bfc32302 chapter 1-b

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1

BFC 32302 Traffic Engineering and Safety Lecturer: Dr. Basil David Daniel

RAFFIC FLOW HEORY

RAFFIC FLOW HEORY

1) SPEED (v)

Speed is ......defined as rate of motion, or distance per unit time

Space Mean Speed, v s

… is the average travel speed

T!""#$ "%&' P!!METES

∑=

=n

i

i

s

t

nLv

1

n numer of travel times oserved

% length of the high*a+ segment (m)

ti travel time of the i-th vehicle totraverse the section (hr)

∑=

t

nLv s

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RAFFIC FLOW PARAME ERS

RAFFIC FLOW PARAME ERS

Time Mean Speed, v t… is the arithmetic mean of the measured speeds of allvehicles passing a fied roadside point during a given intervalof time (the individual speeds are no*n as /spot speeds0)

n numer of vehicles oserved

v i

spot speeds (mhr)

% average length travelled + the vehiclesn

v

v

n

i

i

t

∑=

= 1

elationship et*een Space Mean Speed and Time Mean Speed

s

2

s

st

vvv

σ

+=t

2

t

tsvvv

σ

−=or

s2 variance of the space mean speed

t2 variance of the time mean speed

n

)vv( 2ti∑ −

n

t

L

vt

= ∑

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Example 1

xample 1

Three vehicles pass a ilometer post at 34, 56 and 67 mhr,respectivel+. 'hat is the time mean speed of the three vehicles8

!lso, find the approimate space mean speed.

mhr633

547560=

++=t v

78

3

)6354()6375()6360( 2222 =−+−+−

=t σ

mhr8.6163

7863 =−= sv

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RAFFIC FLOW HEORY

RAFFIC FLOW HEORY

2) 9&%:ME (9)

9olume is ......the numer of vehicles oserved or predicted to pass a pointduring a given time interval.

;) !TE &" "%&' (

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RAFFIC FLOW HEORY

RAFFIC FLOW HEORY

7) DE=S#T> ()

Densit+ is ......the numer of vehicles occup+inga given length of lane orroad*a+, averaged over time.

:suall+ epressed in vehiclesm.

Densit+ can e measured directl+through aerial photograph+.

Densit+ can also e calculated usingthe e

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RAFFIC FLOW HEORY

RAFFIC FLOW HEORY

6) SP!$#=@ (s)

Spacing is ......the distance (meters) et*een successive vehicles in a trafficstream, measured from front umper to front umper.

3) AE!D'!> (h)

Aead*a+ is ......the corresponding time (seconds) et*een successive vehiclesas the+ pass a point of a road*a+.

Spacing and Aead*a+ are related to

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RAFFIC FLOW HEORY

RAFFIC FLOW HEORY

5) %!=E &$$:P!=$> (%&)

%ane &ccupanc+ is ......the ratio of the time that vehicles are present at a detectionstation in a traffic lane compared to the time of sampling.

%& Total time vehicle detector is occupied to

Total oservation time T

to % B $ *here % average length of vehicle

v s $ distance et*een loop detector

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RAFFIC FLOW HEORY

RAFFIC FLOW HEORY

Densit+ can e estimated using the epression ......

%& 1444

% B $

%ane occupanc+ ma+ also e epressed + , *hich is …

Sum of lengths of vehicles %i

%ength of road*a+ section D

Then, densit+ can e estimated using the epression ......

% *here % average length of vehicles

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Example 2

xample 2

During a 34-sec period, a detector is occupied + vehicles for thefollo*ing times? 4.;7, 4.;C, 4.74, 4.;2 and 4.62 sec.

a) Determine the lane occupanc+.) Estimate the values of

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)

3.41 vehm

v s 1;.CC ms 7.5 mh

< 3.41 × 7.5 ;44.; vehhr

344.2

10000327.0

+

×

∑

+

ot

)CL(n

96.1

)344.2(5 +

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RAFFIC FLOW HEORY

RAFFIC FLOW HEORY

C) $%E!!=$E (c)

$learance is ......the distance (meters) et*een successive vehicles in a trafficstream, measured from front umper to ac umper.

