International Journal of Advances in Engineering Sciences and Applied Mathematics

, Volume 5, Issue 2, pp 177–194

# Estimating capacity for eight-lane divided urban expressway under mixed-traffic conditions using computer simulation

## Authors

• Ravikiran Puvvala
• Department of Civil EngineeringBirla Institute of Technology and Science
• Balaji Ponnu
• Department of Civil EngineeringBirla Institute of Technology and Science
• Department of Civil EngineeringBirla Institute of Technology and Science
• S. Velmurugan
• Principal Scientist and Head, Traffic Engineering and Safety DivisionCentral Road Research Institute (C.R.R.I.)
Article

DOI: 10.1007/s12572-013-0089-z

Puvvala, R., Ponnu, B., Arkatkar, S. et al. Int J Adv Eng Sci Appl Math (2013) 5: 177. doi:10.1007/s12572-013-0089-z
• 265 Views

## Abstract

Expressways in India are vastly different from other roads of the country based on roadway and traffic conditions and additionally, there is no perfect strict lane discipline. Nevertheless, there is not much research literature available specific to these categories of roads in India. The knowledge of roadway capacity is an important basic input required for planning, design, analysis and operation of roadway systems. Hence, this work aims to model traffic flow on Indian urban expressways with specific reference to Delhi–Gurgaon expressway and estimate its capacity using the micro-simulation model, VISSIM. Field data collected on traffic flow characteristics on expressways are used in calibration and validation of the simulation model. The validated simulation model is then used to estimate passenger car unit (PCU) values for different vehicle types and derive capacity value. It was found that the PCU value for each of the vehicle categories decreases with increase in vehicular flow under uncongested regime. It was also found that the PCU value for heavy and larger vehicle types are higher under congested regime as compared to their respective PCU values near capacity. The capacity of a eight-lane divided urban expressway in level terrain with 14.0 m wide road space is found to be about 9700 PCU/h, for one direction of traffic flow.

### Keywords

Mixed traffic flowExpresswaysSimulationPassenger car unitCapacity

## 1 Introduction

An urban expressway is defined as an arterial highway for motorized traffic, with divided carriageways for high speed travel, with full control of access and usually provided with grade separators at location of intersections. They are the highest class of roads in the Indian Road Network. Higher design speeds, restriction on slow moving vehicles, varied traffic composition with high amount of cars characterize these roads. With such operational difference and with many urban expressways such as Delhi–Gurgaon, Delhi–Noida Direct (DND) Flyway, Noida–Greater Noida Expressway (NGN), being in existence and more number of them such as the Kundli–Manesar–Palwal Expressways being built, a thorough understanding of their traffic operation is imperative. Traffic flow in Indian expressways is quite interesting to be studied due to two reasons. First, the traffic is multi-class with vehicles such as cars and pickups with their high maneuverability and heavy vehicles such as trucks and buses. The speeds of these vehicles may vary from 40 to over 100 km/h. Traffic movement on Indian expressways may be said to be quasi-lane disciplined, with some vehicles following a lane-based driving and many others not. Such a lack of lane discipline can be attributed to combination of factors viz. enforcement and education. Indian drivers are not educated about the importance of sticking to their lanes other than for overtaking and improving driving speeds. There are neither video cameras mounted at select locations of the roads nor a central monitoring system that reports violations. Consequently vehicles tend to take any lateral position along the width of roadway, based on space availability. When such different types of vehicles with varying static and dynamic characteristics are allowed to mix and move on the same roadway facility, a variable set of longitudinal and transverse distribution of vehicles may be noticed from time to time. Hence expressways remain as a partially heterogeneous traffic characterized by poor lane discipline. Given this significant difference in the nature of traffic flow in expressways in relation with other kind of roads in India as explained above, there are not much research work on either design or operation of these facilities.

Under heterogeneous or partially heterogeneous conditions, expressing traffic volume in terms of vehicles per hour per lane is irrelevant as there is either no or partial lane discipline. One way to represent the heterogeneous traffic flow is to express each vehicle category in terms of the interference it causes to the flow in terms of a standard vehicle category such as car. Such a measure is called the passenger car unit (PCU) as known in India or passenger car equivalent (PCE) worldwide. In general, heterogeneous flows are expressed as PCU per hour taking the whole width of the carriageway into account. But there are many complexities in expressing a vehicle as its equivalent PCU. PCU values of any vehicle category are highly sensitive to the given roadway and traffic conditions such as roadway width, traffic composition, flow and speed of the traffic stream. Hence, adopting a single PCU for a given vehicle is not accurate but rather a dynamic or stochastic PCU that accounts for all the factors should be adopted.

For correct estimation of PCU values, it is necessary to study accurately the influence of roadway and traffic characteristics and the other relevant factors on vehicular movement. Study of these complex characteristics in the field is difficult and time consuming. Also, it may be difficult to carry out such experiments in the field covering a wide range of roadway and traffic conditions. Hence, it is necessary to model road–traffic flow for in depth understanding of the related aspects. The study of these complex characteristics, which may not be sufficiently simplified by analytical solution, can be done using alternative tools like computer simulation. Simulation is already proven to be a popular traffic-flow modeling tool for developing various applications related to the traffic flow on roads. VISSIM is one of the most widely accepted simulation package for simulation of both homogenous and heterogeneous traffic flows.

