Driving Behavior at Signalized Intersections Operating under Disordered Traffic Conditions

Abstract

A higher degree of heterogeneity in vehicle class and drivers, coupled with non-lane-based driving habits, creates several challenges in traffic flow analysis. This study investigates vehicles’ microscopic driving behavior at signalized intersections operating under weak lane discipline with mixed traffic (disordered) conditions. For this purpose, a comprehensive vehicular trajectory data set is developed from field-recorded video footage using a semi-automated tool for data extraction. Microscopic parameters such as relative velocity, spacing between vehicles, following time, lane preference, longitudinal and lateral speed profile, hysteresis evidence, and lateral movement of different vehicle classes during different traffic phases are presented in the study. The data is then segregated into three flow conditions: stopped flow, saturated flow, and unaffected flow. It is found that smaller vehicles prefer near-side lanes over far-side lanes. Motorized three-wheeler (3W) and motorized two-wheeler (2W) vehicle classes exhibit the greatest lateral velocity, lateral movement, and aggressiveness. This results in several interactions between vehicles as a function of different leader–follower vehicle pairs. Signalized intersections with more heterogeneity in traffic composition, especially higher composition of 2W and 3W vehicle classes, exhibit higher levels of aggressive driving behavior that might lower safety standards. As a practical application, ranges of various driving behavior parameter values for different leader–follower combinations and traffic conditions are quantified in the study. The observations and results are expected to help better understand prevailing driving behavior in disordered traffic and contribute toward robust calibration of microscopic traffic flow models for better replicating disordered traffic conditions at signalized intersections.

Keywords

Operations Traffic flow theory and characteristics ACP50 traffic flow

Unprecedented vehicular growth (around 8% in India) ( 1 ) has resulted in considerable traffic and travel growth on the roads of metropolitan cities and has subsequently resulted in vehicular delays, long queues, and traffic congestion ( 2 ). The congestion is often visible at the junctions where traffic from two or more approach roads intersects. Based on the requirement (demand) and the available warrants, different traffic signals are provided at the intersections (nodes/junctions) as a key instrument to maneuver the traffic onto its desired path, facilitating safe and smooth traffic operations ( 3 , 4 ). A signalized intersection controls the traffic by apportioning the right-of-way to a specific movement or group of non-conflicting movements periodically. The key point of providing the intersection is to dissipate the conflicting traffic movements while providing higher safety standards, efficiency, and the best possible level of service (LOS). However, to address traffic operations and safety problems, detailed knowledge of traffic flow characteristics and behavior is needed ( 5 ). The key to understanding traffic behavior at a composite level is the availability of a detailed dataset that provides insight into varying macroscopic and microscopic parameters based on the geometric, environmental, and human conditions in the field ( 6 ). In developed countries, the traffic adheres to proper lane discipline and is mostly homogeneous in composition (designated hereafter as an ordered traffic condition). On the other hand, the traffic in developing countries like India is highly heterogeneous, where vehicles with varying static and dynamic characteristics interact with each other. Moreover, vehicles occupy any available lateral position on the carriageway, exhibiting weak lane discipline (disordered traffic conditions), and, as a result, vehicle interactions become multifaceted. Considering the fundamental differences in traffic behavior between ordered and disordered traffic conditions, dedicated studies to explore traffic flow behavior in disordered traffic conditions are imperative.

Several traffic flow models at both macroscopic and microscopic levels have been developed over the years to study traffic flow behavior ( 7 ). Macroscopic models are concerned with describing the aggregate behavior of traffic flow by evaluating the fundamental relationships between vehicle speed, flow, and density. On the other hand, microscopic models describe traffic behavior as emerging from discrete entities (vehicles) interacting with each other and capture drivers’ tactical maneuvering decisions in different situations ( 5 , 8 ). These models have a profound application in the area of traffic safety and capacity analysis to help deduce aggregate traffic flow characteristics from the behavior of individual drivers. These models also form an integral component of microscopic traffic simulators. Microscopic traffic flow models consider different behavioral aspects such as acceleration, lane changing, gap acceptance, and so forth ( 9 ). Initially, driving behavior models focused on car following behavior, where the behavior of the follower was modeled as a function of its leader ( 10 , 11 ). With the advent of microscopic traffic simulators, general acceleration models and integrated driving behavior models, which capture both car following behavior and lateral shift behavior, were developed ( 12 , 13 ). A comprehensive review of different driving behavior models has been provided by Toledo ( 8 ). A vast body of literature deals with the specification, estimation, and calibration of these microscopic models for their application in the domain of traffic safety and operations. Various driving behavior models such as the intelligent driver model (IDM), stimulus-response ( 11 , 14 ), and psycho-physical ( 15 ) models are calibrated and validated for both ordered and disordered traffic conditions. Past studies have used microscopic datasets like vehicular trajectory data ( 16 – 20 ) to calibrate the microscopic traffic models for disordered traffic conditions.

