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1. INTRODUCTION

The information on traffic volume is an important input

required for planning, analysis, design and operation of

roadway systems. Highway capacity values and speed-

flow relationships used for planning, design and operationof highways, in most of the developed countries, pertain

to fairly homogeneous traffic conditions comprising

vehicles of more or less uniform static and dynamic

characteristics. But the traffic scenario in developing

countries like India differs significantly from the conditions

of developed countries in many respects. In Indian road

traffic, the heterogeneity is of high degree with vehicles

of widely varying static and dynamic characteristics. Under

this condition, it becomes difficult to make the vehicles to

follow traffic lanes. Consequently, the vehicles tend to

choose any advantageous lateral position on the road basedon space availability. Under the said traffic conditions

expressing traffic volume as number of vehicles passing

a given section of road per unit time will be inappropriate

and some other suitable base needs to be adopted for the

purpose. The problem of measuring volume of such

heterogeneous traffic has been addressed by converting

the different types of vehicles into equivalent passenger

cars and expressing the volume in terms of Passenger

Car Unit (PCU) per hour. The PCU is the universally

adopted unit of measurement of traffic volume, derived

by taking the passenger car as the standard vehicle.

The interaction between moving vehicles in a traffic stream

is highly complex and is influenced by a number of

roadway and traffic factors. The accurate estimation of

the magnitude of vehicular interaction for different

roadway and traffic conditions is the prerequisite for better

operation and management of roadway facilities in their

prevailing conditions.

Since the traffic flow phenomenon is influenced by

several stochastic variables of random nature, micro-

simulation technique has been found to be a versatile tool

to model complex traffic systems for study of their

characteristics over a wide range of operating conditions.

The present study is aimed at studying the vehicular

interactions in heterogeneous traffic under different

roadway and traffic conditions and hence check for the

accuracy of the available PCU estimates for the different

categories of vehicles on Indian roads for a range of traffic

volume and roadway conditions.

2. LITERATURE REVIEW

After the introduction of the term PCU in the

Highway Capacity Manual (HCM), USA in the year

1965, considerable research effort has been made toward

Paper No. 542

STUDY OF THE EFFECT OF TRAFFIC VOLUME AND ROAD WIDTH ONPCU VALUE OF VEHICLES USING MICROSCOPIC SIMULATION

V. THAMIZH ARASAN*AND K. KRISHNAMURTHY **

ABSTRACT

The knowledge of traffic volume is an important basic input required for planning, analysis and operation of roadway

systems. Expressing traffic volume as number of vehicles passing a given section of road or traffic lane per unit time will be

inappropriate when several types of vehicles with widely varying static and dynamic characteristics are comprised in the

traffic. The problem of measuring volume of such heterogeneous traffic has been addressed by converting the different types

of vehicles into equivalent passenger cars and expressing the volume in terms of Passenger Car Unit (PCU) per hour. The

vehicles of highly heterogeneous traffic with widely varying physical and operational characteristics such as the one

prevailing on Indian roads, occupy based on the availability of space, any convenient lateral position on the road withoutany lane discipline. The interaction between moving vehicles under such heterogeneous traffic condition is highly com-

plex. The results of the study, provides an insight into the complexity of the vehicular interaction in heterogeneous traffic.

The PCU estimates, made through microscopic simulation, for the different types of vehicles of heterogeneous traffic, for a

wide range of traffic volume and roadway conditions indicate that the PCU value of a vehicle significantly changes with

change in traffic volume and width of roadway.

* P ro fe ss or

** Research Scholar Written comments on this Paper are invited and will be received upto 15th November, 2008.

E -mail: [email protected] Engineering Division, Dept. of

Civil Engineering, IIT Madras, Chennai - 600 036 E- mail : [email protected]} }


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134 ARASAN & KRISHNAMURTHYON

the estimation of PCU values for different vehicle types

under various roadway conditions. For example, Huber

(1982); Krammes and Crowely (1986) suggested thatthe factors which are considered in evaluating the level

of service may be taken as the variables to describe the

impedance to travel in PCU estimation. Keller and James

(1984) developed a procedure to estimate Passenger

Car Equivalent (PCE) values for large vehicles moving

over an urban network using TRANSYT simulation

model. As per this procedure, the amounts of delay caused

by different vehicle types were taken as the basis to

estimate the PCE values.

Srinivas Peeta et al. (2003) modelled the car-truck

interactions on freeway sections using microscopic trafficflow models. The car-truck interactions were modelled by

associating a discomfort level for every non-truck driver

in the vicinity of the trucks. It was observed that this

discomfort is affect by the driver socioeconomic

characteristics, and situational factors such as time-of-day,

weather, and ambient traffic congestion levels. Al-Kaisy

et al. (2005) found that the HCM suggested PCU factors

for heavy vehicles is applicable only under free-flow

conditions and hence, attempted to derive passenger car

equivalents for heavy vehicles during congestion. It is found

from the review of the literature that several studies onestimation of PCU values of vehicles in heterogeneous

traffic have been conducted. For example, Terdsak and

Chanong (2005) studied the effect of motor cycles on traffic

operations on arterial streets of Bangkok. They found that

the derived PCU of motor cycles showed a decreasing

trend with increase in share of motor cycles in the traffic

stream. Zhang et al. (2006) adopted the vehicle moving

space (VMS) as the measure to derive passenger car

equivalents for vehicles of different categories for Chinese

roadway and traffic conditions. Chandra and Sikdar(2000)

through an empirical study found that for a given road width,

an increase in volume level of heterogeneous traffic causes

more density on the road resulting in reduced uniform speed

of vehicles. The lower speed difference between cars and

subject vehicles yield smaller PCU value for the vehicle

type. Chandra and Kumar (2003) studied the effect of road

width on PCU of vehicles on two-lane highways and found

that the PCU value increased with increase in width of

roadway. Justo and Tuladhar (1984) developed mathematical

models to derive PCU values for vehicles on urban roads

based on empirical data under mixed traffic flow. Ramanayya

(1988) estimated the PCU factors for different vehicle types

at different levels of services taking the Western car as theDesign Vehicle Unit DVU. The review of literature on the

subject matter reveals that studies conducted are mostly

related to fairly homogeneous traffic conditions, and the

few studies conducted under heterogeneous trafficconditions are not comprehensive enough to replicate the

field conditions accurately. Hence, it was decided to make

an attempt to study the vehicular interaction in heterogeneous

traffic in a comprehensive manner and derive PCU values

for different vehicle types through this research work.

