Ingeniería y Análisis de Tráfico - India

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ters of Traffic FlowTransportation Systems Engineering 1. Fundamental Parame

Dr. Tom V. Mathew, IIT Bombay 1.1 February 19, 2014

surements of quantity, whichbe predicted. The parameters can be mainly classified as : mea

ch the characteristics canThus the traffic stream itself is having some parameters on whi

speed of 40 kmph rather than 100 or 20 kmph.

umed to move on an averagespeed of a highway is 60 kmph, the whole traffic stream can be ass

e, if the maximum permissibleare within certain ranges which can be predicted. For exampl

n, assumes that these changesThe traffic engineer, but for the purpose of planning and desig

behavior.

onding to the changes in the humancharacteristics will vary both by location and time corresp

rough a street of definedof such units interacts with each other. Thus a flow of traffic th

uman but also by the way a grouponly by the individual characteristics of both vehicle and h

rm in nature. It is influenced notbehavior being non-uniform, traffic stream is also non-unifo

e behavior. The driver or humanThe traffic stream includes a combination of driver and vehicl

1.2 Traffic stream parameters

presented.

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

thorough knowledge of traffic streamcharacteristics. Understanding traffic behavior requires a

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

parameters provide informationhas several parameters associated with it. The traffic stream

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

f traffic and to design the facilitiesTraffic engineering pertains to the analysis of the behavior o

1.1 Overview

Flow

Fundamental Parameters of Traffic

Chapter 1


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tn=q

expressed in vehicles/hour is given byq. Then the flowt

, passing a particular point in one lane in a defined periodtnby counting the number of vehicles,

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

oint on a highway or a givenvolume, which is defined as the number of vehicles that pass a p

cles on a road. One is flow orThere are practically two ways of counting the number of vehi

1.4 Flow

given instant is the space mean speed.

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

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

surement while space meanare traveling at the same speed. Time mean speed is a point mea

nlikely event that all vehiclesspeeds will always be different from each other except in the ucified time period. Both meanvehicles occupying a given section of a highway over some spe

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

les passing a point on a highwayTime mean speed is defined as the average speed of all the vehic

1.3.4 Time mean speed and space mean speed

ortable travel conditions.uniformity between journey and running speeds denotes comf

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

cceleration and deceleration. Thethat the journey follows a stop-go condition with enforced aess than running speed, it indicatesjourney including any stopped time. If the journey speed is l

en for the vehicle to complete thedistance between the two points divided by the total time tak

y between two points and is theJourney speed is the effective speed of the vehicle on a journe

1.3.3 Journey speed

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

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

hich the vehicle is brought to ain motion. i.e. this speed doesnt consider the time during wtime duration the vehicle wasmoving and is found by dividing the length of the course by the

lar course while the vehicle isRunning speed is the average speed maintained over a particu

1.3.2 Running speed


(1.2)t


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

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

over which it was measured.

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

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

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

traffic volume for the year by 260.

ding the total weekdayoccurring on weekdays over a full year. It is computed by divi

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

in a year divided by 365.

r of vehicles passing the sitegiven location over a full 365-day year, i.e. the total numbe

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

to be used in many design purposes.ions into a single volume countvolume are commonly adopted which will average these variat

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

1.4.2 Types of volume measurements

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

ork trips, which are relativelytimes the average hourly volume. These trips are mainly the w

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

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

in enabling predictions to be made.

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

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

least.variations and affects the traffic stream characteristics the

s the most consistent of all thewill be more pronounced in rural than in urban area. But this i

otoring month of summer, butseason to season. Volume will be above average in a pleasant m

ations can also be observed fromhour is also as important as volume calculation. Volume vari

day, hour to hour and within aThe variation of volume with time, i.e. month to month, day to1.4.1 Variations of Volume

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


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B A

xn=k

as,

ksity, in one lane of the road at that point of time and derive the denxnnumber of vehicles,

, count thexh a length of roadis generally expressed as vehicles per km. One can photograp

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

1.5 Density

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

ign of a highway and the relatedfluctuations in flow. All which eventually determines the des

ribution of traffic on road, and thea particular route with respect to the other routes, the dist

dy establishes the importance ofing, moving-car observer method, etc. Mainly the volume stu

l counting, detector/sensor count-Volume in general is measured using different ways like manuatween AADT and ADT.The relationship between AAWT and AWT is analogous to that be

Figure 1:1: Illustration of density


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

nsity, and speed, a few otherFrom the fundamental traffic flow characteristics like flow, de

1.6 Derived characteristics

maneuver and comfortable driving.

ch in turn affects the freedom toAgain it measures the proximity of vehicles in the stream whi

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

ty is also equally importantthe point A and B divided by the distance between A and B. Densi

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

(1.3)x


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tn=q

, that is,tmeasured in time intervalt

nBut the flow is defined as the number of vehicles

(1.4)t=ih1

tnhas been measured are added then,

, over which flowtin time period,hbumper and the next past a given point. If all headways

ime between the passage of one reara given point. Practically, it involves the measurement of t

ssive vehicles when they crossheadway is defined as the time difference between any two succe

way or simply headway. TimeThe microscopic character related to volume is the time head1.6.1 Time headway

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

tn=

t

1=

ih1tn

xn

=k

, that isxat a distance ofxn) is the number of vehicleskBut the density (

(1.6)x=is1

xnbeen measured are added,

over which the density hasxcevehicle at a point of time. If all the space headways in distan

cle to rear bumper of followingfrom a photograph, the distance from rear bumper of lead vehi

n time. It involves the measurementcorresponding points of two successive vehicles at any give

ned as the distance betweenAnother related parameter is the distance headway. It is defi

1.6.2 Distance headway

is often referred to as simply the headway.

f flow. Time headwayis the average headway. Thus average headway is the inverse oavhwhere,

(1.5)avh

xn

=x

1

=is1xn


ce-versa. Thus travel time is inverselytime required to reach the destination also decreases and vi

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

1.6.3 Travel time

and is sometimes called as spacing.

s the inverse of densityis average distance headway. The average distance headway iavsWhere,

(1.7)avs


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(a) (b)

(c)

time

st

ance

distance

time

distance

time


position.

ationary and maintains the samemovement. In figure 1:2(c), the vehicle in between becomes st

osition reverses its direction ofthe vehicle at first moves with a smooth pace after reaching a p

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

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

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

ory) plane is a curve which is called as a trajectory. The trajectt, x) in a (t(xrepresentation ofng the road stretch. This graphicalwill be a functions the position of the vehicle for every t alo

xandtand timexn distancea road stretch relative to time. This plot thus will be betwee

ves the relation of its position onrespect to time. This analysis will generate a graph which gi

e position of the vehicle withTaking one vehicle at a time, analysis can be carried out on th

