Heterogeneous traffic flow modelling: a complete methodology

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1 Transportmetrica Vol. 7, No. 5, September 2011, Heterogeneous traffic flow modelling: a complete methodology Ch. Mallikarjuna a * and K. Ramachandra Rao b a Department of Civil Engineering, Indian Institute of Technology Guwahati, Guwahati , Assam, India; b Department of Civil Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi , India (Received 31 March 2009; final version received 11 February 2010) A comprehensive methodology for modelling the heterogeneous traffic is presented in this article. Considering the no-lane discipline and the presence of various sizes of vehicles, several microscopic and macroscopic traffic variables are analysed for their suitability in describing the heterogeneous traffic. Applicability in the modelling process and the feasibility in collecting field data are the important criteria used in deciding the suitable traffic variables. In place of occupancy, its variant termed as area occupancy was found to be suitable in describing the heterogeneous traffic. Vehicle size, mechanical characteristics, lateral distribution of vehicles and the lateral gaps maintained by them are found to be more suitable microscopic traffic variables. Data on these variables have been used in modifying the cell structure and the updating procedures of the cellular automata (CA)-based traffic flow model. A customised video image processing-based data collection technique has been used in collecting the field data on these variables. The modified CA model with the relevant parameter values has been used in simulating the flow. Model results are validated using the field data and the results expressed in terms of cells are found to be better in capacity analyses under heterogeneous traffic conditions as well as fit into the established traffic flow theory. Keywords: heterogeneous traffic; traffic flow modelling; cellular automata; video image processing; data collection 1. Introduction Traffic composed of identical vehicles and following the lane discipline is termed as homogeneous. Traffic comprising of motorised and non-motorised two-wheelers (TWs) and three-wheelers along with several other vehicles with no-lane discipline is termed as heterogeneous. This heterogeneous traffic is clearly different from the one with the presence of trucks which has also been termed as heterogeneous traffic. The absence of lane discipline results in vehicular movement that is influenced by the presence of vehicles in the front as well as on the sides. This led to a complex traffic behaviour and it cannot be analysed by using conventional microscopic and macroscopic traffic variables. Using conventional measurement techniques, it is also difficult to collect the data. Modelling methodology to be adopted in these conditions would also be considerably different compared to the existing traffic modelling methodologies. Traffic flow variables, *Corresponding author. c.mallikarjuna@iitg.ernet.in ISSN print/issn online ß 2011 Hong Kong Society for Transportation Studies Limited DOI: /

2 322 Ch. Mallikarjuna and K.R. Rao relationships among the variables and the observed data on these variables are the crucial inputs for the traffic flow modelling purposes. Any efforts in the area of traffic flow modelling should consider the above aspects and it is even more crucial when dealing with the heterogeneous traffic. In this scenario, formulating new theoretical and modelling concepts or adopting the conventional microscopic and macroscopic traffic flow concepts are the available alternatives for the researchers. Several researchers (Chari and Badarinath 1983, Palaniswamy et al. 1985, Ramanayya 1988, Kumar 1994, Singh 1999, Oketch 2000) have attempted to model the heterogeneous traffic and most of these models are microscopic in nature. Some researchers (Chari and Badarinath 1983, Singh 1999) have proposed alternative measures for density, but where exactly they fit into the overall modelling process and the relationship with the other traffic variables were not clearly discussed. Explicit vehicular interactions under varying traffic conditions are modelled in these studies. Vehicle composition and the gap maintaining behaviour were the important input data to these models. In most of these studies, video recording techniques were utilised in collecting the data on vehicular interactions. Video recording technique requires extensive manpower to collect the data on vehicular interactions and is prone to error. Some other data collection techniques, such as dualloop detectors, image processing-based traffic data collection techniques, can be used to estimate vehicle lengths which in turn can be used in estimating vehicle width (Lan and Kuo 2002). Using these techniques, vehicle lengths under free-flow conditions can be found with a fair amount of accuracy. To overcome the errors observed in forced-flow conditions in measuring vehicle lengths, Zhang et al. (2005) proposed a new dual-loop algorithm which can handle erroneous raw loop actuation signals. Lateral gap data that are equally important to model the vehicular interactions can be collected using a recently developed image processing software called TRAZER (Mallikarjuna et al. 2009). Implementing the cellular automata (CA) concept for modelling the heterogeneous traffic has been suggested by some researchers (Lan and Chang 2005, Hsu et al. 2007, Mallikarjuna and Ramachandra Rao 2009). Lan and Hsu (2006) have proposed new variants for density and flow using the modified CA structure developed for modelling the heterogeneous traffic. These variants have been derived based on generalised definitions for speed, flow and the density (Edie 1965, Maerivoet 2006). Mallikarjuna and Ramachandra Rao (2006) have proposed a new variant for occupancy termed as area occupancy and this variable was found to be suitable for CA-based modelling methodology. Mallikarjuna and Ramachandra Rao (2009) have proposed a detailed methodology in formulating the CA structure for modelling the heterogeneous traffic. Field traffic data collected using the video image processing-based software, TRAZER (Mallikarjuna et al. 2009), has been utilised in formulating this CA structure. In this article, an effort is made to develop a comprehensive methodology to model the heterogeneous traffic. While choosing the appropriate traffic variables, factors such as the usefulness in describing the traffic, data measurability and usefulness in modelling are taken into consideration. Important microscopic variables, such as lateral gaps, longitudinal gaps and lateral distribution of vehicles have been utilised in formulating the CA structure. Data collected on these variables using video image processing software, TRAZER, have been analysed. Relationship between area occupancy and a variant of flow measured in terms of cells has been utilised in calibrating and validating the proposed CA model. Model validation was done using the field data collected on different road sections. Data collected from the simulation model in terms of cells, which are the basic

