chapter 5 4e lecture on traffic stream characteristics
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traffic stream characteristicsTRANSCRIPT
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Chapter 5 1
Chapter 5: Traffic Stream Characteristics
Explain the difference between uninterrupted flow and interrupted flow
Explain the three principal traffic-stream parameters and how to obtain them
Explain the relationship among the three macroscopic principal traffic-stream parameters
Chapter objectives: By the end of this chapter the student will be able to:
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Chapter 5 2
5.1 Types of traffic facilities
Uninterrupted flow facility
No external factors to cause periodic interruption of flow. Traffic flow is a product of interaction between vehicles and geometric and environmental conditionsE.g. Basic sections of a freeway
Interrupted flow facility
Have external devices that periodically interrupt traffic flow Constant stopping and restarting neededE.g. Urban streets and arterials
Remember it does not mean the quality of operation.
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Chapter 5 3
5.2 Traffic stream parameters
Macroscopic parameters Microscopic parameters
Volume or flow rate, v or q = 1/h
Headway (or time headway), h
Speed, S or v Speeds of individual vehicles, s
Density, k or D = 1/d Spacing (or distance headway), d
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Chapter 5 4
5.2.1 Volume and flow rate
Can you define these?
AADT
AAWT
ADT
AWT
DDHV = AADT * K * D
What’s the difference between “Volume” and “Flow (or Flow rate)”?
Sub-hourly volume and flow rate
Define PHF = (peak hourly volume) / (max. rate of flow for that hour)
PHF = V/(4 * V15)
What does this tell you?
v = V/PHF
= peak flow rate for the 15-minute peak period
(Review Tables 5.1 and 5.2 & 5.3 queuing)
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Illustration of Daily Volume Parameters
Chapter 55Prob 5-4 is similar to this one.
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6
Hourly Volumes
Chapter 5
DDHV=ADT*K*D
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Subhourly Volume and Rates of Flow
Chapter 5 7
If capacity is 4,200 vph, then the 15-min capacity volume is 4,200/4 = 1,050.
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Peak Hour Factor, PHF
Chapter 5PHF
Vv
VGiven
PHF
Example
V
VPHF
flowofrate
volumeHourlyPHF
m
:_
875.0200,1*4
200,4
:
*4
__.max
_
15
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Example: Prob. 5-6
Chapter 5
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Chapter 5
5.2.2 Speed and travel time
Time mean and space mean speed: Know the difference?
Time mean speed (TMS)
Average speed of all vehicles passing a point over some specified time period TMS = ∑ (d/ti)/n
Space mean speed (SMS)
Average speed of all vehicles occupying a given section over some specified time period or harmonic mean of individual speeds. SMS = d/(∑(ti)/n) = nd/∑(ti)
(See page 101 and Table 5.5)
sft
n
nnSMS
sftn
nnTMS
/7.583
)2*0.440.88
/0.662
)0.440.88
Every 2 seconds vehicles arrive at
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Illustrative Computation of TMS and SMS
Chapter 5 11
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Chapter 5 12
5.2.3 Density and occupancy
Definition: the number of vehicles occupying a given length of highway or lane (vpm, vpmpl, v/km, v/km/lane)
Relationship among v, S, D:
v = S * D
Flow rate = Speed * Density
Unit length (1 mile or 1 km)
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Chapter 5 13
Speed
ELpt
Speed
Lpt v )()('
Occupancy as a surrogate parameter for density
Density is difficult to measure. So, we use “occupancy” as a surrogate measure for density. This can be obtained by traffic detectors of any kind.
Occupancy: the percent of the roadway (in terms of time) that is covered (occupied) by vehicles.
Apparent occupancy
Actual occupancy
Speed
ELLpt v
)(
This is the occupancy measured at a point.
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Chapter 5 14
Flow rate, speed and occupancy are given; estimate density
ELL
miftOD
v
app
5280
mi
veh
hourmi
hourveh
S
q
Speed
rateFlowD
_
Typically occupancies given by the detectors are apparent occupancies.
dv
app
LL
miftOD
5280
But if average flow rate and average speed for a certain time period are given, density can be computed as:
(Eq.5-7)
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Chapter 5 15
Derivation of the Density-Occupancy Relationship
ELLOD
ELLD
ELL
S
q
S
ELL
T
N
T
TO
S
ELLN
S
ELLNT
S
ELLt
tNhrT
t
ELL
t
ELLmphS
Vapp
V
V
SMS
SMS
Voapp
SMS
V
SMS
Vo
SMS
Vp
po
p
V
p
VSMS
52805280
5280
5280
1
5280
5280
3600
3600
1
5280
3600
3600
5280
3600
3600/
5280/)(
)(
)()(
Estimate SMS using detector data
Compute total time occupied (not occupancy) by N vehicles detected in time period T
Solve the first equation for average time occupied by each vehicle
Plug in the 3rd eq into 2nd eq
Compute the occupancy Oapp. N/T turned out to be flow rate, q. Also q/SMS is density by definition. Now the relation between occupancy, Oapp, and density, D, was established.
Solve for D. Voila, you get Eq. 5.7.
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Chapter 5 16
5.2.4 Spacing and Headway: Microscopic Parameters
These are in English units.
D (Density) = 5280 / da where da is average spacing
v (Flow rate) = 3600 / ha where ha is average headway
S (Average speed) = da / ha
Spacing or Space headway
Headway or Time headway
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5.3 Relationships among flow rate, speed, and density
Flo
w (
v)
Density (D)
Do you remember whose flow model is used for this?
S = Sf –(Sf/Dj)*D
v = S*D
= [Sf –(Sf/Dj)*D] *D
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5.3 Relationships among flow rate, speed, and density (2)F
low
(v)
Density (D)
Optimal flow or capacity
Optimal (critical) density
Jam density
Mean free speed
Optimal speed
Speed is the slope. S = v/D
Do you remember whose flow model is used for this?
S = Sf –(Sf/Dj)*D
Uncongested flow Congested
flow
Unstable flow area
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Beck St. NB Work Zone Entry Area,
Chapter 5
0 200 400 600 800 1000 1200 14000
10
20
30
40
50
60
70
80
90
Uncongested
Congested
Statistical Model
Flowrate (veh/h/ln)
Spee
d (m
i/hr
)
0 10 20 30 40 50 600
10
20
30
40
50
60
70
80
90
Uncongested
Congested
Statistical Model
Greenberg
Density (veh/mi/ln)
Spee
d (m
i/hr
)