3. SCOPE AND OBJECTIVES

The proposed research work aims at analyzing the

characteristics of the heterogeneous traffic flow to

identify appropriate theoretical distributions for various

traffic variables influencing the traffic streamcharacteristics, and study of the flow characteristics and

vehicular interactions at micro level. The specific

objectives of the research work are as follows.

1. To quantify the impedance caused to traffic flow

by the different categories of vehicles in

heterogeneous traffic in terms of PCU, over a wide

roadway and traffic conditions using simulation

technique and

2. To study the effect of road width and traffic volume

on PCU values of vehicles.

4. THE SIMULATION FRAMEWORK

Simulation being a versatile tool for modelling traffic

flow, the simulation technique has been used to study

the heterogeneous traffic flow characteristics on Indian

Roads by a few researchers in the past (e.g., Ramanayya

(1988), Kumar and Rao (1996) and Marwah and Singh

(2000)). These modelling attempts, however, are not

comprehensive enough to replicate the field conditions

fully due to various limitations of the studies. Research

attempts made at IIT Madras (Arasan and Koshy, 2004& 2005) to comprehensively model heterogeneous traffic

flow has resulted in replication of the field conditions

satisfactorily. This simulation model has been used to

simulate the heterogeneous traffic flow over a wide range

of roadway and traffic conditions. The model is capable

of simulating the traffic flow for any specified composition

and traffic volume on a given width of roadway over

specified time duration. As the variables influencing the

traffic flow are random and stochastic in nature,

appropriate statistical distributions are used to represent

them in the model. The inter-arrival times (timeheadways) of vehicles are randomly generated from


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HIGHLIGHTSOFTHE 178THCOUNCILMEETING 135STUDYOFTHE EFFECTOF TRAFFIC VOLUMEAND ROAD WIDTHON PCU VALUEOFVEHICLES USING MICROSCOPIC SIMULATION

Fig. 2. Simulation framework

specified statistical distributions. As per the methodology,

the entire road space is considered as single unit. The

road space will be considered to be a surface made ofsmall imaginary squares (cells of convenient size 100

mm in this case); thus, transforming the entire space

into a matrix. The vehicles will be represented with

dimensions as rectangular blocks occupying a specified

number of cells whose co-ordinates will be defined

before hand. The front left corner of the rectangular

block is taken as the reference point, and the position of

vehicles on the road space is identified based on the

coordinates of the reference point with reference to the

origin chosen at a convenient location on the space. This

technique will facilitate identification of the type and

location of vehicles on the road stretch at any instant of

time during the simulation process (Fig. 1).

Fig. 1. Reference axes for representing vehicle positions

The simulation process, which is intended to model

traffic flow through mid-block sections of urban roads,

basically, consists of the following three modules: (i) Vehicle

generation; (ii) Vehicle placement; and (iii) Vehicle

movement. The flow chart shown in Fig. 2 depicts the major

logical steps involved in the overall simulation process

involving the three modules.

For the purpose of simulation, the time scan procedure

is adopted. The scan interval chosen for the simulation is 0.5

second. The arrival of vehicles on the road stretch will be

checked for every 0.5 second and the arrived vehicles will

be put on to the entry point of the study stretch of the road, on

first-come-first-served basis. In the vehicle-generation module,

the first vehicle is generated after initialization of the various

parameters required to simulate heterogeneous traffic flow.

Then, the generated vehicle is added to the system when the

current time (clock time) becomes equal to the cumulative

headway. At this stage, the module for adding vehicles named

Add Vehicle will be activated to facilitate the process. At

higher traffic flow levels, there is a chance of more than onevehicle arriving during each scan interval (0.5s). To address

this issue, an additional clock for scanning with a precision of

0.05s is provided, so that a maximum of 20 vehicles can be

added in one second. The precision of 0.05s, decided basedon field studies, is intended to account for the maximum

possible number of smaller vehicles, like motorised two

wheelers, auto-rickshaw, etc. that may arrive in large numbers

in short periods on multilane highways. Thus, the logic

formulated for the model also permit admission of vehicles in

parallel across the road width, since it is common for smaller

vehicles such as Motorised two-wheelers to move in parallel

in the traffic stream without lane discipline. Vehicles admitted

to the simulation road stretch are then allowed to move based

on the various movement logics formulated. Various

manoeuvre for a vehicle moving on the simulation road stretch

include free forward movement with desired speed,

acceleration manoeuvre, movements leading to lateral shifting

and overtaking of slower vehicles, movements involving

deceleration and following of the front vehicle for want of

sufficient gaps for overtaking, etc. When the cumulative

precision time is equal to the scan interval, the module for

vehicle movement Move All Vehicles will be activated to

move all the vehicles in the simulation road stretch, with their

current parameter values. The above process will be

continued until the clock time matches with the assigned totalsimulation time.