3 Transportmetrica 323 units of vehicles in the modified CA structure, are found to be conforming to the fundamental traffic flow theory. The organisation of the remainder of this article is presented below. Section 2 deals with the traffic variables that are used in modelling the heterogeneous traffic. Methodology used in developing the CA structure is presented in Section 3. Field data collected on various traffic variables is briefly discussed in Section 4. Section 5 deals with the calibration and validation of the CA model. Detailed description of various results obtained in the process of validation is also presented in this section. Summary of the overall methodology and the important conclusions are presented in Section Traffic variables 2.1. Macroscopic traffic characteristics Flow, speed and density are the commonly used macroscopic traffic characteristics. Measurability of each of these depends on the kind of equipment used and length of time and space periods over which the measurements are taken. Definitions and the feasibility of data collection on flow, speed and density are not discussed here. Definitions for occupancy and the variant of occupancy called area occupancy are discussed in the following sections Occupancy Occupancy is defined as the percentage time the road section is occupied by a vehicle over a given period of time. Occupancy is equivalent to density under equilibrium conditions but only somewhat related to density under non-equilibrium conditions (Revised Monograph on Traffic Flow Theory: A State-of-the-Art Report 1997). P N i¼1 ¼ O i, ð1þ T O i ¼ l i þ d, ð2þ v i where is the occupancy, O i is the time the i-th vehicle occupied the detector, l i is the length of the i-th vehicle, v i is the speed of i-th vehicle and d is the detector s length. When both density and occupancy are measured over a general measurement region, A, (Figure 1) they can be related in the following manner (Daganzo 1997): ðaþ ¼kðAÞlðAÞ ð3þ where occupancy, density and average vehicle length are measured over time and space. Occupancy measured over time is related to the density and average vehicle length measured over space as follows: k l, where is measured over time, density (k) and average vehicle length ð l Þ are measured over space. In the case of traffic with different vehicle lengths, it is apparent that occupancy is more meaningful than density. Even this improved traffic measure is not suitable when the ð4þ

4 324 Ch. Mallikarjuna and K.R. Rao T Spatial region Space ds L General measurement region (A) Temporal region Time dt Figure 1. Time space diagram showing the temporal, spatial and the general data measurement regions. traffic is heterogeneous. In the heterogeneous traffic, most of the time vehicles travel on the central portion of the road for different reasons. Since occupancy is a function of length and speed of the vehicle, in the case of homogeneous traffic it could consider the effect of large slow-vehicle s impedance by means of its length (generally long vehicles are wide-bodied vehicles). In the case of heterogeneous traffic (observed on Indian roads), traffic is composed of some short vehicles whose weight to horsepower ratio is more. Effects of these vehicles are more pronounced when these vehicles are obstructing the vehicles behind while travelling on the middle of the road. Lengths and widths of the vehicles that are sharing the road space are also found to be not correlated. In order to represent heterogeneous traffic, we propose to modify the formula for occupancy. This formula would incorporate vehicle area and total road width, and is discussed in detail in the following section Area occupancy Occupancy may not exactly depict the collective traffic behaviour moving in a 3-D region, including 2-D for the roadway (longitudinal and transverse) and 1-D for the time (Lan and Hsu 2006). To overcome these difficulties, in estimating this new metric, absolute width of the road is considered irrespective of number of lanes. If this is the case, at any time instance there can be more than one vehicle, depending on the vehicle size, moving across the road width. This term is also considering the size of the vehicle, which has a significant bearing on the traffic behaviour in heterogeneous traffic conditions. When considering a small section (e.g. detector) of the road, area occupancy expresses for how long a particular size of the vehicle is moving on that section of the road. Like occupancy, area occupancy is also measured over time (temporal area occupancy, the term area occupancy is used throughout this report to refer to this quantity) and is formulated as follows; P N i¼1 A ¼ O i w i d, ð5þ T W d where A is the area occupancy, O i is the occupancy time of the i-th vehicle in seconds, w i is the width of the i-th vehicle, W is the road width, d is the length of the road section under consideration and T is the observed time period in seconds.