There is a very less literature available on capacity of expressways which has also found a mention in the 11th Five Year plan (2007–2012) report. Considering all the above, it is imperative and timely to initiate a study on the capacity of expressways depending upon the carriageway/roadway widths and other relevant parameters. Thus, this study is aimed at developing capacity estimates for urban expressway segments under varying traffic conditions, which will help in meeting the country’s need for design, analysis, operations and management of expressways. To this end, the traffic flow on the Delhi–Gurgaon Expressway has been studied and modeled through simulation. The objective of this study is to estimate and study the possible variation of PCU values of different categories of vehicles at various traffic flow levels under heterogeneous traffic conditions prevailing on basic urban expressway section of India in level terrain. VISSIM is used to model the heterogeneous traffic-flow. Field data collected on traffic flow characteristics such as free speeds, acceleration, lateral clearance between vehicles, etc. are used for calibration and validation of the simulation model in VISSIM. The validated simulation model is then used to derive PCU values for different types of vehicles. The estimated PCU values for different vehicle types were then used to derive a capacity estimate in PCU/h for the observed traffic composition.

## 2 Literature review

Simulation has been recognized as one of the best tools for modeling of traffic flow under homogeneous as well as heterogeneous conditions. Fellendorf and Vortisch [16] presented the possibilities of validating the microscopic traffic flow simulation model VISSIM, both on a microscopic and a macroscopic level in homogeneous flows. Hossain [17] calibrated the heterogeneous traffic model in VISSIM to match saturation flows measured by video at an intersection in the city of Dhaka, Bangladesh. Matsuhashi et al. [26] assessed the traffic situation in Hochiminh city in Vietnam, using image processing technique and traffic simulation model (VISSIM). It was found that the high number of motorcycles in the network interfere with other vehicles which reduces average speed of traffic stream drastically. Further, the simulation model was applied for deriving the benefits of increasing the share of public transport. Lownes and Machemehl [24] performed sensitivity of car-following parameters in VISSIM. Huang and Tang [18] calibrated Verkehr in Staedten simulation using VISSIM, for a bay rapid transit project by visual verification and moreover acceptance criteria were defined for volumes. Zhang et al. [38] conducted a study using VISSIM to evaluate a proposed feedback-based tolling algorithm to dynamically optimize High Occupancy Toll (HOT) lane operations and performance. Ishaque and Noland [20] demonstrated the feasibility of modeling vehicle–pedestrian interactions using VISSIM and provided a tool for evaluating policies that affect both vehicle and pedestrian flows.

Many researchers tried to build their own simulation software for studying heterogeneous traffic flow. Arasan and Koshy [4] developed a heterogeneous-traffic-flow simulation model to study the various characteristics of the traffic flow at micro level under mixed traffic condition on urban roads. The vehicles are represented, with dimensions, as rectangular blocks occupying a specified area of road space. The positions of vehicles are represented using coordinates with reference to an origin. For the purpose of simulation, the length of road stretch as well as the road width can be varied as per user specification. The model was implemented in C++ programming language with modular software design. The model is also capable of showing the animation of simulated traffic movements over the road stretch. Dey et al. [14] developed a simulation program coded in Visual Basic language. The authors performed number of simulation runs to determine the capacity of a two-lane road and to study the effect of traffic mix, slow moving vehicles and directional distribution of traffic on capacity and speed. Mathew and Radhakrishnan [25] presented a methodology for representing nonlane-based driving behavior and calibrating a micro-simulation model for highly heterogeneous traffic at signalized intersection. Calibration parameters were identified using sensitivity analysis, and the optimum values for these parameters were obtained by minimizing the error between the simulated and field delay using genetic algorithm. Velmurugan et al. [35] studied free speed profiles and plotted speed–flow equations for different vehicle types for varying types of multi-lane highways based on traditional and microscopic simulation model VISSIM and subsequently estimated roadway capacity for four-lane, six-lane and eight-lane roads under heterogeneous traffic conditions with reasonable degree of authenticity. Arkatkar [5] analyzed heterogeneous traffic flow using microscopic simulation technique. Bains et al. [7] developed a model in VISSIM for simulating the traffic on Mumbai-Pune expressway and estimating the capacity values.

In the developed world such as Europe, United States, Canada and Australia the traffic flow is homogeneous with cars and trucks being the two main categories of vehicles. Researchers in traffic flow in these countries have used PCE for converting trucks into equivalent car units for capacity and level of service estimation. A review of existing literature reveals that many different methods have been used for estimation of PCE values. PCE can be estimated based on (i) delay (Craus et al. [13]; Keller and Saklas [21]), (ii) speed (Linzer et al. [23], Van Aerde and Yagar [32]), (iii) density (Huber [19]; Webster and Elefteriadou [36]), (iv) headway (Werner and Morall [37]; Krammes and Crowley [22]) and (v) queue discharge(Al-Kaisy et al [1, 2]). As all these studies have confined themselves to estimation of PCE for heavy vehicles only (Trucks or Buses) under homogeneous traffic, the results of these studies are not applicable for Indian conditions where heterogeneous traffic with ten different categories of vehicles.