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5. TRAFFIC CHARACTERISTICS

The different types of vehicles present in the

heterogeneous traffic, for the purpose of this study, weregrouped into eight different categories as follows. 1.

Motorized two-wheelers (M.T.W), which include motor

cycles, scooters and mopeds, 2. Motorized three-

wheelers (M.Th.W), which include Auto-rickshaws

three wheeled motorized paratransit vehicles to carry a

maximum of three passengers and tempos three

wheeled motorized vehicles to carry small quantities of

goods, 3.Cars including jeeps and small vans, 4. Light

commercial vehicles (LCV) comprising large passenger

vans and small four wheeled goods vehicles, 5. Bus, 6.

Truck, 7. Bicycle and 8.Tricycle, which includes cycle-

rickshaw- three wheeled pedal type paratransit vehiclesto carry a maximum of two passengers and three wheeled

pedal type vehicles to carry small amount of goods over

short distances. As this study pertains to traffic flow on

urban arterials, animal drawn vehicles were not

considered as these vehicles are not permitted/present

in negligible number on these roads. Each animal drawn

vehicle, if present, was taken to be equivalent to two

tricycles for the purpose of simulation.

The average overall dimensions of the vehicle types

and the field observed lateral and longitudinal clearances

between the vehicles are as shown in Tables 1 and 2respectively. The lateral clearance-share values are used

to calculate the actual lateral clearance between vehicles

based on the type of the subject vehicle and the vehicle

by the side of it. For example, at zero speed, if an auto-

rickshaw is beside a bus, then the clearance between

the two vehicles will be 0.2 + 0.3 = 0.5 m. The longitudinal

clearance, at zero speed can be calculated by the same

procedure. The field observed acceleration rates of the

different types of vehicles, for three different speed

ranges, are shown in Table 3.

6. MODEL VALIDATION

6.1 Data Collection

Heterogeneous traffic flow, in one direction, onstraight and level stretch of a four-lane divided road with

raised curbs, in the southern part of Chennai city, India

was considered for model validation. The width of the

road space available for each direction of flow is 7.5 m.

Out of the total width of 7.5 m, a 1.5 m wide road space,

adjacent to the curb, is reserved for bicycles by making

paint marking on the pavement surface. The traffic flow

on the stretch was measured for one hour by video

capturing the traffic flow and making classified count of

vehicles after transferring the video data to a computing

work station. A total of 3704 vehicles were observed to

pass through the section during the observation periodof one hour. It was found during the traffic count that

Overall dimension (m)

Vehicle type Length Breadth

(1) (2) (3)

Buses 10.3 2.5

Trucks 7.5 2.5

LCV 5.0 1.9

Cars 4.0 1.6

M.Th.W. 2.6 1.4

M.T.W. 1.8 0.6

Bicycles 1.9 0.5Tricycles 2.5 1.3

TABLE 1. OBSERVED VEHICULAR DIMENSIONS

TABLE 2. MINIMUMAND MAXIMUM LATERAL CLEARANCES

Lateral-clearance share (m)

Vehicle type At zero speed At a speed of 60 km/h(1) (2) (3)

Buses 0.3 0.6

Trucks 0.3 0.6

LCV 0.3 0.5

Cars 0.3 0.5

M.Th.W. 0.2 0.4

M.T.W. 0.1 0.3

Bicycles 0.1 0.3*

Tricycles 0.1 0.3*

* Maximum speed of these vehicles is 20 km/h

TABLE 3. ACCELERATION RATES OF DIFFERENT CATEGORIES

OF VEHICLES

Rate of acceleration at various

speed ranges (m/s2)

Vehicle type 0-20km/h 20-40 km/h Above

40 km/h

(1) (2) (3) (4)

Buses 0.89 0.75 0.67

Trucks 0.79 0.50 0.43

LCV 0.82 0.45 0.35

Cars 1.50 1.10 0.95

M.Th.W. 1.01 0.45 0.30

M.T.W 1.35 0.80 0.60

Bicycles 0.10 - -

Tricycles 0.07 - -


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there were no animal drawn vehicles present on the study

stretch. Also, trucks and tricycles constituted respectively

0.28 and 0.15 per cent of the vehicles. The percentagesbeing very small for the purpose of simulation, the trucks

which are close to buses in respect of size and speed,

were considered as buses and each of the tricycles, which

are close to bicycle in dynamic characteristics were

considered to be two bicycles. The observed composition

of the traffic after the above said modification is depicted

in Figure 3. The simulation model requires the free speed

parameters of vehicles to initialize and assign the speed

during their placement in the simulation stretch. The free

speed parameters obtained through field measurement

during lean traffic periods on the study stretch, are shown

in Table 4. The free speed of cars (for any vehicle)depends on the make of the car, the age of the car, the

level of maintenance of the car, the age, sex and the

behaviour of the driver. These factors fall over a wide

range under Indian conditions. This is the reason for a

wide range in the value of free speeds of cars.

Fig. 3. Composition of field observed traffic

TABLE 4. FREE SPEED PARAMETERSOF DIFFERENT TYPES

OF VEHICLES

Free speed parameters in km/h

Vehicle Mean Minimum Maximum Standard

type Deviation

(1) (2) (3) (4) (5)

Bus 53 38 68 7

LCV 50 37 65 7

Car 60 40 90 14

M.Th.W 45 30 55 7

M.T.W. 48 25 60 12

Bicycle 14 10 18 3

For the observed traffic volume of 3704 vehicle/h

the inter arrival time between successive vehicles,

namely the time headway () has been found to be

1.03 seconds. The grouped headway data with a classinterval of 0.8s, was found, using chi-square test, to

fit into Negative Exponential distribution. The

calculated chi-square value is 12.19 which is less the

critical value from chi-square table for 7 degrees of

freedom at 5 per cent level of significance of 14.07

and thus confirms the goodness-of-fit. The details of

the 2 test are given in Table 6.