5 Transportmetrica 325 Figure 2. Graphical representation of factors considered in area occupancy measurements. In the above formula, the numerator value takes care of the occupancy time (similar to occupancy); the amount of time a vehicle with a given area is spending on the road section under consideration. Its value will depend on the composition of traffic and speeds of the vehicles. Figure 2 gives the graphical representation of the area occupancy measurements over a short section (e.g. induction loop) of the two-lane road. It is assumed that there are two vehicles on the road at a time instance T 1 and both vehicles are travelling at the same speed. Figure 2(a) shows the top view of a two-lane road on which two vehicles (vehicles shown with solid lines) are just entering into the detection area at the time instance T 1 and their respective positions at the time instance T 2 (vehicles shown with dotted lines). From the definition of occupancy, the difference between T 1 and T 2 gives the occupancy time of the large-sized vehicle. Occupancy time for small vehicle is different from large vehicle. As discussed earlier in these kinds of situations (RHE traffic), representing time space evolution of vehicles in a 2-D time space diagram may not help in identifying the real traffic conditions. Figure 2(b) shows the 3-D time space evolution of the vehicles is. In addition to the time and space, road width is represented in the third dimension.

6 326 Ch. Mallikarjuna and K.R. Rao The volume (time road width detector length) in between the two horizontal planes shown in Figure 2(b) represents the total control volume. Two vertical planes which are shown in the figure represent the time instances at which the large-sized vehicle enters and leaves the detection zone. The volume which is common to the vertical and horizontal planes ((T 1 T 2 ) vehicle width d ) represents the time spent by the large-sized vehicle area in the detection zone. Extending this to the total vehicles which may have crossed the detection zone during the observed period, the formulation of area occupancy is obtained as shown below: A ¼ P i ðt 2 T 1 Þ i w i d ) T W d P i ðl i þd Þ v i w i d T W d P ) i O i w i d : ð6þ T W d This formulation has been found to be a better explanatory variable in studying the heterogeneous traffic. This variable is useful in correlating the gap maintaining behaviour of vehicles with the varying traffic conditions as discussed in Section Microscopic characteristics Analysis of microscopic characteristics, such as individual vehicle characteristics, lateral gap, longitudinal gap and lateral position of the vehicles, which are useful in describing the heterogeneous traffic as well as in developing the CA-based models, are presented below Vehicle characteristics Traffic composition is one of the major factors influencing the lane discipline observed in heterogeneous traffic. In car following, when the leading vehicle is TW, there will be a considerable gap on the side of this vehicle. The following vehicle travelling may utilise this gap as well as some portion of the adjacent lane. Hence when modelling the heterogeneous traffic, it is necessary to incorporate this behaviour in the model. In addition to the physical characteristics, widely varying mechanical characteristics are also very important when dealing with heterogeneous traffic. To replicate this behaviour, the basic cell structure in the CA model has been modified accordingly (Figure 4). The parameters, such as p 0, p dec, a n and d n that are used in the longitudinal updating procedure (Section 3.2) take different values (Tables 2 and 3) corresponding to the mechanical characteristics of various vehicle types Lateral gap In the heterogeneous traffic, in addition to the driver s discomfort, the presence of small vehicles influence the lateral gaps (g lat in Figure 3) maintained by different vehicles. Since lane discipline is not enforced under heterogeneous traffic conditions, even in the absence of small vehicles many vehicles tend to travel in the middle of the road. Lateral gaps maintained by different vehicles may influence speeds as well as longitudinal gaps. This gap maintaining behaviour may vary from vehicle type to vehicle type. Utility of this variable in formulating the CA structure is discussed in Section 3.

7 Transportmetrica 327 g cl g long g lat Figure 3. Lateral and longitudinal gaps maintained by vehicles with staggered car following behaviour Longitudinal gap Under heterogeneous traffic conditions, there may be more than one leading vehicle for the corresponding following vehicle. Measuring or estimating the longitudinal gaps in these conditions requires trajectory data. From the filed data, it has been observed that the separation in the centrelines (g cl in Figure 3), and lateral and longitudinal gaps maintained by the vehicles are interdependent on one another. While developing the vehicle updating procedure, it is necessary to consider this behaviour. In the present CA model, this behaviour is not incorporated due to lack of understanding on the interaction of these three variables. It has been assumed that longitudinal gap is a function of vehicle type and the speeds of the leading and following vehicle types Lateral position of the vehicle Under heterogeneous traffic conditions where significant number of TWs and threewheelers are present, lateral positions maintained by different vehicles under different traffic conditions are not the same. In left side driving environment which is prevalent in India, it is assumed that fast moving vehicles stick to rightmost portion of the road space. This is not true when significant numbers of fast moving TWs are present in the traffic stream. The vehicle distribution in the lateral direction under different traffic conditions is very crucial while modelling the traffic flow. The cell structure adopted in the present CA model allows the vehicles to take a finite number of lateral positions, but the segregation of vehicles under different traffic conditions is not considered in this study. 3. Developing the CA model 3.1. Cell structure The presence of vehicles with different physical and mechanical characteristics makes it necessary to alter the conventional cell structure and along with it the updating procedures used in the CA models. This nature of heterogeneous traffic is also necessitating the study of lateral movements in addition to the longitudinal movements. Vehicle s mechanical characteristics, specifically the acceleration behaviour, constrain the cell length that can be adopted for heterogeneous traffic flow modelling. In this study, the cell length is taken as 0.5 m considering the slow/heavy vehicles present in the heterogeneous traffic. The lateral gap information is important in deciding the effective vehicle width under varying