1.7.1 Single vehicle

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

ot. Time space diagram can bethe trajectory of vehicles in the form of a two dimensional plmovement of vehicles. It showsTime space diagram is a convenient tool in understanding the

1.7 Time-space diagram

the travel time represents an average measure.

f a vehicle fluctuates over time andproportional to the speed. However, in practice, the speed o

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


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vehicles4=k

. Hence, the density is given astat time2xand1xof road between

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

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

agram for a set of vehiclesheadway and time headway. Figure 1:3 shows the time-space di

erived characteristics like spacelike speed, density and volume. It can also be used to find the d

ntal parameters of traffic flowTime-space diagram can also be used to determine the fundame

1.7.2 Multiple Vehicles

convex upwards denotes deceleration.

leration. But a curve which ismotion; and if the curve is concave downwards it denotes acce

urving sections denote acceleratedvehicle. A straight line denotes constant speed motion and c

-moving) denote a stopped vehicle while shallow sections show a slowt(xhorizontal portions of

) denote a rapidly advancing vehicle andt(xFrom the figure, steeply increasing section of

vehicles3=q

is given asq. Therefore, the volume2tand1tthat 6 vehicles are present between the time

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

e definition, volume is theWe can also find volume from this time-space diagram. As per th

(1.8)1x2x


vehicles at that point.

average time headway betweenlines gives the time headway. The reciprocal of flow gives the

en the vehicles represented by thewhen they cross a given point. Thus, the horizontal gap betwe

een any two successive vehiclesSimilarly, time headway is defined as the time difference betwat that time.

e space headway between vehiclesspace headway. The reciprocal of density otherwise gives th

y two consecutive lines representsvehicles at any given time. Thus, the vertical gap between an

onding points of two successiveway. Space headway is defined as the distance between corresp

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

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

nging over an interval) are calledAgain the averages taken at a specific location (i.e., time ra

(1.9)1t2t


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tTime

(h)headway

distance

(s)spacing

1x

2x

2t1t


Delhi, 1987.

. Prentice-Hall, NewFundamentals of Transportation Engineering5. C. S Papacostas.

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

. Prentice-Traffic Engineering4. William R McShane, Roger P Roesss, and Elena S Prassas.

Jersey 07632, second edition, 1990.

. Prentice - Hall, Inc. Englewood Cliff NewFundamentals of Traffic Flow3. Adolf D. May.

New Delhi, 1987.

. Khanna Publishers,Traffic Engineering and Transportation Planning2. L. R Kadiyali.

Washington, D.C., 2000.

. National Research Council,Transportation Research Board1. Highway Capacity Manual.

1.9 References

stream can be computed using moving observer method.

ers. Speed and flow of the trafficspace diagram also can be used for determining these paramet

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

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

1.8 Summary

Figure 1:3: Time space diagram for many vehicles


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ons of Traffic FlowTransportation Systems Engineering 2. Fundamental Relati

1=tv

is given by,tvdof time. It is the simple average of spot speed. Time mean speees passing a point over a durationAs noted earlier, time mean speed is the average of all vehicl

)tv2.2 Time mean speed (

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

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

s chapter. The relationship betweenrelationship between them will be discussed in detail in thi

nd space mean speed and thespeed are the two representations of speed. Time mean speed a

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

2.1 Overview

Fundamental Relations of Traffic Flow

Chapter 2

iviq=1in

=tv

given by,

le. Then the time mean speed isstudies, speeds are represented in the form of frequency tab

is the number of observations. In many speednvehicle, andthiis the spot speed ofivwhere

(2.1),iv=1i

n

n


is the spot speedivroad, and lettemporal. This is derived as below. Consider unit length of a

l weightage is given instead ofThe space mean speed also averages the spot speed, but spatia

)sv2.3 Space mean speed (

is the number of such speed categories.n, andivis the number of vehicles having speediqwhere

(2.2),iq=1in


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1given byis the time the vehicle takes to complete unit distance and isitvehicle. Letthiof

it=st

is given by,stsuch vehicles, then the average travel timenIf there are

.iv

1=n

1n

1=svis the average travel time, then average speedavtIf

(2.3).iv

n=sv

. Therefore, from the above equation,st

1

=1i

n

iq=1in

=sv

frequency table, then,

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

(2.4).iv

iq

=1i

n

iv=tvis the average of spot speed. Therefore,tvTime mean speedSolution

speed.

an speed and space meanIf the spot speeds are 50, 40, 60, 54 and 45, then find the time me

Numerical Example

is the number of such observations.inspeed andivvehicle will haveiqwhere

(2.5)iv

50+40+60+54+45=n

249

=5

n

=sverefore,= 49.8. Space mean speed is the harmonic mean of spot speed. Th5 15

=iv1 1+

50

1+

40

1+

60

1+

54

5=45

speed range

time mean speed and space mean speed.

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

Numerical Example

.82.= 4812.0

frequency

2-5

6-9

1

10-13

4

14-17

0

7

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

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

he frequencyThe time mean speed and space mean speed can be found out from tSolution

iqandi.qivfor that speed range is same as the frequency. The termsiqflow

= 3.5 seconds. The volume of2


are also tabulated,iv


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No. speed range )ivaverage speed ( )iqvolume of flow ( iqiv iq

iv

1 2-5 3.5 1 3.5 2.29

2 6-9 7.5 4 30.0 0.543 10-13 11.5 0 0 0

4 14-17 15.5 7 108.5 0.45

total 12 142 3.28

50 50

100 100

10 m/s 10 m/s10 m/s 10 m/s

20 m/s20 m/s20 m/s

50 50

10 m/s

5 = 12/= 60ssec n20 = 5/= 50sh

100 = 10/= 1000fk5 = 12/= 60fnsec20 = 5/= 100fh

50 = 20/= 1000sk

iviq=tvn be computed as,and their summations given in the last row. Time mean speed ca

d and space mean speedFigure 2:1: Illustration of relation between time mean spee

142

=iq

iq=svSimilarly, space mean speed can be computed as,.83.= 1112 iq12=

iv

2010+1212=tvis given bytvspeed

50 = 20 vehicles/km. Therefore, by definition, time mean/= 1000sKof spacing. Therefore,is the number of vehicles in 1 km, and is the inverseKwill be 60/5 = 12 vehicles. The density

snobserved at A in one hourwhich is 5 sec. Therefore, the number of slow moving vehicles

will be 50 m divided by 10 m/ssh100 m spacing. Therefore, the headway of the slow vehicle

he second set at 20m/s withThe first vehicle is traveling at 10m/s with 50 m spacing, and t

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

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

2.4 Illustration of mean speeds

.65.= 328.3

2010+1020=svthe mean of vehicle speeds over time. Therefore,

. Similarly, by definition, space mean speed ism/s= 1524

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

This is same asm/s.3.= 1330

112

1+12

10


py the road stretch for longermean speed weights slower vehicles more heavily as they occu

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

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

Itm/s.3.= 1320


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2+sv=tv

relation:

) is given by the followingsv) and space mean speed(tvThe relation between time mean speed(

speed

2.5 Relation between time mean speed and space mean

preferred over time mean speed.