The cumulative frequency of the field observed and

theoretical headways, plotted on the same set of axes, is

shown in Fig. 5. It can be seen that both are matching

with each other well.

6.2. Model Calibration

There are several probability distributions available

to describe the vehicle arrival pattern and headway

distribution of traffic flow. In this study Poisson

distribution and Negative exponential distributions were

found to fit well for vehicle arrival pattern and headway

distribution respectively (Rao et al. (1988)). The Chi-

square goodness of fit test shows that observed

frequencies have significant fit with Poisson distribution

for vehicle arrival pattern. The calculated chi-square

value is 12.136 against the critical value from chi-square

table for 9 degrees of freedom at 5 per cent level of

significance of 16.92. Thus, it is found that, thecalculated chi-square value is less than the table value

as shown in Table 5. This confirms the goodness-of-

fit. The Poisson arrival pattern is also pictorially

depicted in Fig. 4.

Fig. 4. Observed vehicle arrivals pattern


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TABLE 6. GOODNESS-OF-FIT TESTFOR HEADWAY DISTRIBUTION

Class Interval Theoretical Frequency of Theoretical Frequency Observed Frequency

headway >Lower class limit in the class (E) in the Class (O)

(1) (2) (3) (4) (5)

0.0 0.8 3704 2000 2055 0.486

0.8 1.6 1704 920 944 0.624

1.6 2.4 783 423 395 1.872

2.4 3.2 360 195 175 1.976

3.2 4.0 166 90 72 3.423

4.0 4.8 76 41 32 2.040

4.8 5.6 35 19 18 0.046

5.6 6.4 16 9 5 1.578

6.4 7.2 7 7 8 0.143

7.2 & More 3

2 Value at 5 per cent level of significance for 7 degrees of freedom = 14.07 2 Value = 12.19

E

EO 22 )( =

TABLE 5. GOODNESS - OF - FIT TESTFOR VEHICLE ARRIVAL PATTERN

No. of Veh. Observed No. Expected No. Theoretical Frequency Observed Frequency

Arrivals ( r ) of Arrivals of Arrivals in the Class (E) in the Class (O)in 5 seconds

(1) (2) (3) (4) (5) (6)

0 2 4 23 14 3.606

1 12 19

2 60 51 51 60 1.622

3 89 89 89 89 0.000

4 117 117 117 117 0.000

5 136 122 122 136 1.561

6 105 107 107 105 0.028

7 71 80 80 71 0.996

8 48 52 52 48 0.364

9 28 30 30 28 0.204

10 14 16 16 14 0.246

11 10 8 12 18 3.508

12 & Above 8 4

2

Value at 5 per cent level of Significance for 9 degrees of freedom is = 16.92 12.136

E

EO 22 )( =


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Fig. 5. Observed and theoretical headways

statistical basis, are shown in Table 7. It can be seen

that the simulated speed values significantly replicate

the field observed speeds of the different categories ofvehicles.

6.3. Model Validation

It is desirable to validate simulation models based

on traffic characteristics that are derived out of the

simulation process. Accordingly, it was decided to

compare the speeds of each categories of vehicles

obtained through simulation with the corresponding

observed values. The speed values were derived by

simulating the traffic over a 7.5 m wide straight stretch

of road of 1400 m length. The middle 1000 m was the

observation stretch. The initial 200 m length at the entry

point was used as a warm up zone and a 200 m length at

the exit point was also excluded from the analysis. To

ensure stable flow condition during the measurement,

the simulation clock was set to start only after the first

50 vehicles crossed the exit end of the road stretch.

During the simulation process, the time taken by each

vehicle to traverse the specified simulation stretch was

observed to estimate the speed maintained by each

vehicle. Then, a histogram of simulated and observed

speeds was made as shown in Fig. 6. It can be seen that

the observed and simulated speeds are matching to a

greater extent in all the cases.

The details of the comparison of the simulated and

observed speeds of different categories of vehicles on

Fig. 6. Comparison of observed and simulated speeds

TABLE 7. DETAILSOF COMPARISONOF THE OBSERVEDAND

SIMULATED SPEEDS ON STATISTICAL BASIS

7. VEHICULAR INTERACTION

The study of vehicular interaction is intended to quantify

the relative impact of the presence of each of the different

types of vehicles on traffic flow. This can be achieved by

estimating the PCU values for the different categories of

vehicle in the traffic. After a careful study of the various

approaches adopted for estimation of PCU of vehicles, it

was found that the methodology of approach of Transport

and Road Research Laboratory (TRRL), London, UK

may be appropriate for the heterogeneous traffic being

dealt with. The PCU has been defined by TRRL (1965)

as follows: on any particular section of road under

particular traffic condition, if the addition of one

vehicle of a particular type per hour will reduce the

average speed of the remaining vehicles by the same

amount as the addition of, say x cars of average size

per hour, then one vehicle of this type is equivalent tox PCU. This definition has been taken as the basis for

Vehicle Observed Simulated Difference Squared

type average speedin (Deviation) deviation

speed in km/h

km/h

Buses & 31.47 30.39 1.08 1.17

Trucks

LCV 30.86 30.50 0.36 0.13

Cars 33.4 32.31 1.09 1.19M.Th.W 31.18 32.31 -1.13 1.28

M.T.W 33.59 35.12 -1.53 2.34

Bicycles 13.63 15.73 -2.1 4.41

Total 7.29 10.51

dmean

= Mean of observed difference =7.29/6 = 1.21

tstatistic, to= d

mean/(S

d/K),

where K= Number of data sets =6

Sd

2 = 10.51/5= 2.102, where Sd

is the Standard Deviation;

Sd

=1.449

to

= 1.21/(1.449/6) =2.06

The critical value of t statistical for 0.05 level of significance and5 degrees of freedom, obtained from standard t-distribution table,

is 2.57. Thus, it can be seen that the value of t statistic calculated

based on the observed data (to) is less than the corresponding

Table value. This implies that the simulated speeds significantly

represent the observed speeds


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derivation of PCU values, in this study.