8 328 Ch. Mallikarjuna and K.R. Rao Figure 4. Modified cell structure in the CA-based heterogeneous traffic flow model at two different occupancy levels. traffic conditions. Effective vehicle width is the summation of actual width and the gaps maintained on both sides. This effective width is the basis in deciding the cell width used in the CA model. Cell width may vary depending on the effective vehicle width that is varying with the gap maintaining behaviour. This behaviour is represented in Figure 4 and gaprelated data at different traffic conditions should be the basis in adopting this cell structure. The number of vehicles that can travel side-by-side vary depending on the occupancy/density and the same is shown in Figure 4. This results due to the fact that at higher occupancy levels vehicles maintain less lateral gaps and more vehicles can travel side-by-side. The effective widths of various types of vehicles have been found from the field data collected (Section 4) and the same are presented in terms of cells in Tables 2 and Longitudinal updating procedure Longitudinal updating procedure in this study is adopted from Knospe et al. (2000) with the modifications discussed in this section. One of the important features of Knospe s model is that the acceleration is delayed for standing vehicles and directly after braking events. The delay in acceleration is modelled using the slow-to-start ( p 0 ) parameter and, the delay after braking has been modelled using the brake light probability (p bl ) parameter. For homogeneous traffic, these values are the same for all the vehicles present in the traffic stream. This is not true for heterogeneous traffic and these parameters are modified accordingly. The delay in acceleration for stationary vehicles and immediately after braking is considered to be different for various types of vehicles observed in the heterogeneous traffic. Another parameter called the slow down probability ( p dec ) is also considered to be different for various vehicle types. In addition to these changes, maximum allowable speeds, accelerations and decelerations are considered to be different and these values are chosen in accordance with the field data. Data related to these modifications of the model are given in Tables 2 and 3. Effects of these modifications along with the modified cell structure have been evaluated through various parametric studies. The effect of the reduced cell length on various model parameters has been analysed through parametric studies (Mallikarjuna and Ramachandra Rao 2009).

9 Transportmetrica 329 Updating procedure used in the present model, represented mathematically is given below; (1) Determination of the randomisation parameter: p ¼ p(v n (t), b nþ1 (t), t h n, ts ) ¼ p bl if b nþ1 (t) ¼ 1 and t h n 5 ts, ¼ p 0 if v n (t) ¼ 0, ¼ p dec in all other cases. (2) Acceleration: If (b nþ1 (t) ¼ 0) and (b n (t) ¼ 0) or ðt h n ts Þ then: v n (t þ 1/3) ¼ min(v n (t) þ a n (v n,l n ), v max ) t h n ¼ (g n(t) þ maximum(0,v nþ1,anticipated (t) security distance))/v n (t) (3) Braking rule: v n (t þ 2/3) ¼ min(v n (t þ 1/3), g eff n ) if (v n (t þ 2/3) 5 v n (t)) then: b n (t þ 1) ¼ 1. (4) Randomisation, brake: If (rand( ) 5 p) then: If ( p ¼ p bl or p 0 ) v n (t þ 1) ¼ max(v n (t þ 2/3) d n (l n ), 0) If ( p ¼ p dec ) v n (t þ 1) ¼ max(v n (t þ 2/3) 1, 0) If ( p ¼ p bl ) then: b n (t þ 1) ¼ 1. (5) Car motion: x n (t þ 1) ¼ x n (t) þ v n (t þ 1). where t h n is the available time headway for n-th vehicle, t s is the interaction headway, b n (t)is the binary variable denoting brake light s status of the n-th vehicle (if equal to 1, brake light is on, if equal to 0 brake light is off), security distance is the parameter used to offset the anticipated movement of leading vehicle, g eff n is the effective gap available after considering anticipated movement of leading vehicle, l n is the length of the n-th vehicle, a n is the acceleration of the n-th vehicle and d n is the deceleration of the n-th vehicle. (t þ 1/ 3) and (t þ 2/3) denotes various stages at which speed values are updated within each updating step Lateral updating procedure When vehicles are following lane discipline like in homogeneous traffic, lane changes are classified into two types, namely discretionary and mandatory. Under heterogeneous traffic conditions where vehicles are not following lane discipline, the term lane change has no relevance. Under these conditions, vehicles adjust their lateral positions in a way that optimises the usage of the road space. In this study, emphasis is given on how the vehicle moves laterally under different traffic conditions. Lateral movements carried out by car and TW with the modified CA structure is shown in Figure 5. Each lateral division of the