Research Motivation

Signalized intersections have become vulnerable to complex vehicular maneuvers, movements, and interactions associated with disordered traffic conditions, resulting in excessive delays, conflicts, and accidents ( 4 ). Therefore, models based on microscopic aspects that explore the intricacies involved in the interaction of different leader–follower vehicle class combinations could be a better approach in modeling the disordered traffic, specifically at signalized intersections. But, the efficiency of a microscopic traffic model depends on its ability to replicate the local traffic characteristics. Past literature reports that a microscopic model might not accurately simulate the driving behaviors of all regimes or traffic scenarios and is only able to predict the traffic behavior to an acceptable approximated level ( 21 ). Past studies have adopted different techniques such as manual search, mathematical optimization, and heuristic search for calibrating different driving behavior models. Recently, to optimize different parameters of driving behavior models, heuristic-based algorithms like genetic algorithms (GA) ( 21 , 22 ) and simultaneous perturbation stochastic approximation (SPSA) ( 23 ) have been widely used. But the values in these studies are obtained from optimizing the macroscopic parameters of travel time or delay. It is well articulated that different variables or driving behavior representative parameters (DBRPs)—such as relative speed, spacing, acceleration of various vehicles under different conditions, space headways, lateral shift, and lane changes—form key inputs to different driving behavior models, especially for disordered traffic conditions ( 3 , 16 , 24 ). Therefore, the values of different DBRPs would govern these models’ efficacy in modeling traffic behavior. Comprehending the variation in DBRPs can facilitate robust calibration and validation of different driving behavior models.

Further, the range of different driving behavior parameter values derived empirically for different traffic conditions can also facilitate the validation of the driving behavior parameters obtained through optimization. Empirically derived values or ranges for DBRPs could act as constraints during the optimization process to develop the specific study section’s calibration parameters efficiently. Raju et al. ( 22 ), using trajectory data for the midblock section, reported values of different driving behavior parameters. The derived parameters are provided as input to the traffic simulation model, and the developed simulation model was found to represent the field conditions aptly. However, the derivation of different driving-behavior-related parameters using trajectory datasets for signalized intersections seems unreported. Available studies concerning signalized intersections with disordered traffic conditions calibrate existing traffic models or explore a single DBRP or a few DBRPs. A study estimated the time headways at signalized intersections using simulation ( 25 ), but the results are conflicting when motorized two-wheelers (2W) are introduced into the traffic mix. The lateral movement and seepage nature of 2W might be the reason for the conflicting results. Studies have also tried to calibrate the microsimulation models to predict traffic behavior at a signalized intersection using optimization techniques ( 21 , 26 , 27 ). But the results are derived based on assumed ranges as constraints during optimization. The range of DBRP values, the reason for selecting the specific range, and the resulting calibration parameters are different in each study.

With this motivation, the present study reports on an effort to analyze the driving behavior at signalized intersections under disordered traffic conditions. The variation in different driving behavior parameters—such as average longitudinal and lateral speed profiles, lane preference, lateral movement, relative spacing, relative speed, headway, vehicle following time, lane preference, standstill distance, and acceleration from a standstill— are studied by vehicle type, using a set of empirical vehicle trajectories extracted for three signalized intersections with varying traffic composition, degree of saturation, cycle length, and roadway geometry. As an important outcome, the study provides a range of values for different driving behavior parameters at signalized intersections which can be used for calibration and validation of microscopic traffic models.

The rest of the manuscript is organized as follows. After defining the need for the study, data collection and extraction of vehicular trajectories is detailed. Preliminary analysis of the extracted data is performed to check the speed oscillation at signalized intersections, highlighting the need to study the disordered traffic conditions at microscopic levels. The data is segregated into three different flow conditions based on observed field conditions. Different traffic parameters explained previously are studied, and inferences are drawn.