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

i2viq

=2

) can be computed in the following equation:2the next subsection. The standard deviation(f the formula is given inis the standard deviation of the spot speed. The derivation o2where,

(2.6)sv

ik=if

,kto the total densityikdenote the proportion of sub-stream densityifLet

(2.11)k.=ik

.kthe total densitySimilarly the summation of all sub-stream density will give

(2.10)q.=iq

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

(2.9)ivik=iq

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

(2.8)svk=q

is,sv) and mean speedk), density(q. The fundamental relation between flow(nv. . .

,iv, . . .2v,1vhaving speednq, . . .iq, . . .2q,1qa stream of vehicles with a set of sub-stream flow

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

2.5.1 Derivation of the relation

speed.ivis the frequency of the vehicle havingiqwhere,

(2.7)2)tv(iq


(2.12).k


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ivik

=sv

space mean speed is given by,

speed, thenivvehicles hasikfSpace mean speed averages the speed over space. Therefore, i

iviq=tv

Time mean speed averages the speed over time. Therefore,(2.13).k

2ivik

=tv

can be written as,tvSubstituting 2.9,

(2.14).q

ikk=tv

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

(2.15)q

2ivifk

=

i2v

k

2ivif

=

q

2))sv

iv+ (

sv(

if

=tv

can be written as,tvand doing algebraic manipulations,svBy adding and subtracting

sv

)sviv(.s.v+ 22)sviv+ (

2)sv(if=

(2.16)sv

2svif

=

(2.17)sv

2)sviv(if+

sv

)sviv(if.s.v2+

sv

2+ifsv=tv

by definition is 1.Therefore,

if. ivon of. The numerator of the second term gives the standard deviatiivmean speed of

is thesv) will be zero, sincesviv(ifThe third term of the equation will be zero because

(2.18)sv

2+sv=

+ 0 (2.19)sv


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

e vehicles are the same, then spotstandard deviation cannot be negative. If all the speed of th

r than space mean speed sinceby the space mean speed. Time mean speed will be always greate

ation of the spot speed dividedHence, time mean speed is space mean speed plus standard devi

(2.20)sv


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iq

=sv

The space mean speed can be computed as:

iq

88=

iv

2qv=2

The standard deviation can be computed as:

38.= 203187.4

83800=

t2v

q

2+sv=tv

can also be computed as:tvThe time mean speed can also

727.= 138252.2888

727.13838 +.= 20

sv

q=k

The density can be found as:

184.= 2738.20

88=

v


(2.22)v.k=2n

distance.Therefore,will be density1vin a road stretch of distance2nof vehicles

n unit distance. Therefore numberSimilarly, by definition, density is the number of vehicles i

(2.21)q.=1n

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

.1nerver at A for one hour bekm/hr.(Fig 2:2). Let the number of vehicles counted by an obs

vkm, and assume all the vehicles are moving withvconcept. Let there be a road with length

is can be derived by a simpledensity is called the fundamental relations of traffic flow. Th

c flow, namely speed, volume, andThe relationship between the fundamental variables of traffi

2.6 Fundamental relations of traffic flow

km/3 vehicle.= 438.20


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7 5 4 3 28

Bv km

6 1

A


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

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

be zero because the vehicles are not moving.

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

on where vehicles cant move.3. When more and more vehicles are added, it reaches a situati

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

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

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

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

on between the density and theThe flow and density varies with time and location. The relati

2.7.1 Flow-density curve

They will be explained in detail one by one below.

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

ed and flow, can be representedThe relation between flow and density, density and speed, spe

2.7 Fundamental diagrams of traffic flow

to the space mean speed will also be same.

in the above equation refersvat,This is the fundamental equation of traffic flow. Please note th

(2.23)v.k=q

). Therefore,2n=1nwill also be same.(ievof vehicles in the stretch of distance

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

arameters of traffic flowFigure 2:2: Illustration of relation between fundamental p


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flow(q)

C

B

A

q

O

density (k)

ED

jamk2kmaxk1k0k

maxq


. It is possible to have twouoccurs at speedmaxqshown in figure 2:5. The maximum flow

peed. This relationship isAt maximum flow, the speed will be in between zero and free flow s

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

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

2.7.3 Speed flow relation

later.

tted lines. These will be discussedpossible to have non-linear relationships as shown by the do

les becomes zero. It is alsospeed. When the density is jam density, the speed of the vehic

ith their desire speed, or free flowCorresponding to the zero density, vehicles will be flowing w

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

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

mum, referred to as the free flowSimilar to the flow-density relationship, speed will be maxi

2.7.2 Speed-density diagram

oad.will be higher since there are less number of vehicles on the r1kdensity

. Clearly the speed at2kand slope of the line OE will give mean speed at density1kdensity

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

s D and E correspond to samecan travel when there is no flow. It can also be noted that point

e speed with which a vehicleand the slope of the line OA gives the mean free flow speed, ie th

he parabola at O,and the corresponding flow is zero. OA is the tangent drawn to tjamkdensity

. The point C refers to the maximummaxkmaximum flow and the corresponding density ishe point B refers to theThe point O refers to the case with zero density and zero flow. T

Figure 2:3: Flow density curve


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speedu

density (k) jamk

fu

0k

Figure 2:4: Speed-density diagram

flow q

q

uspeedu

maxQ

fu

2u

1u

0u


Figure 2:5: Speed-flow diagram


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sp

eedu

flow q

flowq

density k

sp

eedu

density k maxq


New Delhi, 1987.


2.9 References

as discussed in the last section of the chapter.

ther combined in a single diagramspeed-density, speed-flow and flow-density. They can be toge

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

ntal diagrams of traffic flowalways greater than or equal to space mean speed. The fundame

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

es of speed. It is possible toTime mean speed and space mean speed are two important measur

2.8 Summary

could observe the inter-relationship of these diagrams.

s shown in figure 2:6. Oneare called the fundamental diagrams of traffic flow. These are a

peed-density, and flow-densityThe diagrams shown in the relationship between speed-flow, s

2.7.4 Combined diagrams

different speeds for a given flow.