10 330 Ch. Mallikarjuna and K.R. Rao TW (5) TW CAR (2) CAR CAR (4) CAR (1) (3) CAR Figure 5. Some of the possible lateral movements under heterogeneous traffic conditions. road is called a sub-lane. With the given CA structure, different types of lateral movements are possible and some of the possible lateral movements are shown in Figure 5. There can be many other lateral movements, but in this work it is restricted to five. In all of the lane changes, the subject vehicle can shift laterally both in left and right directions depending on the gap availability in the corresponding directions. Any vehicle may perform lane changing manoeuvre based on two criteria, namely incentive criterion and safety criterion. Any vehicle changes lanes if the gap available in the front is less than its anticipated speed in the next time step. This suggests the intention of the vehicle to shift lanes. At the same time, the other lane must be more attractive and safe. The target lane is more attractive if the gap available in the target lane is more than the gap available in the current lane. Target lane is safe if no vehicle is expected to be on the target lane near the intended location of lane changing. With certain probability, a vehicle will change lanes when the following conditions are satisfied. Lane changing rules used in the present model are as follows. Incentive criterion (1) (v n þ a n (v n, l n )) 4 g n (2) (v n þ a n (v n, l n )) 4 v nþ1. Safety criteria (3) g n,o,f 4 v n (4) g n,o,b 4 v max of the corresponding back vehicle þ D, where a n is the acceleration of the vehicle which is a function of speed, is the non-zero parameter, value of which is greater than one, g n is the gap in the front on the same lane, g n,o,f is the gap in the front on the other or target lane and g n,o,b is the gap in the back on the other or target lane. One more incentive criterion is added through which a driver would decide whether to change lanes or not. This incentive criterion is added to consider the effect of front vehicle s speed on the following vehicle in lane changing. The parameter is significant in the sense that the vehicle which is changing lanes may look for a sufficiently large gap compared to its anticipated speed in the next time step. Because the gap in the same lane is slightly less than what is required for the anticipated speed and the gap in the target lane is slightly more, the vehicle may not always change lanes. The overall procedure adopted in the CA model is shown in Figure 6.

11 Transportmetrica 331 Allocating vehicles based on composition and global occupancy Updating vehicle s longitudinal position Assigning vehicle characteristics Repositioning the vehicles with updated speeds Finding gaps in the same sub-lane and on adjacent sub-lanes Extracting local measurements in cells and vehicles Updating vehicle s lateral position Extracting global measurements in cells and vehicles Figure 6. Outline of CA model for simulating heterogeneous traffic. 4. Data collection Video image processing software, TRAZER, has been utilised in collecting the trajectory data over a road length of 50 m. This software has the capability to classify the vehicles and to capture the lateral movement of vehicles. A detailed methodology adopted in TRAZER can be found in the work of Mallikarjuna et al. (2009). Various data collected from the trajectory data are presented in the following sections Microscopic data from the trajectories Acceleration/deceleration data corresponding to different vehicles has been extracted from the trajectory data (Mallikarjuna et al. 2009). Acceleration data of the stationary vehicles have been utilised in arriving at the appropriate values for the parameter p 0 corresponding to various vehicle types. Lateral distribution of vehicles and the gaps maintained by vehicles under different traffic conditions are the other key data extracted from the trajectories. Lateral gaps are measured with respect to the closest side vehicles if more than one vehicle is present on the sides. Longitudinal gaps are obtained for those vehicles which can be seen in one frame of the video, i.e. if the front vehicle is not visible in the same frame, no gap is calculated for the subject vehicle. Dependency of lateral gap maintaining

12 332 Ch. Mallikarjuna and K.R. Rao behaviour on various traffic characteristics has been analysed. Various combinations of macroscopic and microscopic variables are tested to know whether there exists any consistent relationship among them. The relations obtained with different combinations are presented in the following sections Lateral distribution of the vehicles From the analysis of the data on lateral distribution of vehicles, it has been observed that the traffic volume and composition are the important factors influencing the lateral distribution of vehicles (Mallikarjuna 2007). A common feature observed was that the three-lane road on which data was collected was being utilised as a two-lane road irrespective of the traffic volume. When traffic volumes are relatively high, segregation of TWs and light multirole vehicles (LMVs) has been observed. At low traffic volumes, this kind of segregation has not been observed. Under free-flow conditions (relatively low traffic volumes), road space utilisation is uniform, i.e. lateral distribution of vehicles is not influenced by the type and the size of the vehicle Lateral gaps Corrected trajectories and vehicle dimensions (length and width) are the inputs in extracting the lateral gap data. Influence of flow, speed, occupancy, area occupancy and fraction of major vehicle type present in the traffic stream on the gap maintaining behaviour has been analysed. LMV LMV, LMV Auto, LMV TW and TW TW are the vehicle combinations that are utilised for this purpose. Influence of flow, fraction of LMVs, occupancy, speed and area occupancy, on the lateral gap maintaining behaviour of LMV LMV vehicle combination is presented in Figure 7. Average lateral gap for this vehicle combination decreases with increasing flow, occupancy and area occupancy. The gap increases with increasing speed and fraction of LMVs present in the traffic stream. Among the macroscopic characteristics, area occupancy has been found to be consistently correlated with the lateral gap maintaining behaviour for different vehicle combinations (Table 1). Area occupancy showing negative correlation with the average lateral gap consistently for all the vehicle combinations is as shown in Table 1. The area occupancy values obtained in this study falls in the range 2 6.5%. Corresponding to these area occupancy values there is no significant variation in the gaps maintained by vehicles. The effective vehicle widths resulting from this data have been used in deciding the cell widths presented in Tables 2 and 3. The following linear relationships are formulated from the observed data for lateral gap and area occupancy. Average lateral gap for LMV LMV, (m) ¼ area occupancy þ 1.58, Average lateral gap for LMV three-wheeler, (m) ¼ area occupancy þ 1.44, Average lateral gap for LMV TW, (m) ¼ area occupancy þ 1.63, Average lateral gap for TW TW, (m) ¼ area occupancy þ These equations are useful in dynamically updating the gaps maintained by various vehicles under different traffic conditions. The variation in the gap maintaining behaviour has significant influence on the cell structure to be used when modelling various traffic conditions.