There have been many studies in India on where PCE is called PCU or passenger car unit. Chandra et al. [12] and Chandra [10] proposed a methodology to derive dynamic PCU values based on the relative space requirement of a vehicle type compared to that of a passenger car as the basis of measure. They developed a mathematical model for PCU estimation as the ratio of the speed and projected area ratio of car and subject vehicle. Chandra and Kumar [11] 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. Basu et al. [9] developed a neural network (NN) model to study the non-linear effect of traffic volume and its composition level on the stream speed. The effect of traffic volume and composition on PCE for different types of vehicles under mixed traffic condition was investigated for an urban mid-block section. It was found that the PCE of a vehicle type varies in a non-linear manner with traffic volume and composition. The capacity estimated from this study for Indian expressways has been compared with the capacity values given obtained from multi-country reports (Bang et. al. [8]). There is a great degree of difference in the capacity values of different countries, by virtue of the differences in vehicle characteristics, traffic composition, driver behavior and lane-discipline. In Brazil, the capacity suggested for freeways is 2500 PCU/hour/lane. US-HCM (TRB, 2000) [30] suggests a maximum flow rate on a basic freeway as 2400 PCU/hour/lane. In Indonesia (DGH, 1995) [15], the capacity of four lane divided intercity roads is given as 1900 LVU/hour/lane where LVU refers to light vehicle units. The manuals of highway capacity in most of the countries prescribe that average capacity per lane on different highways is equal. They assume that highway capacity is constantly proportioned to its number of lanes. There have been many studies aimed at assessing the roadway capacity for varying carriageway widths including single lane, intermediate lane, two-lane bi-directional, four-lane and six-lane highways (Tiwari et al. [29]; Velmurugan et al. [33]; Chandra and Kumar [11]; Chandra [10]; Velmurugan et al. [34] and Arkatkar and Arasan [6]) during the last two decades.

With regards to the estimation of capacity of expressways ‘US Highway Capacity Manual (HCM)-2000’ is the most referred document though the (MORTH [27]) had stipulated tentative capacity figures without undertaking detailed studies. In the absence of capacity and level-of-service guidelines for expressway segments between interchanges, in India, MORTH has given a user friendly method considering the default values given in HCM-2000 and subjective adoption of the necessary parameters. Based on the review of literature both at National and International levels, the following important points have been identified: (1) Though most of the researchers in India in the past have aimed at assessing the roadway capacity for varying carriageway widths, but only a limited number of studies have been carried out to determine the capacity of expressways in India, and (2) The guidelines suggested by HCM may not be applied directly under Indian conditions, as the conditions are vastly different on Indian expressways. In view of the above points and considering the fact that a huge network of expressways has been planned in future, there is an urgent need to determine the capacity of such roads for appropriate design.

## 3 Objective and scope

The general objective of the research work reported here is to quantify the vehicular interaction in terms of PCU values of different categories of vehicles and then deriving capacity estimates for a eight-lane divided urban expressway under heterogeneous traffic conditions prevailing in India. A commercially available simulation model, named, VISSIM, is used to study the vehicular interactions, at micro-level, over a wide range of traffic flow conditions. Field data collected on traffic flow characteristics such as free speed, acceleration, lateral clearance between vehicles, etc. are used in calibration and validation of the simulation model. The validated simulation model is then used to derive PCU values for different types of vehicles. The effect of variation of traffic volume on PCU value is studied by deriving PCU values for the different types of vehicles, for a set of traffic-volume levels falling over a wide range. Finally, a check for the accuracy of the estimated PCU values is also made.

## 4 The simulation model

Simulation technique is one of the well-known techniques to study traffic flow and its characteristics. Simulation gives us the advantage of being able to study how the created model behaves dynamically over time or after a certain span of time. Traffic characteristics on roads as a system vary with time and with a considerable amount of randomness and simultaneous interactions. The most difficult and critical process in simulating any traffic flow scenario or for that matter any physical phenomena is to calibrate the simulated model to capture or replicate the ground reality with the desired accuracy. Given this, the results obtained through a validated simulation model would be more accurate than those obtained through analytical results.

The simulation model followed in the present study is shown in the form of a flow chart in Fig. 1. Data in the form of videos collected from the study site was analyzed and this information is used for building the simulation model in the software VISSIM 5.40. Then the model was calibrated and validated for rendering it suitable for replicating the conditions at site. Using this validated simulation model, roadway capacity estimation PCU estimation were done.

## 5 Model calibration and validation

Model calibration is an iterative process of comparing the model to reality, making adjustments (or even major changes) to the model, comparing the revised model to real conditions, making additional adjustments, comparing again, and so on. The comparison of the model to reality is carried out by tests that require data on the system’s behavior plus the corresponding data produced by the model. The input data required for the above mentioned heterogeneous traffic-flow model are related to four aspects viz. road geometrics, traffic characteristics, driver reaction time and vehicle performance. The power of simulation as a tool for the study of traffic flow lies in ability of the model to include the effect of the random nature of traffic. Hence, the random variables associated with traffic flow such as headway distribution are expressed as frequency distributions and input into the simulation model. These data, pertaining to one direction of traffic flow, was collected at a selected stretch of an expressway for model calibration and validation purposes.