7.1. Vehicular Interaction in Cars-only Traffic

Though the prime objective of this study is to quantify

the vehicular interactions in terms of PCU under

heterogeneous traffic, it will be appropriate to estimate

the PCU values of different vehicle types while moving

with cars-only traffic stream to provide a set of basic

PCU values of the different types of vehicles. This will

provide information on the absolute amount of impedance

caused by a vehicle type while moving in the traffic

stream, which comprises of cars and the subject vehicles

only. In this regard, the model was first used to simulate

homogeneous traffic (100 per cent passenger cars) in

one direction, on four-lane, divided urban road to develop

the fundamental speed-flow diagram. Thus, the width

of road space available for movement of traffic in one

direction will be 7.5 m. The total length of road stretch

considered for the experiments is 1400 m, with 200 m

sections at the entry and exit excluded from output data

collection as warm-up and stabilizing section. The central

1000 m stretch was considered as the observation stretch,

the various traffic flow parameters were recorded while

vehicles were moving through it. To account for the

variation due to randomness, the simulation runs were

repeated using three different-random number streamsto check for the consistency of the results. Then a

graphical relationship between average speed and traffic

volume was developed as depicted in Fig. 7. Using the

speed-flow curve, the capacity of 7.5 m wide road space

under homogeneous traffic condition, with traffic flow

in one direction, was then obtained to be about 3250

passenger cars per hour as shown in Fig. 7.

Since, speed is the performance measure identified

to estimate the PCU values, average speed of cars-only

Fig. 7. Speed-flow relationship on 7.5 m wide road underhomogeneous traffic condition Fig. 8. Variation of PCU values of buses

traffic for a set of selected volume levels were estimated

by simulating the homogeneous traffic flow, starting from

very low volume to capacity level. The impedance causedby a vehicle type, in terms of PCU, for a chosen volume

level was estimated by replacing a certain percentage

(the observed percentage composition of the subject-

vehicle in the field- Fig. 3) of cars in the homogeneous

traffic stream with the subject-vehicle type, such that,

the average speed of cars remained the same as before

the replacement of the cars. The number of subject

vehicle can be adjusted on trial basis by observing the

average speed of cars in each trial. If the average car

speed is more, after replacement, than the average car

speed under homogeneous traffic, it is to be inferred

that, the introduced number of subject vehicles is

inadequate to compensate for the removed cars. Similarly,

if the average speed of cars, after replacement, is less

than the average car speed under homogeneous traffic,

it is to be inferred that the introduced subject-vehicle

volume is more than the equivalent volume of cars. After

regaining the original speed of cars by adjusting the

number of subject vehicles, the PCU value of the vehicle

type can be estimated using the relation,

addedtypevehiclesubjectofNumber

removedcarsofNumbertypevehiclesubjectofValuePCU

=

The logic behind the above approach is that, as stated

in the definition of PCU, the introduced subject vehicle

type creates more or less the same effect on the traffic

stream that is equivalent to that of the cars removed

from the stream. The PCU value of the subject-vehicle

was determined, following the said procedure, for the

same set of traffic volume levels selected for cars-only

traffic. Then a plot relating the chosen traffic volume

levels and the corresponding PCU values of the subject

vehicle was made. Such plots made for the different

vehicle categories are shown in Figs. 8 through 12.


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It can be seen that in all the cases (Fig. 8 through 12) that at

lower volume levels, the PCU value of the subject vehicle

increases with increase in traffic volume. Whereas, at highervolume levels, the PCU value of the subject vehicle

decreases with increase in traffic volume. The reasons for

these trends can be explained as follows. The lower

magnitude of PCU values at the low-volume level may be

attributed to the longer space headway between the vehicles

at lower volume levels. Then, the presence of subject

vehicles may not impose severe impedance to movement

of cars, even though the free speed of subject vehicle is

less than the free speed of cars. Due to the availability of

larger gaps, cars can overtake the subject vehicle without

considerable reduction in speed. As the volume of traffic

increases, however, the headway between the vehicles tendsto decrease, resulting in increased magnitude of impedance

caused to the movement of cars. It was observed that, the

relative difference between the average speeds of cars

and the subject vehicles decreases as the traffic volume

increases. At volumes near capacity level, the speed

difference between cars and subject vehicles tends to vanish,

due to reduced speed of the vehicles irrespective of their

free speed and operational capabilities. This causes

considerable reduction in the impedance caused by the

subject vehicle to the movement of cars, which results in

lesser PCU value for the subject vehicle.

7.2. Vehicular Interaction under Heterogeneous

Traffic

As a first step towards quantifying the vehicular

interactions under heterogeneous traffic, speed-flow

relationship for heterogeneous traffic flow was developed

on 7.5 m wide road space by conducting simulationexperiments taking the field observed traffic composition

as the basis. The developed relationship is depicted in Fig.

13. The average stream speed for a traffic volume level

was estimated by taking the weighted average speed of

different vehicles obtained from the simulation output. It

can be seen that, the developed speed-flow relationship

under heterogeneous traffic follows the well established

parabolic trend, indicating the validity of the model for

simulating highly heterogeneous traffic flow. The capacity

of 7.5 m wide road space under heterogeneous traffic,

for the observed traffic composition, was estimated to beabout 4150 vehicles per hour.