13 Transportmetrica 333 (a) Avg. gap (m) (c) Avg. gap (m) Flow (Veh h 1 ) Occupancy (%) (e) Avg. gap (m) (b) Avg. gap (m) (d) Avg. gap (m) Fraction of LMVs Speed (Km h 1 ) Area occupancy (%) Figure 7. Influence of various traffic characteristics on average lateral gap observed for LMV LMV vehicle combination. Table 1. Correlation between average lateral gap and various traffic characteristics. Flow Speed Fraction a Occupancy Area occupancy LMV LMV LMV three-wheeler LMV TW TW TW Notes: a For LMV LMV, LMV three-wheeler combination, fraction denotes the fraction of LMVs and in remaining two cases it is fraction of TWs. TW, two-wheeler Longitudinal gaps Difference in centrelines of vehicles following one another is found to be influencing the longitudinal gaps when staggered following is observed in the traffic. When vehicles are following one another and lateral difference in the centrelines is high, the following vehicle tends to follow the leading vehicle more closely (Mallikarjuna 2007). Under similar traffic conditions when the lateral difference is less, following vehicles maintain more longitudinal gap. Under heterogeneous traffic conditions if TWs are either leading or following the other vehicles, staggered following is more visible. From the data it has been observed that

14 334 Ch. Mallikarjuna and K.R. Rao Table 2. Different parameters used in validating simulation model for urban traffic. Vehicle type Percentage Length Width Mean, Vmax (cells s 1 ) SD of Vmax (cells s 1 ) Acceleration (cells s 2 ) Deceleration (cells s 2 ) Security distance Interaction headway (s) p 0 p dec p lc Car TW HMV Auto Note: TW, motorised two-wheeler; HMV, heavy motor vehicle; and auto, motorised three-wheeler.

15 Transportmetrica 335 Table 3. Different parameters used in validating simulation model for rural traffic. Vehicle type Percentage Length Width Mean, Vmax (cells s 1 ) SD of Vmax (cells s 1 ) Acceleration (cells s 2 ) Deceleration (cells s 2 ) Security distance Interaction headway (s) p 0 p dec p lc Car TW Bus Truck LCV Auto Note: TW, motorised two-wheeler; LCV, light commercial vehicle; and auto, motorised three-wheeler.

16 336 Ch. Mallikarjuna and K.R. Rao with the increase in the difference between centrelines of the vehicles, longitudinal gap maintained by the following vehicles decreases. 5. Calibration and validation of the CA model 5.1. Data collection in the CA model In this study the macroscopic traffic variables, such as flow, speed and density are defined differently to incorporate the heterogeneous nature of the traffic (Lan and Hsu 2006, Mallikarjuna and Ramachandra Rao 2006). The basis for these modifications follows conventional traffic measurements over a general measurement region (Figure 1). Since lane discipline is absent under heterogeneous traffic conditions, measurements taken over a single lane have no relevance under these conditions. To overcome these problems, each cell (which is a part of the vehicle) is considered as one vehicle and each sub-lane is considered as one lane while taking measurements over the general measurement region (Figure 4). On account of the above assumptions, the cells (unit vehicle size) inevitably follow the lane discipline. A measurement region of width W, length L and at time T is considered while taking the measurements. The traffic variables, such as flow, speed and density are defined over this measurement region by qðsþ ¼ d ðsþ jsj, ð7þ kðsþ ¼ tðsþ jsj, vðsþ ¼ qðsþ kðsþ ¼ d ðsþ tðsþ, ð8þ ð9þ where d(s) and t(s) are the total distance travelled and the total time spent by all the cells over the considered general measurement region, respectively, whereas s denotes the volume of the general measurement region. The units for flow, density and speed are cells per second, cells per unit cell length and cell length per second, respectively, for one cell width of the road. Since the density represents the cell occupancy, it is expressed as the percentage occupancy in this study. Multiplying these values with the number of lateral divisions of the road, one gets the values for the total road width. Measurements taken on a car that passes the measurement region is described here. The size of the car is taken as 2 9 cells and it is assumed that the car is travelling with constant speed of 2 m s 1 (4 cells s 1 ) such that it takes 5 s to traverse a stretch of 10 m (20 cells) road length. It is also assumed that all the 18 cells (vehicle area) enter as well as leave the measurement region within the stipulated measurement period. About 18 cells of the cars in the region are considered as separate vehicles and the time taken by these 18 cells to traverse the measurement region is 180 s and the distance traversed by these 18 cells is 360 cells. The volume of the measurement region is 10 s 20 cells 5 cells. If only one car passes through the measurement region, from Equations (7) and (8), the flow value becomes 0.36 cells per second per unit road width (cell width), whereas the density value becomes 0.09 cells per unit road length (cell length) per unit road width (cell width).