Figure 2:6: Fundamental diagram of traffic flow


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Transportation Systems Engineering 3. Traffic Stream Models

fv

fv=v

equation for this relationship is shown below.

d in figure 3:1 to derive the model. Theassumed a linear speed-density relationship as illustrateGreenshield. GreenshieldThe first and most simple relation between them is proposed by

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

e parameter of traffic flow changesMacroscopic stream models represent how the behaviour of on

3.2 Greenshields macroscopic stream model

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

ese researches yielded manyhas been done over the past several decades. The results of th

ters, a great deal of researchTo figure out the exact relationship between the traffic parame

3.1 Overview

Traffic Stream Models

Chapter 3

fv

.kfv=q

Now substituting equation 3.1 in equation 3.2, we get

(3.2)k.v=q

gure 3:3. Also, we know thatbetween flow and density is parabolic in shape and is shown in fi

an be derived. This relationbetween speed and flow is established, the relation with flow c

0). Once the relationkwhenfvvbecomes zero, speed approaches free flow speed (ie.

el. It indicates that when densityequation ( 3.1) is often referred to as the Greenshields mod

is the jam density. Thisjkis the free speed andfv,kis the mean speed at densityvwhere

(3.1).k

jk


(3.3)2k

jk


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density (k)

speedu

0k

fu

jamk

Figure 3:1: Relation between speed and density

s

peed,uu

flow, qq0u

fu

maxq


Figure 3:2: Relation between speed and flow


23/785


flow(q)

C

B

A

q

O

density (k)

ED

jamk2kmaxk1k0k

maxq

q

=khis, putSimilarly we can find the relation between speed and flow. For t

Figure 3:3: Relation between flow and density 1

jk

.vjk=q

and solving, we getin equation 3.1v

dq

it to zero. ie.,

and equatek3 with respect toflow. To find density at maximum flow, differentiate equation 3.

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

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

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

(3.4)2v

fv

fvfv

= 0dk

jk=k

= 0k2.jk

jk=0k

,0kDenoting the density corresponding to maximum flow as

2

jk.fv=maxq

. Substituting equation 3.5 in equation 3.3maxqcan derive for maximum flow,

, we0kjam density. Once we getTherefore, density corresponding to maximum flow is half the

(3.5)

2

fv

2jk

.

jk

jk.fv=

2

2

jk.fv

2j.kfv

=

4


4


24/785


fvfv=0v

, substitute equation 3.5 in equation 3.1 and solving we get,0vthe speed at maximum flow,

am density. Finally to getThus the maximum flow is one fourth the product of free flow and j

jk.jk

fv=0v

2

iy=1in

.ix=1in

iyix=1in

n=b

can be solved as,bandamethod, coefficients

. Using linear regressionvdenotes the speedxandkis densityysuch thatbx+a=ybe

een them. Let the linear equationdensity observations and then fitting a linear equation betw

tained from a number of speed anddensity directly from the field, approximate values can be ob

mine exact free flow speed and jamcalled calibration process. Although it is difficult to deter). This has to be obtained by field survey and this isjk) and jam density (fvfree flow speed (

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

3.3 Calibration of Greenshields model

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

(3.6)2

)yiy)(xix(=1in

=b

Alternate method of solving for b is,(3.8)

x

by=

a

(3.7)2)ix=1i

n

(2ix=1i

n

n.

k

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

rameters of the GreenshieldsFor the following data on speed and density, determine the pa

Numerical example

respectively.iyand

ixare the mean ofyand xis the number of samples, and nare the samples,iyandixwhere

(3.9)2)xix(=1i

n

v

171

129

5

20

15

70

40

25



25/785


x(k) y(v) )xix( )yiy( )yiy)(xix( )2xix(

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

x=xThe solution is tabulated as shown below.

quation 3.9.Denoting y = v and x = k, solve for a and b using equation 3.8 and eSolution390=

n

y=y= 97.5, 4

85=n

7.2947equation 3.9, b =

= 21.3. From4

fv= 40.8 andfvHere

(3.10)k2.08.= 40vequation will be,

97.5 = 40.8 So the linear regression= 21.3 + 0.2xby=a= -0.22.13157

8.40=jk= 0.2. This implies,jk

2048.40=maxqn 3.6, i.e.,and 204 veh/km respectively. To find maximum flow, use equatio

ey are obtained as 40.8 kmphGreenshields model are free flow speed and jam density and th

= 204 veh/km. The basic parameters of2.0

308.40k Therefore, k == 30 in equation 3.10. i.e, 30 = 40.8 - 0.2v

n be found out by substituting2080.8 veh/hr Density corresponding to the speed 30 km/hr ca

=4

jkln0v=v

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

3.4.1 Greenbergs logarithmic model

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

ential model, Pipes generalizedthem are Greenbergs logarithmic model, Underwoods expon

came up. Prominent amongof Greenshields model was questioned and many other models

ensity. Therefore, the validityfield we can hardly find such a relationship between speed and d

and density was assumed. But inIn Greenshields model, linear relationship between speed

3.4 Other macroscopic stream models

= 54 veh/km.2.0


predict the speeds at lower densities.

ows the inability of the model tothat as density tends to zero, speed tends to infinity. This sh

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

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

(3.11)k


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density, k

speed,v

Figure 3:4: Greenbergs logarithmic model

speed,v

density, k

k

.efv=v

model as shown below.

erwood put forward an exponentialTrying to overcome the limitation of Greenbergs model, Und

3.4.2 Underwoods exponential model

Figure 3:5: Underwoods exponential model


ties.Hence this cannot be used for predicting speeds at high densi

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

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

okfree flow speed andThe model can be graphically expressed as in figure 3:5. is thefvwhere

(3.12)0k


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Bk,Bv,BqAk,Av,Aq

k

1fv=vshown by the following equation.more generalized modeling approach. Pipes proposed a model

w parameter (n) to provide for aFurther developments were made with the introduction of a ne

3.4.3 Pipes generalized model

Figure 3:6: Shock wave: Stream characteristics


e-space diagram of the trafficby the line joining the origin and point A in the graph. The tim

ehicles at state A is givenThe flow-density curve is shown in figure 3:7. The speed of the v

respectively.Bq, andBk,Bv, and state B asAq, andAk,Avand flow of state A is denoted as

ow, say state B. The speed, densitycharacteristics changes and they acquire another state of fl

affic block) the steady statedue to some obstructions in the stream (like an accident or tr

e A (refer figure 3:6. Suddenlya constant speed, density and flow. Let this be denoted as stat

icles in the stream are moving withtraffic flowing with steady state conditions, i.e., all the vehuid flow. Consider a stream ofThe flow of traffic along a stream can be considered similar to a fl

3.5 Shock waves

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

re separate equations are usedmodels. The most simple one is called a two-regime model, whe

