sj 5121 - karakteristik arus lalu lintas
TRANSCRIPT
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Karakteristik Lalu Lintas
Kuliah ke - 3SJ-5121 Rekayasa Lalu Lintas
Harun alRasyid Lubis
Program Magister Sistem & Teknik Jalan Raya ITB
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Outline Introduction
Basic Traffic Flow Theory
Definitions ; LHR, VJP
PHF (Peak Hour Factor)
Speed (space mean speed Vs time mean speed)
Traffic Density, Headway and spacing Basic Relationship
Simple Car following theory Queueing theory
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Volume Jam Perencanaan
(VJP)
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Basic Relationship (S,D,V)
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ILLUSTRASI LOS
T ffi Fl C
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Traffic Flow Concepts Volume, speed and density
Average travel speed or space mean speed and time mean speed
If travel times t 1, t2, t3,...,t n are measured for n vehicles traversing asegment of length L, the average travel speed (space mean speed) wouldbe
5 vehicles over a given one-mile section with travel times (in minutes) of1.0, 1.2, 1.5, 0.75 and 1.0 respectively. Average travel time = 5.45/5=1.09min = 0.0182 hr. u = 1/0.0182 = 55.05 mph.
Time mean speed is the arithmetic average of all vehicles passing a givenspot on a roadway section. Space mean speed < time mean speed
=
= nni
t
Ln
it n
Lu
11)/1(
= n
n
ilit n
iln
u
1
1
,)/1(
)/1( speaking, Generally
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Speed-Flow-Density
Relationships Density is defined as the number of vehicles occupying a givenlength of a lane or roadway at a particular instant; density can be
computed using the relationship: k = n/l. Alternatively, if q is therate of flow and u is average travel speed, k = q/u. Unit of densityis vehicles per mile (vpm).
Spacing is defined as the distance (ft) between successive vehicles
in a traffic stream, as measured from front bumper to front bumper;headway is the time (sec) between successive vehicles, as theirfront bumpers pass a given point. Headway (sec/veh) = spacing(ft/veh)/speed (ft/sec). Density = 5,280/spacing. Flow rate or
practical capacity = 3,600/average headway.
jk k - 1
f u =u
j
2
f k k
-k u = q
f u
2u -uj
k = qmmm k u=q
2/k =k jm
2/f
u=mu
4j
k f
u
= mq
Greenshields Model (1935)
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k j 0
u f
Density
Sp
eed
Greenshields Model (1935)
Alternative Functional Forms
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Flow (q)
Density (k)
Optimal flowor
capacity,q max
Optimaldensity, k o
Jamdensity, k j
Uncongestedflow
Congestedflow
Flow-Density
Relationship
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Speed (u)
Flow (q)
Free-FlowSpeed, u f
Uncongestedflow
Congestedflow
Speed-FlowRelationship
Empirical Speed-Flow
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Empirical Speed-FlowRelationship
Traffic flow is not uniform. Rather may follow a Poisson processdescribed by p(n) = e - t ( t)n /n! Poissonian arrivals also imply anegative exponential distribution for vehicle headways
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Speed-Flow relationships
Speed(S) Figure 1: A typical speed-flow relationship
S0
SF
SC
F C Flow (V)
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Equation of S-F Relationship S 1(V) = A 1 B 1V V < F ........................ (2) S 2(V) = A 2 B 2V F < V < C ............ (3)
A1 = S 0 B1 = (S 0 S F) / F A2 = S F + {F(S F S C)/(C F)} B 2 = (S F S C) / (C F)
S 1(V) and S 2(V) = speed (km/h) V = flow per standard lane (veh/h) F = flow at knee per standard lane (veh/h) C = flow at capacity per standard lane (veh/h)
S 0 = free-flow speed (km/h) S F = speed at knee (km/h) S C = speed at capacity (km/h)
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Flow-Delay Curves Exponential function appropriate to represent effects of
congestion on travel times. At low traffic, an increase in flows would induce small increase in
delay. At flows close to capacity, the same increase would induce a
much greater increase in delays.
Time (t) Figure 2: Effects of Congestion on Travel TimestC
t0
C Flow (V)
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Equation of F-D Curve t(V) = t 0 + aV n V < C ........................ (4)
t(V) = travel time on link t 0 = travel time on link at free flow a = parameter (function of capacity C with power n) n = power parameter input explicitly V = flow on link
Parameter n adjusts shape of curve according to link type. (e.g.urban roads, rural roads, semi-rural, etc.)
Must apply appropriate values of n when modelling links ofcritical importance.
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Converting S-F into F-D If time is t = L / S equations 2 and 3 could be written:
t1(V) = L / (A 1 B 1V) V < F .......................... (5)
t2(V) = L / (A 2 B 2V) F < V < C ............. (6)
These equations represent 2 hyperbolic (time-flow) curves of ashape as shown in figure 3.
Use similar areas method to calculate equations. Tables 1 inpaper gives various examples of results.
Time (t) Figure 3: Conversion of Flow-Delay CurvetC
tF
t0F C Flow (V)
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Simple Queuing Theory Applications
Use D/D/1 only when absolutely sure that both arrivals and departures aredeterministic
Use M/D/1 for controls unaffected by neighboring controls
Use M/M/1 or M/M/N as general case
Factors that could affect your analysis:
Neighboring system (system of signals)
Time-dependent variations in arrivals and departures
Peak hour effects in traffic volumes, human service rate changes
Breakdown in discipline People jumping queues! More than one vehicle in a lane!
Time-dependent service channel variations
Grocery store counter lines
G hi ll A l i g Q
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Graphically Analyzing Queues
Vehicles
Time
QueueDissipation
Delay max
Queue attime t 1
Delay of n th
arriving vehicle
Total VehicleDelay
t1
Qmax
D/D/1
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Queuing Components
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Multi-Channel Queues
Numerically Analyzing
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Numerically Analyzing
Queues
1
21
= w
M/M/1
)-2(1 2-2 = Q
Average ArrivalRate
Average DepartureRate
1-2
21 = t
1and /,
M/M/N
( ) = Q N1 1NN! P 21+N
0 +
Q = t
= +=
1
0
0
)1(!!
1N
n
N
C
n
C
C
N N
n
P
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