) @!P (g)

@ap is ......the corresponding time (seconds) et*een successive vehiclesas the+ pass a point of a road*a+.

g h F (%v)c g v

*here g mean gap (sec)

% mean length of vehicles (m)c mean clearance (m)h mean head*a+ (sec)v mean speed (ms)

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RAFFIC FLOW HEORY

RAFFIC FLOW HEORY

$learance (m) @ap (s)

Spacing (m) Aead*a+ (s)

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RAFFIC FLOW HEORY

RAFFIC FLOW HEORY

:=#=TE:PTED "%&'

&ccurs on facilities that have no fied elements (such as trafficsignals or stop signs) eternal to the traffic stream, that causeinterruptions to traffic flo*.

Traffic flo* conditions are thus the result of interactions amongvehicles in the traffic s+stem and et*een vehicles and thegeometric characteristics of the road*a+guide*a+ s+stem.

The driver of the vehicle does not epect to e re

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RAFFIC FLOW HEORY

RAFFIC FLOW HEORY

#=TE:PTED "%&'

&ccurs on facilities that have fied elements causing periodicinterruptions to traffic flo*.

Traffic is stopped or significall+ slo*ed do*n periodicall+irrespective of ho* much traffic eists.

The driver epects to e re

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Answer his!

nswer his!

'hat t+pe of facilities are these8

:ninterrupted flo* facilit+ or #nterrupted flo* facilit+8

UNINTERRUPTED FLOWUNINTERRUPTED FLOW

FACILITYFACILITYINTERRUPTED FLOWINTERRUPTED FLOW

FACILITYFACILITY

BFC 32302 T ffi E i i d S f t L t D B il D id D i l

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RAFFIC FLOW HEORY

RAFFIC FLOW HEORY

:=#=TE:PTED T!""#$ "%&' M&DE%

D

C

B

A

Congestion Capacity

Normal flow

Forced flow

Speed (km/hr)

Flow (eh/hr)

BFC 32302 Traffic Engineering and Safety Lecturer: Dr Basil David Daniel

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RAFFIC FLOW HEORY

RAFFIC FLOW HEORY

#magine several vehicles, driven + rational drivers along a section of

free*a+.

!s vehicles speed and spacing increases, the speeds approach the freespeed, and drivers adopt their o*n speed *hen uninfluenced + othervehicles in the traffic stream (point $).

The dashed curve represents the normal flo* ehaviour if all drivers*ere to have the same free speed (point D).

#t has een oserved that drivers are uninfluenced + other vehicles inthe traffic lane at flo*s aout half the capacit+ flo* (point H).

Maimum traffic densit+ occurs (point !) *hen traffic has virtuall+come to a complete stop.

#n the forced flo* region, each vehicle adopts its minimum spacing andclearance distance.


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RAFFIC FLOW HEORY

RAFFIC FLOW HEORY

SPEED, "%&' and DE=S#T> relationship

!ee"# v !ee"# v

F$% 'De()*t+# k

F$% '

A

A/,

v = A - ,k

A/2

A/,A/2,De()*t+# k

A2 /4,


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RAFFIC FLOW HEORY

RAFFIC FLOW HEORY

Speed-Densit+ relationship

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RAFFIC FLOW HEORY

RAFFIC FLOW HEORY

Speed-"lo* relationship


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RAFFIC FLOW HEORY

RAFFIC FLOW HEORY

Maimum flo* (

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EAMPLE "ES IO#

AMPLE "ES IO#

A traffic stream is moing at a steady state when entering a

mo!ntain grade" #pon entering the grade$ the speed$ densityand flow are %& km/h$ &' eh/km and 1 eh/hr respectiely"

*n the grade$ a tr!ck drops to a speed of 1' km/h ca!sing traffic

to +!nch !p to a density of ' eh/km" ,hen the tr!ck p!lls

oer$ traffic accelerates to the ma-im!m flow !ntil steady state

flow conditions res!me"

Calc!late

(a)the flow of traffic +ehind the tr!ck on the mo!ntain grade

(+)the .am density and free flow speed for this road

(c) the density and speed when traffic res!mes a steady state flow

(d) the ma-im!m flow

bfc32302 chapter 1-b

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