Fig. 9. Variation of PCU values of light commercial

vehicles

Fig. 10. Variation of PCU values of motorised three-wheelers

Fig. 11. Variation of PCU values of motorised two-wheelers

Fig. 12. Variation of PCU values of bicycles


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The PCU values for the different types of vehicles,at various volume levels, were estimated by taking the

average stream speed as the measure of performance.

Accordingly, the stream speed of the heterogeneous traffic

for a chosen volume level was first determined by

conducting simulation experiments with the specified traffic

composition. Then certain percentage (50 per cent) of

cars were replaced by the subject vehicle type in the mixed

traffic stream, such that the average stream speed

remained the same as before the introduction of the

additional subject vehicles in the stream. This was

achieved by varying the number of the subject vehiclesintroduced to substitute the removed cars until the original

speed of the traffic was obtained by simulation. Then, the

number of cars removed divided by the number of subject

vehicles introduced will give the PCU value of that vehicle

type. To account for the variation due to randomness,

three random number seeds were used for simulation and

the average of the three values was taken as the PCU

value. This procedure was repeated for different volume

levels falling over a wide range. The trends of variation of

PCU values for the different types of vehicles, along with

the variation of the traffic stream speed, over traffic

volume, are shown in Figures 14 through 18.

Fig. 13. Speed-flow relationship under heterogeneous traffic

on 7.5 m wide road

Fig. 14. Variation of PCU values of buses

Fig. 15. Variation of PCU values of light commercial vehicles

Fig. 16. Variation of PCU values of motorised three-wheelers

Fig. 17. Variation of PCU values of motorised two-wheelers


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It can be seen that the general trend of variation of

the PCU values of vehicles over volume is the same as

in the case of cars-only traffic. Hence, the explanation

provided for the trend in the case of cars-only traffic is

valid for heterogeneous traffic condition also, the only

minor difference being the flattening of the curve at very-

high-volume levels. This implies that the constrained

condition of movement experienced by the vehicles at

capacity-flow level in cars-only traffic is reached well

before the capacity-flow level in the case of

heterogeneous traffic.

7.3. Effect of Traffic Composition on PCU Values

It is clear that the degree of heterogeneity of traffic

stream affects the speed and other traffic flow

parameters, and influences the magnitude of interaction

between the moving vehicles significantly. The presence

of a vehicle type, other than car, in the cars-only traffic

stream, creates a traffic condition, which is totally

different from the cars-only traffic condition. The change

in the traffic condition make the vehicles to offer varying

amount of impedance to the movement of adjacentvehicles in the traffic stream, depending upon the extent

of variation of traffic stream from cars-only

(homogeneous) traffic condition.

In the light of the said fact, a comparison of the

interactions of different vehicle types in cars-only traffic

and in heterogeneous traffic, the amount of interaction

having been measured in terms of PCU, will be useful.

Figs.19 through 23 illustrate the comparison of PCU

values of different vehicle type and their variations over

traffic volume, in cars-only traffic and heterogeneous

traffic flow conditions. It may be noted that, to facilitateplotting of the variation of PCU in homogeneous and

heterogeneous traffic conditions using the same set of

axes, the traffic volume has been represented using

volume-to-capacity ratio.

Fig. 18. Variation of PCU values of bicycles

Fig. 21. PCU values of motorised three-wheelers on 7.5 mwide road

Fig. 19. PCU values of buses on 7.5 m wide road

Fig. 20. PCU values of light commercial vehicles on 7.5 m

wide road


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It can be seen that, the magnitude of vehicular

interactions measured in terms of (PCU), under cars-only

traffic condition, are significantly higher for all the vehicle

types, when compared to their corresponding values under

heterogeneous traffic condition. Higher PCU values under

cars-only traffic condition may be attributed to the higher

speed difference between the cars and the subject vehicle

speed in cars-only traffic than the difference between car

speed and subject vehicle speed under heterogeneous traffic

condition. For example, at volume-to-capacity ratio value

of 0.75, under cars-only traffic condition, the average speed

of cars is 53.94 km/h and buses is 48.36 km/h, with a speed

difference of 5.58 km/h. Whereas under heterogeneous

traffic condition, the average car speed for the same volume-

to-capacity ratio is 30.95 km/h and the average bus speed

is 28.40 km/h, resulting in a speed difference of 2.55 km/h.

The PCU values of buses at this level of traffic flow under

cars-only traffic and heterogeneous traffic conditions were

3.5 and 2.5 respectively.

7.4. Effect of Roadway Width on PCU Values

As one of the objectives of this research work is to

study the effect of roadway width on PCU values ofvehicles, the PCU values of the different categories of

vehicles were estimated, by simulating traffic flow on

different widths of roads. For the purpose of this study

heterogeneous traffic flow of a selected composition on

three different widths of road, namely, 7.5 m, 11.0 m and

14.5 m (equivalent to the widths of 2,3 and 4 lane roadways

of urban roads) was considered. The PCU values of the

different types of vehicles were considered for a wide

range of traffic-volume levels on the three roadways. Since

the capacity of a roadway section varies with its width,

the PCU values on these roads needs to be comparedbased on some common traffic flow criterion. For this

purpose, volume-to-capacity ratio (v/c ratio) was selected

as the traffic flow criterion common to different widths of

roads. In order to make the above comparison, the PCU

values of different vehicle types were estimated at the

selected volume-to-capacity ratio levels. The plots relating

the PCU values of a vehicle type and the selected volume-

to-capacity ratios, made for the three roadway widths, on

the same set of axes, are shown in Figs. 24 through 27.

