used to predict future

link flows

3.

State and mathematically formulate: (a) User equilibrium conditions, and (b) Wardrops II principle.4.

State the user equlibrium conditions mathematically and explain the terms.5.

Discuss briefly with the help of a block diagram how four step (stage) travel demand modeling is used in transportation

planning.

6.

Suppose you were asked to do travel demand modelling for Mumbai, illustrate the following with a typical sketch. (i)

Study area (ii) Internal zones (iii) External zones (iv) Cordon line (v) Screen line

7.

Geometric Design

A national highway passing through a rolling terrain has two horizontal curves of radius 450 m and 150 m. Design the

required superelevation for the curves as per IRC guidelines.

1.

Derive the expression for computing superelevation at a horizontal curve. Give the step by step procedure for designing

superelevation for a highway.

2.

What are the factors controlling highway alignment?3.

Derive the expression for overtaking sight distance for a two lane bi-directional highway with the help of time-space

diagram. Explain the constants used and the IRC guidelines for their values.

4.

Design the radius of a horizontal curve and the length of its transition curve for a two lane national highway passing

through a plain terrain. Assume: maximum super elevation, all the vehicles travel at the design speed, rate of

introduction of super elevation is 1 in 150, pavement is rotated with respect to centerline, rate of change of centrifugal

acceleration is 0.57 and a ruling design speed.

5.

Discuss the effects of a horizontal curve on vehicle stability and derive the conditions of overturning and skidding.6.

Derive the expression for set back distance with the help of a neat sketch when the sight distance is greater than the

length of the curve for a multilane highway.

7.

Illustrate the overtaking operation with a neat time-space diagram for a two lane highway assuming unidirectional traffic.8.

Derive the relation for the setback distance for a multi lane highway when the sight distance is less than the length of the9.


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curve. Provide neat sketch.

A valley curve is formed by a descending gradient of ( ) 4 percent and an ascending gradient of ( ) 3.3 percent.

Design the length of the valley curve for a design speed of 80 kmph. State assumptions clearly and provide detailed

steps.

10.

Compute the overtaking sight distance for a two lane National Highway for a design speed of 90 kmph. Assume the rate

of overtaking acceleration as 0.6 m/sec and rest of the data based on IRC specification

11.

Compute the setback distance of a two lane National Highway for a design speed of 90 kmph. Assume an OSD of 624

metes, length of the curve as 250 meter, and the rest of the data based on IRC specifications.

12.

A national highway passing through a rolling terrain has two horizontal curves of radius 600 m and 100 m. Design the

required superelevation for the curves as per IRC guidelines.

13.

Derive the relation for the setback distance for a multi lane highway when the sight distance is less than the length of the

curve. Provide a neat sketch.

14.

A valley curve is formed by a descending gradient of 3 percent and an ascending gradient of 4 percent. Design the length

of the valley curve for a design speed of 80 kmph. State assumptions clearly and provide detailed steps.

15.

A huge pipeline is going across a road at the same level. Therefore, a bridge is to be constructed across the pipeline. If

the maximum permissible gradient is 3 %, what is the length of the vertical curve at the top of the bridge. Assume a

stopping sight distance of 150 m.

16.

For a given road following speed data is collected. 25, 31, 36, 39, 42, 44, 47, 48, 49, 51, 52, 52, 53, 54, 55, 56, 57, 57,

57, 58, 59, 60, 60, 62, 63, 64, 65, 66, 66, 68, 68, 69, 70, 70, 71, 73, 75, 79, 85, 89, 90. What is the speed you will

recommend for designing sight distance or radius of circular curve?

17.

Pavement Analysis & Design

Find ESWL at a depth of 50 cm for a dual wheel carrying 2044 kg each. The center to center tyre spacing is 25 cm and

distance between the walls of the tyre is 10 cm.

1.

Design the length and spacing of dowel bars if the the radius of relative stiffness is 80 cm, design wheel load is 3000 kg,

joint width is 2.5 cm, load transfer is 40%, permissible bending, shear, and bond stress are 1400, 1000 and 100 kg/cm

respectively. Assume dowel bars of 2 cm dia.

2.

Calculate the critical load stress in a cement concrete pavement using Westergard's equations, if the wheel load is3.


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5000 kg, modulus of elasticity of concrete 3.0 10 kg/cm , pavement thickness is 20 cm, Poisson's ratio of concrete is

0.15, modulus of sub-grade reaction is 6 kg/cm3 and radius of contact area is 15 cm.

Explain the three main requirements of a bituminous mix. (ii) Find the optimum bitumen content for test result given in

table. (3+3) [6]

Stability Flow

4 499.4 9.0 12.5 34 2.17

5 717.3 9.6 7.2 65 2.21

6 812.7 12.0 3.9 84 2.26

7 767.3 14.8 2.4 91 2.23

8 662.8 19.5 1.9 93 2.18

4.

(i) Explain ESWL. (ii) Find ESWL at depths of 5 cm, 25 cm, and 60 cm for a dual wheel carrying 2044 kg each; the center

to center tyre spacing is 27 cm and the width of the tyre is 26 cm.

5.