17 Transportmetrica Calibration results Main emphasis has been given to understand the heterogeneous traffic behaviour in the free-flow regime. As discussed earlier, all the measurements are taken over a general measurement region. A homogeneous traffic stream is simulated and the results are used to validate the new CA structure and the new data collection methodology. The flow occupancy relationships obtained for different homogeneous vehicle groups over a twolane road are shown in Figure 8(a), and it can be seen that the results obtained conform to the established results available in the literature. The slope of the free-flow branch is equal to the free-flow velocity of the respective vehicle group. In this figure, the flow value represents the number of cells per second per sub-lane that pass the considered road section. Maximum flows achieved in the case of only cars and only buses are 3000 vehicles h 1 and 1800 vehicles h 1, respectively. In another simulation run, about 95% cars and 5% buses (89.1% car cells and 10.9% bus cells) are simulated and the resulting maximum flow achieved over the two-lane road is 12 cells s 1 (Figure 8(b)). In absolute number of vehicles, the maximum flow consists of 111 buses and 2140 cars. To simulate the real heterogeneous traffic behaviour, different types of vehicles are incorporated into the model and the resulting flow occupancy Figure 8. Flow occupancy relationships from the CA model. (a) For cars and buses only (b) for 95% car and 5% buses.

18 338 Ch. Mallikarjuna and K.R. Rao Figure 9. Flow occupancy relationships for heterogeneous traffic. relationship is shown in Figure 9. The simulated traffic stream consists of 50% cars, 5% buses, 20% three-wheelers and 25% TWs. In this case also, the maximum flow equals 12 cells s 1 and under maximum flow conditions, about 1482 cars, 150 buses, 594 threewheelers and 1500 TWs are found to flow in a 1 h period Validation of the simulation model Macroscopic data, such as flow, speed and occupancy measured at a road section (equivalent to the detector of unit length in the simulation model) is available for two road sections. In the case of urban traffic, data has been collected from Dabri road in Noida, Delhi. Video data has been collected and processed using image processing software, TRAZER. Macroscopic data utilised in the model validation has been obtained from the trajectory data. In the case of rural traffic, data has been collected from National Highway-1 (NH-1), connecting Delhi and Amritsar. In this case, video film has been collected and macroscopic data has been obtained manually. Similar data has been collected from the simulation model using a detector of unit cell length. Using these data sets, validation of the simulation model for urban and rural traffic conditions is presented in the following sections Urban traffic From the data collected on Dabri road, it has been observed that the composition of motorised TWs and cars is about 43% and 52%, respectively. Near this location, road is of 10 m wide. From the lateral distribution of vehicles, it has been observed that about 8 m road width was being utilised by the vehicles. Reasons for this behaviour can be attributed to the occasional slow vehicles (non-motorised TWs and three-wheelers) moving on curb side of the road and discomfort to the drivers travelling near the curb. Since it is difficult to consider all these in the simulation model, road width is taken as 8 m. Road stretch is represented in the simulation model as shown in Figure 5 with a cell width of 1.6 m. This cell width has been arrived at based on the actual vehicle width and the lateral gaps maintained by the vehicles. Other important traffic characteristics and CA parameters

19 Transportmetrica 339 Flow (vehicles/hour) Occupancy (%) Observed Simulated Figure 10. Observed and simulated flow, occupancy relationships for urban traffic. used in the simulation model are shown in Table 2. The values attached to the parameters p 0, and p bl are partly based on the field observations and partly based on intuition. The value attached to p dec (stochastic deceleration) is completely based on intuition and on the basis of the assumption that drivers of heavy vehicles may not decelerate unless there is an interaction with the other vehicle. In the case of TWs, since they are small in size, they always have freedom for the movement. Mean and standard deviations (SDs) of free-flow speeds (or maximum speed) and acceleration behaviour observed in the field are also presented in this table. Flow, speed and occupancy obtained for each 1 min interval, collected over a period of 3 h has been utilised in validating the simulation model. Simulated and observed flow occupancy relationships are shown in Figure 10. From these relationships, it can be found that the observed and the simulated data are fairly matching. From these relationships it can also be said that, since observed data on gap maintaining behaviour is limited to certain occupancy range the validity of this model is limited to only these occupancy values. More data is needed to enhance the model s capability to simulate various other traffic conditions. Correlation coefficient between the observed and simulated flow is This seemingly low correlation may be attributed to the grouping of buses, trucks and light commercial vehicles (LCVs) under a single vehicle type called heavy motor vehicles (HMVs) and other Rural traffic An important characteristic of rural traffic is the composition of heavy vehicles, such as trucks and LCV in the traffic stream. In this context, as discussed earlier data collected on NH-1 has been utilised in validating the simulation model. Near the study location, around 15% of heavy vehicles have been observed in the traffic stream. The road width in this case is 7.5 m and in the simulation model it has been considered as 7.4 m. Further, the road is divided into 4 sub-lanes. In this case, sub-lane width is slightly high (1.85 m) compared to the sub-lane width used in the previous case (1.6 m). Higher cell width is taken to replicate the gap maintaining behaviour of vehicles at higher speeds. From Tables 2 and 3, it can be seen that maximum speed of cars is relatively high in this case compared