Fig. 22. PCU values of motorised two-wheelers on 7.5 m wide

road

Fig. 23. PCU values of bicycles on 7.5 m wide road

Fig. 24. Variation of PCU values of buses on 7.5 m, 11.0 m

and 14.5 m wide roads

Fig. 25. Variation of PCU values of light commercial

vehicles on 7.5 m, 11.0 m and 14.5 m wide roads


13/17


It is observed (Fig. 24 through 27) that the PCU valueof a vehicle type, at a given volume-to-capacity level,

increases with increase in width of roadway. There has

been marginal increase in magnitude of PCU values on

14.5 m wide road when compared to the corresponding

values on 11.0 m road. Similarly, there is marginal increase

in the PCU values on 11.0 m wide road when compared

with 7.5 m wide road spaces. It would be useful to know

the reason for the higher PCU values on wider roads. As

the first step in this regard, plots connecting the volume

(volume to capacity ratio) and the speed of the different

types of vehicles were made for 7.5 m, 11.0 m and 14.5m wide roads as shown in Figs. 28 through 32.

Fig. 27. Variation of PCU values of motorised two wheelers

on 7.5 m, 11.0 m and 14.5 m wide roads

Fig. 26. Variation of PCU values of motorised three-

wheelers on 7.5 m, 11.0 m and 14.5 m wide roads

Fig. 28. Speed-flow relationships for cars on 7.5 m, 11.0 mand 14.5 m wide roads

Fig. 29. Speed-flow relationships for buses on 7.5 m,

11.0 m and 14.5 m wide roads

Fig. 30. Speed-f low relationships for light commercial

vehicles on 7.5 m, 11.0 m and 14.5 m wide roads

Fig. 31. Speed-flow relationships for motorised three-

wheelers on 7.5 m, 11.0 m and 14.5 m wide roads

Fig. 32. Speed-flow relationships for motorised two-wheelers

on 7.5 m, 11.0 m and 14.5 m wide roads


14/17


It can be found from the plots that in all the cases,

for a given volume to capacity ratio, the speed of a

vehicle type increases with increase in the width ofroad space. The reason for this may be attributed to

the fact that when vehicles do not follow traffic lanes

and occupy any lateral position on the road space, while

manoeuvring forward, the manoeuvring process

becomes relatively easier on wider roads facilitating

faster movement of vehicles.

As all the vehicles are able to move relatively faster

on wider roads, the reason for higher PCU values on

wider roads cannot be explained using the speed data

shown in Figs. 29 through 34. The increase in width of

roadway invariably provides relatively highermanouverability for all vehicle types on wider roads. The

interaction between the vehicles is quantified in terms

of PCU, which is the amount of impedance caused by a

vehicle type in comparison with that of passenger cars

as the reference vehicle. Comparing the change in

performance of cars while increasing the width of

roadway, with that of subject vehicle will be the

appropriate way to investigate the PCU variation on

different road widths.

Hence, it was decided to calculate the percentage

increase in speeds of all types of vehicles, with increase

in road width, so that the increase in car speed can be

compared with the increase in the speed of other vehicles.

The comparison of speeds of different vehicles at

selected volume-to-capacity levels between 7.5 m to 11.0

m and 11.0 m to 14.5 m wide road spaces are as shown

in Tables 8 and 9 respectively.

It can be seen from the tables 8 and 9 that at all the

chosen volume-to-capacity ratio values, the percentage

increase in speed of cars is higher than the percentage

increase in speed of all the other categories of vehicles.The higher free speed, acceleration and other mechanical

capabilities of cars facilitate cars to gain more speed

with increase in the road width when compared to other

vehicle categories. Hence, it is clear that the increase in

speed difference between cars and other categories of

vehicles with increase in width of road space, has resulted

in increased PCU values with increase in the width of

road space.

8. CHECK FOR ACCURACY OF PCU ESTIMATES

The check for the accuracy of the PCU estimateswas done by simulating homogeneous (cars-only) traffic

TABLE 9. SPEEDSON 11.0 m AND 14.5 m WIDE ROAD SPACES

Speed of the vehicle

type (km/h)

Vehicle Volume to On 11.0 m On 14.5 m Percentage

type capacity wide road wide road increase

ratio in speed

(1) (2) (3) (4) (5)

Cars 0.25 56.95 64.90 14.0

0.50 47.50 54.00 13.7

0.75 35.70 37.70 5.6

Buses & 0.25 49.40 56.00 13.4

Trucks 0.50 42.00 46.20 10.

0.75 31.50 33.10 5.1

LCV 0.25 48.60 54.00 11.1

0.50 42.40 47.00 10.8

0.75 32.50 34.00 4.6

M.Th.W. 0.25 43.50 46.40 6.7

0.50 42.00 44.50 6.0

0.75 35.50 36.60 3.1

M.T.W. 0.25 45.80 51.50 12.4

0.50 44.00 49.25 11.90.75 38.50 40.45 5.1

TABLE 8. SPEEDSON 7.5 m AND 11.0 m WIDE ROAD SPACES

Speed of the vehicle

type (km/h)Vehicle Volume to On 7.5 m On 11.0 m Percentage

type capacity wide road wide road increase

ratio in speed

(1) (2) (3) (4) (5)

Cars 0.25 53.20 56.95 7.0

0.50 41.60 47.50 14.2

0.75 30.95 35.70 15.3

Buses & 0.25 46.50 49.40 6.2

Trucks 0.50 36.90 42.00 13.8

0.75 28.40 31.50 10.9

LCV 0.25 45.90 48.60 5.9

0.50 38.00 42.40 11.6

0.75 29.00 32.50 12.1

M.Th.W. 0.25 42.80 43.50 1.6

0.50 38.00 42.00 10.5

0.75 31.50 35.50 12.7

M.T.W. 0.25 45.20 45.80 1.3

0.50 41.20 44.00 6.8

0.75 34.60 38.50 11.3


15/17


and the heterogeneous traffic flows on the same road

space. For this purpose, first, the cars-only traffic flow

was simulated on 7.5 m wide road space and the roadcapacity was obtained as 3250 cars per hour by making

the speed-flow curve. Then, the flows in cars per hour

corresponding to a set of volume-capacity ratios were

determined. The capacity of 7.5 m wide road, under the

heterogeneous traffic condition is 4150 vehicles per hour.