Design as per IRC37:1974 a flexible pavement for a design life of 12 year having the present ADT of 2000 commercial

vehicles with 7% annual growth. The sub-grade CBR is 8%. Use poorly and well graded granular layers of 20% and 70%

CBR respectively. Provide a wearing course of minimum 5 cm thick.

6.

Using IRC 37:2001 design procedure, find the total thickness needed and the composition of a flexible pavement for a (i)

single lane road and (ii) two lane dual carriage way. Given that the sub-grade CBR is 4%, initial traffic on both directions

is 2000 commercial veh/day, growth factor is 7%, vehicle damage factor is 4.5 and design life is 12 years. Suggest the

changes in the design if the CBR of the sub-grade is improved to 8% (only for case ii).

7.

Calculate the interior stress of a cement concrete pavement using Westergaard's stress equation, if the design wheel load

P=5000 kg, modulus of elasticity E=3.0 10r kg/cm , pavement thickness h=20 cm, Poisson's ratio of concrete

=0.15, modulus of sub-grade reaction K=6.0 kg/cm3 and radius of contact area, a=15 cm.

8.

Design length and spacing of dowel bars. Given that the pavement thickness is 25 cm, radius of relative stiffness is 70

cm, design wheel load is 5000 kg, joint width is 2 cm, load transfer is 40%, permissible shear, flextural, and bond stress

are respectively 1000, 1400, and 100 kg/cm . Assume dowel bars of 2.5 cm diameter and length of the bar should be

multiples of 5 cm. Provide detailed steps and appropriate sketches.

9.

Let the number of load repetition expected by 80 kN standard axle is 1000, 160 kN 100, and 40 kN is 10000. Find the

equivalent axle load if the equivalence criteria is fatigue cracking. Assume the following fatigue cracking model:

10.


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with .

The volume and weight of a Marshall specimen is 475 cc and 1100 gm respectively. Assuming absorption of bitumen in

aggregate is nil, find , , , and ; The specific gravities and weight proportions of aggregate and bitumen

used for the mix is given below.

Item A_1 A_2 A_3 A_4 B

Wt (gm) 1050 1000 300 150 100

Sp. Gr 2.63 2.51 2.46 2.43 1.05

11.

Illustrate the analytical method of proportioning of aggregates with a hypothetical example.12.

Compare flexible and rigid pavements, their failure criteria, design approaches, and influencing design factors.13.

Write notes on: (i) resiliant modulus, (ii) modulus of subgrade reaction, (iii) Abrasion test, and (iv) Ductility test14.

Let the number of load repetition expected by 120 kN axle is 1000, 160 kN is 100, and 40 kN is 10000. Find the

equivalent standard axle load if the equivalence criteria is rutting . Assume 80 kN as starndard axle load and the rutting

model is where and .

15.

Calculate the critical load stress in a cement concrete pavement using Westergard's equations, if the wheel load is

4000 kg, modulus of elasticity of concrete 3.0 10 kg/cm , pavement thickness is 25 cm, Poisson's ratio of concrete is

0.15, modulus of sub-grade reaction is 6 kg/cm and radius of contact area is 15 cm.

16.

Find ESWL at a depth of 40 cm for a dual wheel carrying 2044 kg each. The center to center tyre spacing is 20 cm and

distance between the walls of the two tyres is 10 cm.

17.

Design the length and spacing of tie bars. Given that the pavement thickness is 20 cm, and width of the road is 7 m with

one longiudnal joint. The unit weight of concrete is 2400 kg/cm , the coefficient of friction is 1.5, allowable working

tensile stress in steel is 1750 kg/cm ,allowable bond stress for plain and deformed bars are as 17.5 and 24.6 kg/cm .

18.

The imprints of a dual tandem wheel configuration (one side) is shown in the following figure. Each wheel carries 1540 kg.

What will be the load of a single wheel which replaces these four wheels but results in the same stress as the original at a

depth of (i) 5, (ii) 25, and (iii) 50 cm.

[width=3cm]1319

19.

A new two lane dual carriageway road is proposed to be constructed. The current traffic (2009) on that road is 1800

commercial vehicles/day for both directions. The construction period is 3 years and the traffic grows at 7.5% per year

20.


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during this time. If the design life is 15 years after opening to traffic, growth rate during design life is 8.5% and subgrade

soil has a CBR of 4% compute the thickness and composition of pavement assuming a vehicle damage factor of 2.0.

Three aggregates mixes, named as A, B, and C, need to be mixed to get a certain gradation. The sieve size, the gradation

of A, B, and C, upper and lower limit of the required gradation are given in the table below. Two proportions are planed:

first has 20, 30, 50 % of A, B, and C respectively; and the second has 10, 30, and 60 % of A, B, and C. Verify whether

these proportions satisfies the required gradation.

Sieve Size A B C Upper Lower

0.075 30 5 3 5 10

0.15 75 20 9 12 22

0.3 85 40 18 20 35

1.18 95 70 35 40 55

4.76 100 90 55 60 75

12.7 100 100 85 90 100

25.4 100 100 100 100 100

21.

Prof. Tom V. Mathew 2013-08-14


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