## 6 Study stretch & data collection

The Delhi-Gurgaon Expressway is an 8-lane divided facility that connects the city of Delhi with one of its busiest suburbs, Gurgaon. The traffic on the expressway was video graphed from a vantage point, during both peak and non-peak hours on 20th March, 2012. The study stretch was selected after conducting a reconnaissance survey to satisfy the following conditions: (1) The stretch should be fairly straight, (2) Width of roadway should be uniform, and (3) There should not be any direct access from the adjoining land uses. The stretch is a four lane divided road with 5 m wide central median. The width of main carriageway, with bituminous surfacing, for each of the two directions of traffic flow, is 14.0 m. The 1.5 m wide shoulder, on both sides, is paved with bituminous mix. Also, there is no direct access from the adjoining service road because of raised kerbs as shown in Fig. 2. The overall roadway condition has also been depicted in the form of a Google map in Fig. 3.
Free-flow speeds were ascertained by observing 100 vehicles each in different categories of vehicles during non-peak hours, when a flow is less than 200 vph prevailed. Then on the same day, the traffic flow on the road was observed for 2 h in the evening peak period from 16:24 to 18:24 h. This data was then used for the purpose of model validation. A snapshot of the video-captured data is depicted in Fig. 2. The field data input required for the model were collected at the above location with the help of a digital video camera for capturing the traffic flow movement for a total duration of 1 h. The video was then analyzed at a speed one-eighth of the actual speed to enable recording and measurement of data. The traffic flows observed were 7200 and 8573 vph in the first and second hours respectively. Composition of the traffic stream is given in column (2) of Table 1. Performance parameters such as flow and speed were extracted from the videos at a rate of 25 frames per second for achieving a high accuracy for every 20 s time interval. This data then was aggregated to obtain parameters such as flow and speed for every 1, 5, 30 and 60 min intervals for the purpose of model validation. The speeds of the different categories of vehicles were measured by noting the time taken by the vehicles to traverse a trap length of 30 m. The measured free-flow maximum, minimum and mean speeds of various classes of vehicles and the corresponding standard deviations are shown in columns (3), (4), (5) and (6) respectively of Table 1. The speeds of the different categories of vehicles were measured by noting the time taken by the vehicles to traverse a trap length of 30 m using video graphic data. The free speeds of the different categories of vehicles were also measured for the traffic under free-flow conditions.
Table 1

Input data for heterogeneous traffic flow simulation

Vehicle type

(1)

Composition (%)

(2)

Free-flow speeds (km/h)

Vehicle dimension (m)

Lat. clear. share (m)

Max. Speed (3)

Min. Speed (4)

Mean Speed (5)

Std. Deviation (6)

Length (7)

Width (8)

Min. (9)

Max. (10)

BC

20.80

103

78

90

4.00

4.8

1.9

0.40

0.60

SC

50.00

96

65

82

5.33

4.0

1.6

0.30

0.40

Two-wheeler

22.50

87

33

58

8.33

1.8

0.60

0.10

0.30

Three-wheeler

3.30

63

38

50

4.00

2.6

1.4

0.30

0.40

Bus

2.20

93

64

79

5.00

10.3

2.5

0.40

0.60

LCV

0.60

80

63

73

3.33

5.0

1.9

0.40

0.60

Truck

0.60

69

48

60

4.00

7.5

2.5

0.40

0.60

LCVs Light Commercial Vehicles, BC big cars, SC Small cars

The overall dimensions of all categories of vehicles adopted from literature [4] are shown in columns (7) and (8) of Table 1. Any vehicle moving in a traffic stream has to maintain sufficient lateral clearance on the left and right sides with respect to other vehicles/curb/median to avoid side friction. These lateral clearances depend upon the speed of the vehicle being considered, speed of the adjacent vehicle in the transverse direction, and their respective vehicle categories. The minimum and maximum values of lateral-clearance share values adopted from an earlier study [4], are given in columns (9) and (10) of Table 1, respectively. The minimum and the maximum clearance-share values correspond to zero speed and free speed conditions of corresponding vehicles, respectively. The lateral clearance share values in between the above mentioned traffic flow levels is obtained using linear interpolation in the model. 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 a truck is beside a big car, then, the clearance between the two vehicles will be 0.40 + 0.40 = 0.80 m. The field observed acceleration values of the different categories of vehicles over different speed ranges used for simulation are shown in Table 2.
Table 2

Acceleration values for different vehicle categories

Vehicle type

0–30 km/h (m/s2)

30–60 km/h (m/s2)

Above 60 km/h (m/s2)

Big car

2.15

1.80

1.10

Small car

2.00

1.60

1.10

Two-wheeler

1.10

0.70

0.45

Three-wheeler

0.80

0.30

0.25

Bus

1.40

1.00

0.45

LCV

1.30

0.80

0.55

Truck

1.00

0.62

0.46

LCVs Light Commercial Vehicle

## 7 Simulation model development

A model which accurately represents the design and operational attributes of the study stretch in the simulation software is known as the ‘base model’. The design attributes can be road configuration (carriageways, medians & shoulders), horizontal curvature and vertical gradient. Operational attributes can be the vehicle or driver characteristics and the traffic flow data. When this base model is calibrated and validated to replicate the actual or ground conditions, the model can be used to study different characteristics that were not defined by the user as an input. For example, the width of the road can be defined and in turn the capacity of this road could be measured. The validated base model can also be used to develop a simulated scenario which is desired to be known. The base model development involves the following steps: (i) Development of Base Link/Network, (ii) Defining Model Parameters, (iii) Calibrating the Network, and (iv) Validating the Model.

### 7.1 Development of base link/network

Development of a link/network that accurately depicting the physical attributes of a test site is an important stage in the modeling process. The basic key network building components in VISSIM are links and connectors. In the present simulation model, a unidirectional four lane test section link spanning 1000 m was created representing the study stretch located on the Delhi–Gurgaon Expressway as explained above. Additionally, extra links of length 200 m each were provided at the beginning and end of the main stretch for buffering process. The test section and the buffer links were joined using the connectors. The buffer links provided the spatial warm up sections for vehicles entering and exiting the test section thereby ensuring accurate results.

### 7.2 Defining model parameters

#### 7.2.1 Vehicle model

Vehicle model deals with defining the dimensions of each vehicle type that are plying on the test stretch and are hence considered for the simulation. It is also used to define the acceleration values of vehicles. The dimensions namely the width and the length are considered for the present simulation model as per the description given in Table 1. The acceleration values are given as per Table 2.