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

lso be different in different zones ofof densities. Therefore, the speed-density relation will a

erent relations at different rangeThis is corroborated with field observations which shows diff

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

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

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

3.4.4 Multi-regime models

, a family of models can be developed.nof

hus by varying the valuesis set to one, Pipes model resembles Greenshields model. TnWhen

(3.13)n

jk


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density

A

Bflow

Av

jkBkAk

Bv

Bq

Aq

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

time

distance

AB


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


29/785


BqAq=AB

, thenABas

f the shock-wave is representedgives the speed of the shock wave (refer figure 3:7). If speed o

nsity curve. Slope of the line ABstate B is the line joining the origin and point B of the flow-de

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

e 3:7. Thus the shock wavesthe two stream conditions. This is clearly marked in the figur

nt of the point that demarcatesupstream direction. Thus shock wave is basically the moveme

ng effect of the vehicles in theleads to the formation of a shock wave. There will be a cascadi

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

he same slope which implies thatstream is also plotted in figure 3:8. All the lines are having t

BqAq=AB

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

BqAq) =BkAk(AB

BvBkAvAk=tABBktABAk

tABBktBvBk=tABAktAvAk

t)ABBv(Bk=t)ABAv(Ak

BN=AN

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

(3.16)t)AB

Bv(Ak=BN

Similarly, the vehicles entering the state B is given as

(3.15)t)ABAv(Ak=AN

. Hence,ABAvthe shock wave will be

. The relative speed of these vehicles with respect totBq=ANleaving the section A. Then,

be the number of vehiclesANtis true since the vehicles cannot be created or destroyed. Le

wave boundary (this assumptionleaving the upstream and joining the downstream of the shock

xpressions for the number vehiclesThe above result can be analytically solved by equating the e

(3.14)BkAk


m with relatively lesser densitywhen a stream with higher density and higher flow meets a strea

oving shock waves are formedmoving shock waves and stationary shock waves. The forward m

f shock waves such as forwardbackward moving shock wave. There are other possibilities o

ffic and is therefore called aIn this case, the shock wave move against the direction of tra

(3.17)BkAk


30/785


)x, t(kcan be written as

o right, the continuity equationon the road. Assuming that the vehicles are flowing from left t

ation of the number of vehiclestraffic flow models and theories must satisfy the law of conserv

ervation on a road. In fact, allwriting the balance equation to address vehicle number cons

liest traffic flow models began bywith the behaviour of sizable aggregate of vehicles. The ear

gnored and one is concerned onlycompressible fluid. The behaviour of individual vehicle is i

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

theory of traffic can be developed with themacroscopiclike a stream of a fluid. Therefore, a

f fairly heavy traffic appearsIf one looks into traffic flow from a very long distance, the flow o

3.6 Macroscopic flow models

same flow value but different densities meet.

r when two streams having theforward moving shock wave. Stationary shock waves will occu

denly, there are chances for aand flow. For example, when the width of the road increases sud

)x, t(q+

t

1q2q=p)ot(v

From this the shock wave velocity can be derived as

(3.19)2v2k=1v1k

after will be same, orsystem the flow rate before andregimes of the flow, say before and after a bottleneck. In this

wo equations from two) by solving one equation. One possible solution is to write tx, t(qand

) byx, t(kydenotes the flow. However, one cannot get two unknowns, namelqdensity and

is thekis the time,t,denotes the spatial coordinate in the direction of traffic flowxwhere

= 0 (3.18)x

)x, t(k

continuity equation takes the form

t of each other. Therefore theassumption states that k(x,t) and q (x,t) are not independen

o one. Essentially this. Therefore the number of unknown variables will be reduced tkdensitycan be treated as a function of onlyq, so that flowkdetermined primarily by the local density

isqssume that the flow rateLighthill and Whitham adopted in their landmark study is to a

n alternate possibility whichThis is normally referred to as Stocks shock wave formula. A

(3.20)1k2k

))x, t(k(q+

t


menological relation derived fromfluid-dynamical theory. This has to be either taken as a pheno

cannot be calculated fromkand densityqHowever, the functional relationship between flow

= 0 (3.21)x


31/785


)x, t(k

). Thus, the balance equation takes the formk(q=qof the vehicular density k;

is a functionqerefore, the flow ratethe empirical observation or from microscopic theories. Th

))x, t(k(q+t

)k(dqkinematic waves moving with velocity

d. Solution to LWR models areinitial and boundary conditions are known, this can be solve

. Ifkation, the vehicle densityNow there is only one independent variable in the balance equ

= 0 (3.22)x

)1k(q)2k(q=sv

e propagate at the velocitythe other, and then a shock is said to be formed. This shock wav

tion may shift from one regime tothe flow rate decreases with density. In some cases, this func

s negative whenis positive when the flow rate increases with density, and it ikvThis velocity

(3.23)dk


Jersey 07632, second edition, 1990.

. Prentice - Hall, Inc. Englewood Cliff NewFundamentals of Traffic Flow1. Adolf D. May.

3.8 References

ls.models) and three dimensional representation of these mode

tion of both two and three regimetopics of further interest are multi-regime model (formula

h traffic flow like shock wave. Theare used for explaining several phenomena in connection wit

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

reenshields model assumed aThese models were based on many assumptions, for instance, G

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

3.7 Summary

variable here.

only oneof the shock wave. Unlike Stocks shock wave formula there is1kstream density

and down-2k) are the flow rates corresponding to the upstream density1k(q) and2k(qwhere

(3.24)1k2k


32/785

hodTransportation Systems Engineering 4. Moving Observer Met

0nisq, then flowtperiod,

is the number of vehicles overtaking the observer during aonobserver to be stationary. If

tream to be moving and themotion can be considered. The first case considers the traffic s

tion. Two different cases ofConsider a stream of vehicles moving in the north bound direc

4.2 Theory

unlike all other previous methods.

e observer moves in the traffic streamthe fundamental stream characteristics. In this method, tht the relationship betweenmoving observer method is the most commonly used method to ge

. Thus,u.k=qquationparameters of the traffic flow will provide the third one by the e

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

s. It has the advantage of obtainingprovide simultaneous measurement of traffic stream variable

ment has been developed toMoving car or moving observer method of traffic stream measure

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

s the flow as the product ofSince we have a fundamental equation of traffic flow, which give

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

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

4.1 Overview

Moving Observer Method

Chapter 4

nisk

, then by definition, densitylis the number of vehicles overtaken by observer over a lengthpnIf

.ovobserver moves with speedThe second case assumes that the stream is stationary and the