20 340 Ch. Mallikarjuna and K.R. Rao 6000 Simulated Observed 5000 Flow (Vehicles/hour) Occupancy (%) Figure 11. Observed and simulated flow, occupancy relationships for rural traffic. to urban traffic. Important traffic characteristics and CA parameters used in simulation are shown in Table 3. Flow, speed and occupancy obtained for each 1 min interval collected over a period of 1 h has been utilised in validating the simulation model. In this case, entire data has been collected manually. Observed and simulated flow occupancy relationships are shown in Figure 11. Simulated data points for the occupancy levels that are not corresponding to observed data points are also present in this figure. Range of occupancy values is still less in this case compared to the urban traffic scenario. In this case, observed and simulated flow values are correlated in a better way. Correlation coefficient between observed and simulated flow values is 0.9 in this case Analysis of global measurements When flows and densities are expressed in terms of vehicles, analysing their relationships is difficult and the approach presented here overcame that difficulty. When each sublane is considered as a lane and each cell is considered as a vehicle, it can be assumed that cells are following lane discipline. This can be seen in Figure 5, where individual cell of any vehicle adhere to lane discipline. In this scenario, heterogeneous traffic can be considered as equivalent homogeneous traffic stream composed of cells of identical size. Edie s (1965) generalised definitions for flow, speed and occupancy have been utilised in collecting the data. Macroscopic measurements made in terms of cells adhere to the fundamental relationships among the macroscopic traffic variables (Figures 12 and 13). Since all vehicles are composed of cells and number of cells composing each vehicle type is clearly known (assuming the gap related data is known), it is easy to convert all the variables in terms of vehicles. This information has been utilised in finding the capacities of rural and urban road sections in terms of cells. The analysis of global measurements obtained for urban and rural traffic conditions is presented in the following sections.

21 Transportmetrica 341 Flow (cells/sub-lane/s) Global occupancy Figure 12. Simulated global flow and global occupancy relationship for urban traffic. Flow (cells/sublane/s) Global occupancy (%) Figure 13. Simulated global flow and global occupancy relationship for rural traffic Urban traffic In this analysis, global flow is collected in terms of cells and global occupancy is the percentage of cells filled with vehicles in the CA lattice. Flow occupancy relationship obtained from the simulation model is shown in Figure 12. It can be seen that a maximum flow of 3.5 cells per sub-lane per second is observed at a global occupancy of 20%. Converting flow values from cells per second per sub-lane to vehicles per hour is described in Table 4. Total flow in cells per hour comes out to be 63,000 and for individual vehicle types values are given in column 7 of Table 4. From this information and the corresponding vehicle area in cells (column 5), it is possible to get flow value for each vehicle type. When this flow is converted into vehicles per hour, it comes out to be 3861 and it consists of 2049 cars, 79 HMVs, 39 motorised three-wheelers and 1694 TWs. This maximum flow of 3861 vehicles h 1 is far below the maximum flow observed in Figure 10, which is also in terms of vehicles per hour. The main reason for this difference could be the representation of flow occupancy relationship in terms of absolute number of vehicles. One other reason could be the data points corresponding to the maximum flow (in Figure 3) might be consisting of more small vehicles and less number of heavy vehicles.

22 342 Ch. Mallikarjuna and K.R. Rao This methodology of collecting flow data in cells is useful when flow is composed of different vehicles, which is the case with heterogeneous traffic. It can be seen from Table 4 that vehicle composition, number of sub-lanes and vehicle area in cells are crucial in converting the flow from cell per second per sub-lane to vehicles per hour. Number of sublanes and vehicle area is dependent on the gap maintaining behaviour of vehicles under different conditions. Hence, the data related to gap maintaining behaviour is crucial in developing a realistic flow model Rural traffic The methodology explained in the previous section holds for this case also. When global measurements are taken the maximum flow comes out to be 3.5 cells sub-lane s 1 (Figure 13), which is the same in the case of urban traffic. But the corresponding occupancy value is slightly higher (global occupancy 22.5%) compared to the urban traffic. In this case, the maximum flow in terms of vehicles comes out to be 2295 vehicles h 1. It is composed of 1376 cars, 528 TWs, 115 buses, 115 trucks, 115 LCVs and 46 autos. This maximum flow is true only for the traffic characteristics and CA parameters given in Table 5. Though maximum flow in terms of cells is the same for both urban and rural traffic, flow in absolute number of vehicles is different in these two cases. This concept can also be used in converting the traffic stream into equivalent number of passenger cars. When maximum flows are converted into equivalent passenger cars it Table 4. Converting global flows obtained in cells per second per sub-lane to vehicles per hour, in the case of urban traffic. Vehicle type Percentage of vehicles Length Width Vehicle area Composition Percentage of cells Flow (cells h 1 ) Flow (vehicle h 1 ) Car , TW Truck Auto Table 5. Converting global flows obtained in cells per second per sub-lane to vehicles per hour, in the case of rural traffic. Vehicle type Percentage of vehicles Length Width Vehicle area Composition Percentage of cells Flow (cells h 1 ) Flow (vehicle h 1 ) Car , TW Bus Truck LCV Auto