Knowing the composition of the heterogeneous traffic,

it is possible to know the number of vehicles of each

category present in the traffic stream at the capacity

flow level of 4150 vehicles per hour. The PCU values of

the different vehicle categories, at capacity-flow condition

were obtained from Figures 24 through 28. Then, the

number of vehicles in each category multiplied by the

corresponding PCU value gives the PCU equivalents of

each category of vehicles. The sum of the equivalent

values, then, gives the capacity flow of heterogeneous

traffic in PCU per hour. On the same lines, the flow in

PCU per hour of the heterogeneous traffic, for the

selected set of volume-capacity ratios were estimated.

Then, plots, relating the set of volume to capacity ratios

and the corresponding flow were made for cars-only

and the heterogeneous traffic as shown in Fig. 33.

It can be seen that both the plots are closely relatedto each other indicating that the PCU estimates made,

are fairly accurate at all volume levels. To explain the

accuracy of estimates on statistical basis, paired t test

was performed by relating the flow in number of cars

TABLE 10. STATISTICAL TESTFOR PCU VALUESON 7.5 m WIDE ROAD SPACE

Fig. 33. Traffic volumes in PCU on 7.5 m road space

V/C Ratio Volume in PCU Difference Deviation Square of

Homogeneous Heterogeneous from mean Deviation

traffic Traffic difference from mean

difference

(1) (2) (3) (4) (5) (6)

0.118 382 369 13 -2.6 6.9

0.235 765 766 -1 -16.6 276.7

0.353 1147 1233 -86 -101.6 10,329.4

0.471 1529 1845 -416 -431.6 186,307.8

0.588 1912 2028 -116 -131.6 17,327.5

0.706 2294 2357 -63 -78.6 6183.3

0.824 2676 2596 80 64.4 4143.0

0.941 3059 2778 281 265.4 704,19.2

1.000 3250 2802 448 432.4 186,940.4

= 140 - 481,934.3

per hour for the selected set of volume-to-capacity ratios

and the corresponding heterogeneous traffic flows

expressed in PCU per hour. The details of t test conducted

for 7.5 m wide road space is shown in Table 10.

dmean

= Mean of observed difference = 140 / 9 = 15.56

t statistic of observed speeds, to

= dmean

/(sd

/k), wherek = Number of data sets = 9

sd

2 = 481934.4/ (k-1) = 481934.4/8 = 60241.78, where

sd is the standard deviation; sd = 245.44Therefore, |t

o|= 15.56 / (245.44 /9) =0.20

The critical value of t statistic for 0.05 level of

significance and 9 degrees of freedom, obtained from


16/17


standard t-distribution Table, is 2.26. Thus, it can be seen

that the value of t statistic calculated based on the

observed data (t0) is less than the corresponding tablevalue. Based on the closeness of the plots made for

homogeneous and heterogeneous traffic volumes at

selected volume to capacity ratios, and based on the

statistical test, it may be concluded that the estimated

PCU values are accurate. The results of similar exercises

done for 11.0 m and 14.5 m wide road spaces indicate

that, in these cases too, the respective plots match with

each other. To check for the statistical significance in

this regard, paired t tests were conducted. The calculated

values of t (t0) are 1.42 and 1.01 against the table values

of 2.13 and 2.18 respectively for 11.0 m and 14.5 m

wide road spaces indicating that there are no significant

differences in the volumes of cars-only and

heterogeneous traffic, measured in PCU, at the selected

volume to capacity ratios, in both the cases.

9. CONCLUSIONS

The following are the important conclusions drawn

based on this study:

1. The validation results of the simulation model of

heterogeneous traffic flow indicate that the model is

capable of replicating the heterogeneous traffic flowon mid block sections of urban roads to a highly

satisfactory extent. The validity of the model is further

confirmed by the speed-flow relationships developed,

using the simulation model, for 7.5 m, 11.0 m, and

14.5 m wide road spaces, which are found to follow

the well established trend of the speed-flow curves.

2. The PCU estimates, made through simulation, for

the different types of vehicles of heterogeneous

traffic, for a wide range of traffic volume levels

indicate that the PCU value of a vehicle significantly

changes with change in traffic volume.

3. It is found that, by virtue of the complex nature of

interaction between vehicles under the heterogeneous

traffic condition, at low volume levels, the PCU value

of vehicles increases with increases in traffic volume,

whereas under higher volume conditions the PCU

value decrease with increase in traffic volume.

4. The results of the simulation experiment to study

the effect of road width on PCU values indicate

that for any vehicle type in heterogeneous traffic,

the PCU value increases with increase in the widthof road space.

5. The check performed to ascertain the accuracy of

the PCU estimates by comparing the flow of cars-

only and the PCU equivalent of heterogeneoustraffic on 7.5 m, 11.0 m, and 14.5 m wide road spaces

indicate that, the estimates are fairly accurate.

6. Thus, for the traffic condition considered for this study,

there is reason to treat PCU value of a vehicle type as

a dynamic quantity rather than treating it as a constant.

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