(4.1)tq=0n

, ort

p


(4.2)lk=pn

, orl


33/785


l


ll get the first parameter of thein the opposite direction. Adding equation 4.5 and 4.6, we wi

imply counts the number of vehiclestest vehicle moves in the opposite direction, the observer s

tive speed. In other words, when thethe vehicles will be overtaking, since it is moving with nega

locity. Further, in this case, allwhen the test vehicle is moving in the stream with negative ve

ection can be considered as a caseis negative, because test vehicle moving in the opposite dir

gn of equation 4.6denotes against and with traffic flow. It may be noted that the sia, wwhere,

k l+aq t=

(4.6)atak v+aq t=am

k lwq t=

(4.5)wtwk vwq t=wm

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

t vehicle is run twice once with theonly one equation. For generating another equation, the tes

, butkandqwns,that can be obtained from the test. However, we have two unknoovandt,mto the countsq, kd, which relatesThis equation is the basic equation of moving observer metho

(4.4)tok vq t=pm0m=m

4.3,

, then from equation 4.1 and equationpm-0mis given bymtest vehicle. Let the difference

vehicles will be overtaken by the observer in thepmvehicles will overtake the observer andom

thin the stream. In that casestretch. Now consider the case when the observer is moving wi

is the time taken for the observer to cover the roadtis the speed of the observer and0vwhere

(4.3).tok.v=pnor

Figure 4:1: Illustration of moving observer method


34/785


am+wm=q

stream, namely the flow(q) as:

wm

Now calculating space mean speed from equation 4.5,

(4.7)at+wt

qq=

wkvq=wt

qq=

wvv

l

v

l1

q=

wt

1

v

avgt1

q=

wt

l=avgtis the mean stream speed, then average travel time is given bysvIf

wt

wm

. Therefore,sv

avgt(1wt=

q

wmwt=avgt

avgtwt) =wt

l=

q

l=sv

and can be written as,svspeed

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

,v

wmwt

q=k

) can be found out askparameter of traffic flow density (

the two parameters the thirdThus two parameters of the stream can be determined. Knowing

(4.8)q


results are to be taken.d a number of times and the averageFor increase accuracy and reliability, the test is performe

(4.9)sv


35/785


5.0=wtmoving along with the traffic is

eam while it isTime taken by the test vehicle to reach the other end of the strSolution

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

mber of vehicles overtaken by thevehicles that had overtaken the test vehicle is 10, and the nu

affic stream is 107, number ofin the stream while the test vehicle was moving against the tr

umber of vehicles encounteredwith which the test vehicle moved is 20 km/hr. Given that the n

server test is 0.5 km and the speedThe length of a road stretch used for conducting the moving ob

Numerical Example

4.4 Assumptions

4.3 Proof

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

= 0.025 hrwt=attraffic is

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

= 0.025 hr20

5.0=svcan be found out from equationsvStream speed

= 860 veh/hr025.025+0.0

74.10025.0

860Density can be found out from equation as k =

= 5 km/hr860

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

ree fundamental stream parametersnumber of vehicles overtaken by the test vehicle. Find the th

icle, and last column gives the3 gives the number of vehicles that had overtaken the test veh

ng against the stream, columnthe sample number, column 2 gives the number of vehicles movi

he table. Column 1 givesThe data from four moving observer test methods are shown in t

Numerical Example

= 172veh/km5

Sample no. 1 2 3

1 107 10 74

2 113 25 41

3 30 15 5

4 79 18 9


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

ee fundamental dia-From the calculated values of flow, density and speed, the thrSolution


36/785


37/785



New Delhi, 1987.


4.6 References

are obtained by a single experiment.

oth speed and traffic flow datacollected at a point. Moving observer method is one in which b

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

ry. Speed data are collectedfrom the field which cannot be exactly created in any laborato

ct that they require extensive dataTraffic engineering studies differ from other studies in the fa

4.5 Summary


38/785

ntTransportation Systems Engineering 5. Measurement at a Poi


ighway1. Measuring the present demand for service by the street or h

This can be used for following purposes:

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

Average Annual Daily Traffic (AADT)

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

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

5.2.1 Types of Volume Measurement

5.2 Basic concepts

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

l data concerning the movementTraffic volume studies are mainly carried out to obtain factuassing a section per unit time.measured at a point. Flow can be defined as the no of vehicles pa

he main traffic parameterOut of these we will be discussing the first type here. Flow is t

3. Measurement over a long section

2. Measurement over a short section

1. Measurement at a point

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

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

5.1 Introduction

Measurement at a Point

Chapter 5


39/785



signal timings etc.

ustifying pedestrian signals, trafficThese are used in evaluating sidewalk and crosswalk needs, j

Pedestrian Count

traffic assignment etc.

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

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

Screen Line Count

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

ping center etc.). Vehicles orThese are made at the perimeter of an enclosed area (CBD, shop

Cordon Count

be collected. They include:

he anticipated use of the data toVarious types of traffic counts are carried out, depending on t

5.2.2 Type of Counts

year, such as for a month or a season.

me period of time less than oneAn average 24-hour traffic volume occurring on weekdays for so

Average Weekday Traffic (AWT)

ured.ADT is a valid number only for the period over which it was measas little as two days. AnIt may be measured for six months, a season, a month, a week, or

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

Average Daily Traffic (ADT)

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

Average Annual Weekday Traffic (AAWT)

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

t system3. Evaluating the present traffic flow with respect to the stree

2. Developing the major or arterial street


40/785



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

ed, use of such counters wasto tedious reduction of the voluminous amount of data obtain

icle is conceived by sensors. DueThe frequency shift of energy reflected from approaching veh

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

ear the site, which is detectedthe interruption of a beam generated from a station located n

lsed types mainly depend uponwheels, pass along the tube thereby increasing the count. Pu

Air pulse actuated by vehiclethe contact type counters, pneumatic tubes are mostly used.lsed types, radar types. Amongcounters. These can be mainly grouped into contact types, pu

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

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

Permanent Counters

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

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

Automatic counting

ce and other pedestrian facilities3. For analysis of crosswalks, sidewalks, street corner spa

2. Classification and occupancy studies

1. Turning and through movement studies

specific uses of manual counts are following:

ng the instruments, some othertake some manual observations for every counting for checki

avy traffic. Although it is good toadequate. Mechanical or electrical counters are used for he

lumes, tally marks on a form arethrough the section for a definite time interval. For light vo

es along with its type, passingIn its simplest form an observer counts the numbers of vehicl

Manual counting

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

ne depending upon the durationNumber of vehicles can be counted either manually or by machi

5.2.3 Counting Techniques

ent intersections etc.channelization, computing capacity, analyzing high accid

ing turn prohibitions, designingThese are measured at the intersections and are used in plann

Intersection Count


41/785



n expressed as percentage of dailyFor studying the daily variation, the flow in each hour has bee

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

5.3 Variation of Volume Counts and Peak Hour Factors

to 6 pm.