#### 7.2.2 Desired speed distribution

The simulation model requires the desired speed parameters of vehicles to initialize and assign the speed during their placement in the simulation stretch. The desired speed parameters obtained through field measurement during lean traffic periods on the study stretch, are shown in Fig. 3. The desired speed of cars depends on the make of the car, the age of the car, the level of maintenance of the car, the age, sex and the behavior 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 desired speeds of cars. Hence, the cars were further divided into two categories: small cars and big cars based on their physical size and engine size. The desired speed distribution for each vehicle category was given as input for the simulation model in VISSIM. The maximum and minimum values of the speeds and distribution between these values were defined in the model. The desired speed profiles for the vehicle types such as small cars and big cars are shown in Fig. 4, as examples. The desired distribution curve for any vehicle category is generally a ‘S’ shaped curve as shown in the Fig. 4. Adequate care was taken to ensure that the speed distribution defined in VISSIM represented the values observed in the field.

#### 7.2.3 Vehicle composition and vehicle flow

Vehicle composition and vehicle flow based on field observations is given as an input to simulation model for the given time interval.

#### 7.2.4 Driving behavior characteristics

The driving behavior characteristics mainly include these two features viz. car following behavior and lateral distance. The psycho-physical driver behavior based Wiedermann-74 Car-following model has been used for simulating the vehicle following behavior. The parameters of this car-following model including safety distance during standstill, additive and multiplicative parts of safety distance are given in Table 3. These values were chosen based on trial-and-error method, taking the values obtained in the study by Mathew and Radhakrishnan [25] as base values. For defining the lateral distance between the vehicles the location of the vehicle on a lane, minimum lateral distance at different speeds etc. were given as input (column number 9 and 10 of Table 1).
Table 3

Calibrated parameters (Wiedemann-74 model) for the present study

Parameter

Calibrated values

*Default values

Average standstill distance

1.35 m

2.0 m

0.25

2.0

Multiplicative part of safety distance

0.35

3.0

127 m

0.0 m

250 m

250 m

* Source [28]: VISSIM Version 5:40-01 user manual

### 7.3 Calibration of the simulation model

Calibration is a process of adjusting the model to replicate observed data and observed site conditions to a sufficient level to satisfy the model objectives. This process involves adjusting the following characteristics: desired speed distribution, acceleration/deceleration of vehicle, mechanical characteristics of the vehicle, minimum safety distance, minimum lateral distance and driving behavior characteristics. By giving these parameters as an input to simulation model, simulation runs have to be carried out in order to estimate the output. In the present simulation model, the outputs were the traffic flows and average speeds of the vehicles for 10 different random seed values. All the simulations were run for a total time of 7400 s including a temporal warm-up period of 200 s to ensure accurate simulation results. Flow for each 1 h from the 2 h field data was fed which improved the degree of match between the observed and the simulated. As explained above, a different driving behavior was considered for each vehicle type to account for heterogeneity in the traffic. There was no perfect strict lane discipline among the vehicles as observed from the video (Fig. 2). Hence, an entire road width based simulation where there was a one lane model having an effective width of three lanes was considered in the simulation. Thus each vehicle was free to choose any lateral position and overtake from any side during the simulation on this three lane width without any lane discipline similar to site conditions.

The minimum look ahead distance which defines the distance a vehicle can see forward in order to react to vehicles in front or to the side of it was set to a value of 127 m was found to be appropriate for the present situation. This value of 127 m was taken based on the calibration and validation study conducted by Mathew and Radhakrishnan [25]. The other values were chosen as per the defaults considered in VISSIM which produced the observed conditions with required accuracy. The simulated values and the observed values (speed, flow and area occupancy) were compared and the error was computed. If the error was within the limits, the calibration process was stopped or otherwise the parameters were modified and simulation runs were carried out. This process was repeated and the simulation runs were made till the error was within the satisfactory limits. The calibration process in the form of a flow chart is shown in Fig. 5.

### 7.4 Validation of the simulation model

Validation is the process of checking the results obtained from the calibrated model in terms of simulated values against field measurements for parameters such as traffic volumes average speeds and area-occupancies. The observed traffic volume and composition was given as input to the simulation process. The simulation runs were made with 10 random number seeds for a total run time of 7400 s including temporal warm-up period of 200 s to ensure accurate simulation results. A sample simulation run is shown in Fig. 6.

The average speeds of vehicles from a single run was noted and then the average speed for each vehicle category from all the ten runs were taken as the final output from the model. The inter-arrival time gaps of the heterogeneous traffic flow of vehicles was assumed to follow negative exponential distribution [3] and the free speeds of different categories of vehicles, based on the results of an earlier study (Velmurugan et al. [35]), was assumed to follow normal distribution. These distributions formed the basis for input of the two parameters for the purpose of simulation.

