SJ 5121 - Karakteristik Arus Lalu Lintas

8/7/2019 SJ 5121 - Karakteristik Arus Lalu Lintas

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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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SJ 5121 - Karakteristik Arus Lalu Lintas