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

ropolitan area, proximity to4. Peak Period counting times vary depending upon size of met

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

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

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

een noon Monday and noon1. 24-hour counts normally covering any 24-hour period betw

of the more commonly used intervals are: nd for estimating purposes. Somenational and local highway use, trends of use and behaviour a

us counts are made to establishsystem classification and investment programmes. Continuo

nt in economic calculations, roadengineering design, while daily and annual traffic is importa

ounts are generally significant in allpoints to continuous counts at permanent stations. Hourly c

ods vary from short counts at spotand the application in which the data are used. Counting peri

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

5.2.4 Counting Periods

must be read by an observer at desired intervals.Non-Recording Counters2.

volume. These may be set for various counting intervals.

provides a permanent record of volumes by printing the totalRecording counters1.

sub-divided into two types:

his error. This can further befrom a sample classification count, is introduced to reduce t

uced. A correction factor, obtainednumber of multi-axle vehicles is present, an error is introd

t for every two axles. If significantattached to a counter which is usually set to register one unicle passage operates a switchtransducer unit actuated by energy pulses. Each axle or vehi

rally these make use of aThese are used to obtain temporary or short term counts. Gene

Portable Counters


42/785


av60V

=P HF

.av15Viodfour times the average volume during the peak 15 minutes per

divided byav60Vminute periodfrom traffic counts. It is the average volume during the peak 60

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

ip generation patterns and mayprocedures. The peak-hour factor (PHF) is descriptive of tr

as the basis for most of itsHighway Capacity Manual, which selected 15 minute flow ratess in accordance with thePeak hour factors should be applied in most capacity analyse

the area served.

e economic and social condition ofmost consistent of all variation patterns and represents th

actors. Seasonal variation is thelot depending upon the season, weather and socio-economic f

ut the weekend flows vary aflow for the week. Weekdays flows are approximately constant b

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

weather and other travel conditions.

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

ominant peaks (morning and eveningthis there is one additional feature of this variation: two d

rage hourly volume. Apart fromroads and control of traffic, and is usually 2 - 2.5 times the ave

rtant factor in the design ofday with day is much more useful. Peak Hour Volume is very impo

patterns. Thats why comparingflow. Weekdays, Saturdays and Sundays usually show different

av60V

=P HF

Generalizing,

in the denominator from 4.PHF. But in that case we have to change the multiplying factorrval for the calculation ofOne can also use 5, 10, or 20 minutes instead of 15 minutes inte

(5.1)av15V4

60


0.90 for minor arterial

0.85 for minor street inflows and outflows

which are as follows:

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

0.88 for rural areas

0.92 for urban areas

0.95 for congested condition

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

nceminute flow. The Highway Capacity Manual advises that in absenis the peakavnVwhere

(5.2)avnV

n


43/785


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

219=P HFvolume.

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

me is 65 in this case. The peakintervals within the peak hour (219). The peak 15 minute volu

olumes of the four 15 minuteshown in bold font. The peak hour volume is just the sum of the v

he peak 15 minute periodthe highest volume. The peak hour is shown in blue below with t

e interval withWe can locate the hour with the highest volume and the 15 minutSolution

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

rsection. Calculate the peakThe table below shows the volumetric data observed at an inte

Numerical Example

0.95 for major streets

Table 5:1: Volumetric data


ed to a single standard passengeron traffic variables (such as headway, speed, density) compar

ct that a mode of transport hasrate on a highway. A Passenger Car Unit is a measure of the impa

ngineering, to assess traffic-flowPassenger Car Unit (PCU) is a metric used in Transportation E

5.4 Passenger Car Unit (PCU)

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

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

the84 The actual (design) flow rate can be calculated by dividing.= 0654


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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


lume is just the sum of theminute period shown in a darker shade of blue. The peak hour vo

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

t volume and the 15 minuteused. Once we have this, we can locate the hour with the highes

CU values given in the table areperiod in terms of passenger car units. For this purpose the P

for each 15 minuteThe first step in this solution is to find the total traffic volumeSolution

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

ersection: Calculate the peakThe table below shows the volumetric data collected at an int

Numerical Example

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

ple, typical values of PCU (orcar. This is also known as passenger car equivalent. For exam

Table 5:3: Values of PCU


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6.743=P HF

hour volume by four times the peak 10 minute volume.

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

43.6 PCU). The peak 10 minutevolumes of the six 10 minute intervals within the peak hour (7

bij=tE

based on relative delay may be found as

. PCUs for multi-lane highwayshighways, PCUs were based on the relative delay due to trucks

er method. For multi-lanetified this by the relative number of passing known as the Walk

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

5.5.1 Method based on relative delay

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

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

Simulation method

Multiple linear regression method

Headway method

Method Based on Relative Delay

Chandras method

Modified Density Method

passenger car units (PCU) are following:

e methods for determiningis not the norm. This complicates computing of PCU. Some of th

iscipline prevails; car followingtraffic modes with different physical dimensions. Loose lane d

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

5.5 Determination of PCU

.PCU/hr879

5 =.146, or by multiplying the peak 10 minute volume by six, 6PCU/hr85 = 879.0/6.743

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

85.= 05.1466

D D


(5.3)bD


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nC=nE

is calculated as:nvehicle type

, the PCU for anEto zero. Using the speed reduction coefficients,5Csetting the coefficient

lied to multi-lane highways byfor two lane highways with opposing traffic flow, it could be app

though this model was formulatedrelative sizes of speed reductions for each vehicle type. Alare coefficient representing the5Cto1Cnumber of vehicles moving against the current stream,

is theaVis the number of other types of vehicles,rVis the number of recreational vehicles,

rVis the number of truckscVis the number of passenger cars,cVis the free speed,fvwhere

(5.4)aV5c+oV4c+rV3c+tV2c+cV1c+fv=pv

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

d of a traffic stream as function ofMultiple linear regression method try to represent the spee

5.5.2 Multiple linear regression model

decreased with increasing proportion of trucks.

r a given grade and LOSof trucks and the lowest LOS. However, in many cases the PCU fo

de with the highest proportionthe highest PCU was reported for the longest and steepest gra

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

rades of specific length andproportion of trucks. PCUs in the 1965 HCM were reported for g

creased with increasingLOS. However, in many cases the PCU for a given grade and LOS de

proportion of trucks and the lowestreported for the longest and steepest grade with the highest

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

h and percent, proportionPCUs in the 1965 HCM were reported for grades of specific lengt

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

is thebition j andis the delay to passenger cars due to vehicle type i under condijwhere D D

mH(=tE

ulated asPCUs on level terrain at low levels of service. The PCU is calc

d is best suited to determineIn 1976, Werner and Morrall suggested that the headway metho

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

raffic stream is that they take upRealizing one of the primary effects of heavy vehicles in the t

5.5.3 Method based on headway

coefficient for passenger cars.

is the speed reduction1Cis the speed reduction coefficient for vehicle type n andnCwhere1C

cP)bH


(5.5)tP


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mh ch cp tp

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

)i/VcV(=i)P CU(

area to calculate the PCU value.

pe and its projected rectangularThis method uses two factors: namely, velocity of vehicle ty5.5.4 Chandras method

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

stream.