To check for the temporal validity of the model, the different parameters such as vehicle speeds, flows and area occupancy values obtained using simulation model were compared with the corresponding field observed speeds, flows and area occupancy values for every 1, 5, 15 and 60 min intervals within the 2 h (observed traffic). In the present simulation model, the outputs were the traffic flows, average speeds and area occupancy values of the vehicles for 10 different random seed values. The comparison of the observed and simulated speeds, flows and area occupancy values for an observed traffic conditions are shown in Fig. 7 through Fig. 9 for every 5 min and for every 15 min intervals within the 2 h (observed traffic) in Fig. 10 through Fig. 12, as examples. The graphs were plotted based on the average speed and flow values, derived through the output of ten random runs. The same check was also done for 30 and 60 min intervals with respect to each of the vehicle types. It can be seen that in all the cases, the simulated speed values, simulated flow values and simulated area-occupancy values are found to be satisfactorily matching with the speeds, flows and area-occupancy values as observed in the field for all the vehicle categories. The procedure given by Arasan and Dhivya [31] was used for estimating the area occupancy values for observed and simulated traffic conditions.
The details pertaining to the statistical validation through the paired t test for different parameters: speeds, flows and area occupancy (simulated and observed traffic conditions for every 5, 15 and 30 min intervals) are given in the Table 4. The estimated t-statistic, p and t-critical values obtained from standard t-distribution table are also given in Table 4 for 5 % level-of-significance (95 % confidence level) along with their respective degrees-of-freedom.
Table 4

Model validation: comparison of observed and simulated flows and speeds

Traffic flow parameter

Traffic interval (min)

t-statistic value

t-critical value

p-value

Critical p-value

Degrees of freedom

Speed

5

1.52

2.07

0.22746

0.05

23

Speed

15

0.997

2.37

0.35308

0.05

7

Speed

30

1.03

3.18

0.38017

0.05

3

Flow

5

0.95

2.07

0.35181

0.05

23

Flow

15

0.801

2.37

0.44942

0.05

7

Flow

30

0.558

3.18

0.61559

0.05

3

A-O

5

0.539

2.07

0.59831

0.05

23

A-O

15

0.321

2.37

0.75729

0.05

7

A-O

30

0.220

3.18

0.83989

0.05

3

A-O-Area Occupancy

From the table, it may be noted that, in all the cases, the value of estimated t-statistic is lesser than the critical value of t-statistic obtained from standard t-distribution table. This implies that there is no significant difference between the observed and simulated traffic flow parameters, for a level of significance of 5 %.

#### 7.4.1 Model application

The VISSIM model can be applied to study various traffic scenarios for varying roadway and traffic conditions. In this study, the application of the model is to study the relationship between traffic flow and speed on an urban expressway with six categories of vehicles as given in column number 2 of Table 1. It has also been used to quantify the relative impact of each category of vehicle on traffic flow in comparison to a reference vehicle category car, by estimating their PCU values at different volume levels under heterogeneous traffic conditions prevailing on an urban expressway considered for the study. Further, the estimated PCU values were used to derive capacity estimate for one direction of traffic flow on a chosen urban expressway, based on the traffic composition observed in the field through data collection.

#### 7.4.2 Speed-flow relationships and capacity

One of the basic studies in traffic flow research is to examine the relationship between speed and volume of traffic. The capacity of the facility under different roadway and traffic conditions can be estimated using these relationships. In this study, speed-flow relationship was developed using the validated simulation model for a heterogeneous flow with vehicle composition and roadway conditions same as that observed in the field. The average speed of the stream was plotted for different simulated volumes, starting from 500 vph to the capacity of the road.

The following procedure was adopted for finding the capacity of the facility for developing the speed-flow relationships. During successive simulation runs with increments in traffic flow from near-zero volume level, there will be a commensurate increase in the exit volume at the end of simulation stretch. After a specific number of runs, the increments in the input traffic volumes will not result in the same increase in the exit volume. Such a decrease in exit volume (in spite of increase in the input) in successive runs indicates that the facility has reached its capacity. The speed-flow relationships, thus developed based on the every 1 and 5 min intervals speed and flow data for a eight-lane divided expressway (roadway space based on the four lanes in one direction of traffic flow) are depicted in Fig. 13a, b respectively. The 1 min intervals speed and flow data (120 points) and 5 min intervals speed and flow data (24 points) obtained from the observed data for 2 h was also plotted in Figs. 13a, b. It is clear from the figures, that the curves follow the well established trend. These graphs were plotted based on the average speed and flow values, derived through the output of ten random runs. The estimated values of capacity (vehicles/hr/direction), thus obtained using simulation model, based on every 1 and 5 min interval data, for the observed traffic composition, are given in Table 5.
Table 5

Estimated roadway capacity of eight- lane divided urban expressway

Flow type

Traffic composition

Estimated capacity (veh/h/dir)

Observed (5 min interval)

Heterogeneous (column 2 of Table 1)

9720

Simulated (5 min interval)

Heterogeneous (column 2 of Table 1)

9606

Observed (1 min interval)

Heterogeneous (column 2 of Table 1)

10740

Simulated (1 min interval)

Heterogeneous (column 2 of Table 1)

10470

From Table 5, it may be observed that the capacity estimate obtained using 1 min interval data is significantly higher than the capacity estimate obtained using 5 min interval data. This is quite intuitive: when the interval considered is smaller (1 min in this case), the flow levels are multiplied by higher factor for converting it into hourly flows, which may result in a higher capacity value. In the case of 1 min speed-flow relationship, there are more number of points in the congested regime as compared to the 5 min speed-flow relationship. This may be attributed to the distribution of more number of speed and flow points over a wider range. The capacity values obtained from every 1 and 5 min observed and simulated speed and flow data are found to be matching satisfactorily.

#### 7.4.3 Estimation of PCU values

As explained in the introduction, capacity of a highway facility with heterogeneous traffic flow with vehicles of widely varying static and dynamic characteristics is best expressed in terms of PCU/hr. Different vehicle categories such as buses, light commercial vehicles, trucks, motorized two-wheelers and motorized three wheelers are expressed into equivalent PCU. This necessitates an accurate estimation of PCU, which varies dynamically with various traffic flow parameters such as stream speed, vehicle composition and volume-capacity ratio. Chandra [10] developed the concept of dynamic PCU considering the various traffic interactions and flow characteristics. The PCU for a vehicle can be calculated using Eq. (1).
$$PCU_{i} = \frac{{{\raise0.7ex\hbox{{V_{c} }} \!\mathord{\left/ {\vphantom {{V_{c} } {V_{i} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{{V_{i} }}}}}{{{\raise0.7ex\hbox{{A_{c} }} \!\mathord{\left/ {\vphantom {{A_{c} } {A_{i} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{{A_{i} }}}}}$$
(1)
where, PCUi is the PCU of the subject vehicle i; Vc = Average speed of cars in the traffic stream, Vi = Average speed of subject vehicles i; Ac = Projected rectangular area of a car as reference vehicle and Ai = Projected rectangular area of the vehicle type i. For the purpose of this study, the projected rectangular area of the car, (Ac) (reference vehicle) was considered as the average value of the rectangular area of big cars and small cars. The average speed (Vc) of the car (reference vehicle) for the given flow level, was estimated as the weighted average of the speeds of big cars and small cars, based on their composition in the traffic composition. The PCU values of different vehicle types were estimated using Eq. (1), based on the average speed and flow values, derived through the output of ten random runs.
To emphasize their dynamic nature, PCU values for different categories of vehicles under heterogeneous traffic conditions at different volume-capacity (V/C) ratios in the uncongested regime (upper part of speed-flow relationship as shown in Fig. 13a) and congested regime (lower part of speed-flow relationship as shown in Fig. 13a) were estimated using simulation. The capacity values for the calculation of these V/C ratios were obtained from the speed-flow graphs (Fig. 13a). For the purpose of simulation, different traffic volume levels corresponding to these V/C ratios with same composition as observed in the field (as in column 2 of Table 1) were considered. Outputs obtained from simulation runs served as inputs for Eq. (1), for calculating the PCU values of different types of vehicles at different volume levels. The computed values for uncongested and congested traffic regimes are shown in Table 6 and Table 7, respectively. The variation of PCU values of different vehicle categories, over traffic volume, as an example, is depicted in Fig. 14.
Table 6

PCU Estimates of different vehicles at different V/C ratios (uncongested regime)

V/C

Truck

Bus

L.C.V

M.Th.W

M.T.W

0.12

3.59

4.26

1.47

0.81

0.19

0.23

3.41

4.08

1.36

0.79

0.19

0.35

3.33

3.98

1.33

0.75

0.19

0.46

3.32

4.06

1.32

0.71

0.18

0.58

3.28

3.93

1.35

0.70

0.18

0.70

3.08

3.87

1.31

0.68

0.17

0.81

3.03

3.99

1.31

0.65

0.17

0.93

3.04

3.69

1.28

0.63

0.16

0.96

3.22

3.74

1.29

0.62

0.16

0.96

3.02

3.82

1.31

0.61

0.16

0.99

3.02

3.66

1.37

0.60

0.16

1.00

2.86

3.71

1.30

0.60

0.15

M.Th.W*–Motarized 3-wheeler M.T.W*–Motarized 2-wheeler

Table 7

PCU Estimates of different vehicles at different V/C ratios (Congested Regime)

V/C

Truck

Bus

L.C.V.

M.Th.W.

M.T.W.

0.99

3.16

3.72

1.28

0.61

0.15

0.99

3.16

3.72

1.28

0.61

0.15

0.98

2.90

3.76

1.32

0.60

0.15

0.93

3.09

3.82

1.50

0.60

0.15

0.96

2.96

3.82

1.31

0.61

0.16

0.97

2.90

4.13

1.30

0.61

0.15

0.97

2.90

4.13

1.30

0.61

0.15

0.94

3.03

4.02

1.31

0.60

0.16

M.Th.W*–Motarized 3-wheeler M.T.W*–Motarized 2-wheeler

It can be seen from the Tables 6 and 7 and fig. 14 that the PCU values are the highest for buses, then for truck, then light commercial vehicles, then motorized three-wheelers and motorized two-wheelers have the least PCU value, this being irrespective of the V/C ratio. These results are quite intuitive: the heavier and larger is the vehicle, the lesser its manoeuvrability, the greater its hindrance to other vehicles and greater is its PCU. It can also be observed that the PCU value for a given vehicle category decreases as V/C ratio increases for all the vehicle categories for the traffic flows in uncongested regime till capacity. This phenomenon could be explained by the fact that the speed difference between the subject vehicle category and the reference vehicle (car) decreases as V/C ratio increases. The PCU value for heavy and larger vehicle types (buses, trucks, etc.) are found to be higher under congested regime as compared to their PCU values near capacity. The PCU value for smaller vehicle types (motorised three-wheelers and motorised two-wheelers) are found to be relatively same under congested regime as compared to their PCU values near capacity. Under congested traffic flow conditions, all the vehicles move very close to each other resulting in frequent acceleration and deceleration. This condition leads to relatively higher rate of reduction in the speeds of heavy vehicles (trucks, buses, etc.) as compared to smaller vehicles. As a result of this, under congested traffic regime, the difference in percentage speed change between cars and heavy vehicle types is higher as compared to the smaller vehicle types, resulting in higher PCU values.

#### 7.4.4 Disrtribution of PCU values

The distribution of the PCU values for different vehicle types was also studied in detail and it was found that for all the vehicle categories, for the given traffic flow level, the PCU values estimated using simulation follow normal distribution, which was also reported by Al-Kaisy et al. [1]. The corresponding normal probability and normality plots for trucks (heavy vehicle) and motorized two- wheelers (smaller vehicle) are depicted in Fig. 15, as examples.