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

erage headwayrespectively denote the average headway for mixed traffic, avt, pc, pc, hmhthat

or each traffic condition Notethe traffic contains only car and truck. Compute the PCU value f

onditions. It is assumed thatThe table given below show headway data for a number of traffic c

Numerical Example

proportion of trucks.

is theTPis the proportion of cars, andCPheadway for a sample of passenger cars only,

is the averageBHes,is the average headway for a sample including all vehicle typMHwhere

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


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

areiAandcAare mean speeds of car and vehicle of type i respectively andiVandcVwhere

(5.6))i/AcA(


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PCU

Percentage of trucks0 0.2 0.4 0.6 0.8

1.75

1.80

1.85

1.90

1.95

2.00

.

n=sV

formula:

theWe have to find the space mean speed for each vehicle type usingSolution Step 1

d.the PCU value for each vehicle type using the Chandras Metho

r various vehicle types. FindThe table given shows the data obtained in spot speed study fo

Numerical Example

problem given above

ge of truck using the data of theFigure 5:1: Graph showing the variation of PCU with percenta

1(=1in

)l/Wck(=tE

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

5.5.5 Density method

different vehicle types to find corresponding PCU values.

iven above to find the areas ofvarious vehicle types given above. Then we can use the table g

ing the areas ofFind the PCU values using Chandras Method. Use the table havStep 2

is the spot speeds.ivWhere n is the no. of observations and

)iv


is the density of the truck in pure homogeneous conditionstkthe lane in homogeneous traffic,

is the width oflWm.),is the density of cars in pure homogeneous conditions(car/kckwhere

(5.7))l/W)tk(


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. 2019.Traffic Using a Modified Density Method

Passenger Car Units for Heterogeneous5. Geetam Tiwari, Joseph Fazio, and Sri Pavitravas.


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hort SectionTransportation Systems Engineering 6. Measurement over a S


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

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

two pointsThis is the effective speed of the vehicle on a journey betweenJourney speed3.

vehicle is in the motion.

e while theThis is the average speed maintained over a particular coursRunning speed2.

cation.This is the instantaneous speed of a vehicle at any specific loSpot speed1.

main categories

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

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

of distance travelled to timetraffic movement. In other words speed of movement is the ratio, and this is a vibrant in everyAs speed defines the distance travelled by user in a given time

6.2 Speed Studies

reasonable speed limits, and to assess safety.

l speed trends, to help determineof congestion. This information is used to determine genera

s select, unaffected by the existenceof free flow. The intent is to determine the speeds that driver

on) of road way under conditionsmeasurements are most often taken at a point (or a short secti

ter, specially speed. SpeedThe main purpose of this chapter is to determine traffic parame

6.1 Overview

Measurement over a Short Section

Chapter 6


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Stream Speed Length

below 15 30

15 -25 60

above 25 90


hod, minimum two observersstart and stops the watch as vehicle passes lines. In this met

ad at each end of trap. ObserverIn this method, markings of pavement are placed across the ro

6.4.1 Pavement markings

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

methods to measure spot speedaverage stream speed ranges (in kmph) Following are the some

tudy length (in meters) for variousspeed of traffic stream. Following tables gives recommended s

lly depending upon the averageusually less than 90m. Distance between two points is genera

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

ng the time it takes a vehicleAutomatic. Spot speeds may be estimated by manually measuri

o main categories: Manual andMethods of conducting spot speed Studies are divided into tw

6.4 Methods of Measurement

5. Research studies.

4. Geometric design,

3. Accidental analysis,

2. Traffic control planning,

1. Speed trends,

ons, including the followingdecisions. Spot speed data have a number of safety applicati

seful in making many speed-relatedare used to determine vehicle speed percentiles, which are u a gathered in spot speed studiesdistribution of a traffic stream at a specific location. The dat

s are used to determine the speedpassing a given spot on a street or highway. Spot speed studie

s of a sample of the vehiclespeed. A spot speed is made by measuring the individual speed

generally measure the spotWhen we measure the traffic parameter over a short distance, we

6.3 Spot Speed Studies


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is only applicable for low traffic conditions.

titute studies and this methodcan be introduced, and magnitude of error may change for subs

tage of this is that substantial errortime is required, markings are easily renewed, and disadvan

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

on to stop the watch when vehiclestop watch and other one is stand at end point to give indicati

ting point to start and stop therequired to collect the data, of which one is stand at the star

Observer 1Observer 2

X

Study length

Vertical Referencepoint

point

End Timing

Start timing

Approachin


recorder then it gives continuous data automatically.

f it is connected through graphicalmethod over short distance it gives quite relevant data and i

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

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

6.4.3 Road Detector (Pressure contact strips)

scope method.ostentatious to proper vehicle are the disadvantages of eno

ion it may be difficult to relatewhich lengthen the study period and under heavy traffic condit

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

s of this method are that it simpletaken by the vehicle to cross the section (fig 6.2). Advantage

aced and measure the timestands at one end of section and on the other end enoscope is pl

urned through 90o. The observerside of the road in such a way that an observers line of sight t

or mounted on a tripod at theEnoscope consists of a simple open housing containing a mirr

6.4.2 Enoscope or Mirror box

Figure 6:1: Pavement Marking


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observer enoscope

Base length

x


2. For automatic methods

1. For Enoscope and Pavement Marking Methods

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

d into some formats, followingThe measured data by the above techniques should be collecte

6.5 Data Collection Sheets

more accurate result.

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

btained. This method is quiteof method that, it gives a permanent record with 100% sample o

re interval. The main advantagevehicle is measured by projecting the films during the exposu

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

e in a selected short time. In thisIn this method a camera records the distance moved by a vehicl

6.4.5 Electronic-Principle Detectors (Photography)

of the vehicle.

alibration gives directly spot speedvehicles speed and returned to the receiving unit, through c

r length depending up on thetowards the moving vehicle, and reflected waves changed thei

tromagnetic waves in a narrow

Ingeniería y Análisis de Tráfico - India

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