#### 7.4.5 Check for accuracy of PCU values

For the purpose of checking the accuracy of the PCU estimates for different vehicle categories the following procedure was adopted. Firstly, PCU values were estimated for each of the vehicle type using speeds of the reference vehicle (cars) and subject vehicle category (for which the PCU is to be estimated), obtained from the observed data for every 5 min interval. Then the vehicles of the different categories were converted into equivalent PCUs by multiplying the number of vehicles in each category, by the corresponding PCU values (through every 5 min observed data). The products, thus obtained, were summed up to get the total traffic flow in PCU/hour based on the observed data for every 5 min interval. Secondly, the heterogeneous traffic flow with same vehicle composition and traffic flow levels as observed in the field for 2 h was simulated and the number of vehicles passing the simulation stretch, in each category during each run was noted along with their speeds for every 5 min interval. PCU values were estimated for each of the vehicle type using speeds of the reference vehicle (cars) and subject vehicle category (for which the PCU is to be estimated), obtained from the simulated data for every 5 min interval. Then the vehicles of the different categories were converted into equivalent PCUs by multiplying the number of vehicles in each category, by the corresponding PCU values (through every 5 min simulation data). The products, thus obtained, were summed up to get the total traffic flow in PCU/hour based on the simulated data for every 5 min interval. Comparison of the traffic flows measured in terms of PCU/h, based on the observed and simulated data, for the flow levels as observed in the field, is shown in Fig. 16. The PCU values of different vehicle types were estimated, based on the average speed and flow values, derived through the output of ten random runs.
It can be seen that the traffic flow values in PCU/hour for observed and simulated scenarios match fairly well, indicating the accuracy of the estimated PCU values. A paired t-test based on the two values was also done in which the calculated value of t-statistic (t0) was 0.521. The critical value of t-statistic for a level of significance of 0.05 for 23 degrees of freedom, obtained from standard t-distribution table is 2.07. This implies that there is no significant difference between the two sets of flows measures in terms of PCU/hour (based on observed and simulated data sets) implying that the estimated PCU values for different vehicles are accurate. Also, comparison of the estimated PCU values based on the observed and simulated speed data for motorised three-wheelers and buses is depicted in Fig. 17 and 18, respectively, as examples. Based on the paired t-test results, it was found that there is no significant difference between both the data sets at 5 % level-of-significance, for 23 degrees of freedom, further indicating the accuracy of PCU estimates. Also as an another check, the simulation was run for 100 % cars and then was compared with the equivalent value of traffic flow in PCU/h. Comparison of the traffic flows measured in terms of PCU and in terms of number of passenger cars, through speed-flow relationship, is shown in Fig. 19. It can be seen that the traffic flow in PCU/h and the cars-only flow in cars/h match to a greater extent, indicating the accuracy of estimated PCU values.

## 8 Conclusions

The following are the important findings of this study:
1. 1.

The validation results of the simulation model VISSIM, used for this study indicate that the model is capable of replicating the heterogeneous traffic flow on expressways to a satisfactory extent.

2. 2.

From the speed-volume curve developed using the simulation model, it is found that, for the observed traffic composition, capacity of a eight-lane divided urban expressway in level terrain with 14.0 m wide road space is about 9700 PCU/h for one direction of traffic flow.

3. 3.

It is found that, the estimated PCU values of the different categories of vehicles are accurate at 5 % level of significance.

4. 4.

It is found that, under heterogeneous traffic conditions, for a given roadway condition and traffic composition, the PCU value of vehicles vary significantly with change in traffic volume. Hence, it is desirable, to treat PCU as dynamic quantity instead of assigning fixed PCU values for the different vehicle categories of road traffic.

5. 5.

Under heterogeneous traffic conditions, the trend of variation of the PCU value, over traffic volume, indicates that: (i) the PCU value for all the vehicle category decreases as V/C ratio increases for all the vehicle categories for the traffic flows in uncongested regime till capacity, (ii) the PCU value for heavy and larger vehicle types (buses, trucks, etc. as compared to cars) are found to be higher under congested regime as compared to their PCU values near capacity, and (iii) the PCU value for smaller vehicle types (motorised three-wheelers and motorised two-wheelers as compared to cars) are found to be relatively same under congested regime as compared to their PCU values near capacity.

6. 6.

It is inferred that the change in the PCU value of the different categories of vehicles, due to change in traffic volume, under heterogeneous traffic condition, is directly influenced by the change in the speed difference between the reference vehicle (car) and the subject vehicle (a chosen vehicle type, other than car).

## 9 Limitations of the study

The driver behavior, considered in this study can be refined further to consider many more physiological and psychological factors.

### 9.1 Future research scope

This study can be further extended to study the following aspects:
1. 1.

The effect of vehicle composition on PCU values can be determined from the validated model.

2. 2.

Area-Occupancy can be used as a parameter of surrogate measure for the density for developing fundamental diagrams and level-of-service criteria.

3. 3.

Developing a concept of stochastic capacity estimates under heterogeneous traffic conditions prevailing on expressways in India. Such estimates would account for vehicle composition in the traffic stream.

4. 4.

The empirical relationship between lateral-clearance share data for different possible pairs of vehicle categories based on the field observed data over a wider range of speeds may refine the validation results further.

## Acknowledgments

The authors (first three authors) would like to thank Central Road Research Institute (CRRI), New Delhi India for extending their valuable support for collecting the traffic data used in this study. They would also like to thank PTV AG, Germany for providing the software VISSIM used in this study.