Data Collection and Analysis

Site Selection and Data Acquisition

Data collection is done from three isolated signalized intersections in three different metropolitan cities, namely Jaipur (Rajasthan), Surat (Gujarat), and New Delhi (the capital of India). The selected intersections are free from any side friction parameters, gradient, and curvature in the vicinity and have proper road signs and markings. Left-hand traffic practice is followed in India. Two of the sites (Delhi and Surat) have well-designed auxiliary lanes for free left-turning (diverging) traffic. The third site in Jaipur does not have any auxiliary lanes for free left turns, but the proportion of left-turning traffic is less than 1% of the total incoming traffic. All the study intersections have a red–green–amber–red type three-signal phasing scheme, and Surat and Jaipur have a heads-up display timer. Carriageway dimensions were measured manually in the field during the data collection. Two tripod-mounted video cameras were deployed at a high vantage point to record the upstream and downstream data simultaneously. The stop line acted as a common point of separation (Figure 1a). Details about the study intersection, signal operations, and traffic are summarized in Table 1.

Figure 1.

(a) Detailed line diagram of the Surat study intersection with camera placement. Screenshot during data extraction process of upstream sections for study intersections of (b) Jaipur, (c) Delhi, (d) Surat.

Table 1.

Study Intersection Details

City	Jaipur	Delhi	Surat
Parameter	Jaipur	Delhi	Surat
Location	MI Road and Motilal Atal road intersection	Lala Ram Charan Aggrawal Chowk	Mahavir Chowk near old Regional Transport Office
Type of intersection	Fixed time with flashing green	Actuated signal cycle	Fixed time
Geometry	Three-legged T-intersection	Four-legged intersection	Three-legged t-intersection
Traffic conditions	Undersaturated–saturated	Saturated–oversaturated	Undersaturated
Signal cycle length (s)	118 (3 s amber time)	190 to 300 (3 s amber time)	165 (4 s amber time)
Green time (s)	70	30 to 45	90
Traffic composition (%)*	28: 37: 2: 32: 1	14: 49: 1 :33: 3	16: 60: 1: 21: 2
No. of cycles data extracted for	4	4	5
No. of vehicles traced	550	650	1,350
Average arrival rate (veh/5 s)	5	4	9
Average queue length observed (m)	63	120	110
Trajectory length (cumulative of U/s and D/s of stop line) (m)	>250	>270	>300
Carriageway width (m)	9.5	14.6	11.5
Average discharge rate (veh/5 s)	7	16	16

Note: No. = number; veh = vehicles; U/s = Upstream section; D/s = Downstream section.

Traffic composition is in the order of: motorized three-wheeler: motorized two-wheeler: bus: passenger car: light commercial vehicle.

Data Extraction and Processing

Because of challenges from weak lane discipline and heterogeneity in traffic, automated trajectory data development techniques are still in the nascent stage for disordered traffic conditions. The available studies have focused on trajectory data extracted using manual or semi-automated methods ( 16 , 20 , 28 ). A semi-automated method of data extraction is used in the present study ( 28 ). The field video data is replayed on a large screen monitor. The Microsoft Windows magnifier tool at 200% magnification is used to avoid loss of accuracy arising from condensed pixels or pixel misrepresentation ( 19 ). Using four-point camera calibration methods and field measured dimensions, the static square image on the monitor is converted to represent actual field coordinates ( 29 ). The traffic stream is classified into five vehicle categories with the Indian Highway Capacity manual ( 30 ) as reference. Vehicle classes are: motorized two-wheelers (2W), motorized three-wheelers (3W), passenger cars (Car), buses (Bus), and Light Commercial Vehicles (LCV). Data extraction is carried out at an accuracy of 0.4 s by manually clicking each vehicle’s position and tracing its trajectory through the intersection.

The semi-automated trajectory data extraction process is a severely taxing and time-consuming process. For reference, trajectory data extraction of 500 vehicles traveling a distance of 250 m at signalized intersections over 500 s (for about four signal cycles) warrants about 100 productive working hours. The data was extracted by only one trained person to maintain consistency in the process. During manual trajectory data extraction, the mistracing of an individual vehicle’s position produces “local” errors. This positional error can consequently give rise to increased or decreased inter-vehicle spacing from the adjacent vehicle. Therefore, information on vehicle kinematics and traffic dynamics is crucial for detecting errors ( 31 ). Researchers have applied different types of smoothing methods to eliminate such errors ( 32 , 33 ). When applied to position data, smoothing can remove the random component of the error ( 34 ). Past studies also report that the smoothing technique could eliminate outliers and reduce the errors in the trajectory data ( 16 , 32 ), even when applied for data extracted using a semi-automated tool for disordered traffic conditions. Averaging is one form of smoothing ( 34 ); therefore a 5-point moving average technique is used to smoothen the extracted vehicular trajectories ( 33 , 35 ). After smoothing the data, the vehicular trajectories are trimmed to represent only the signalized intersection’s influence area. The influence area is the region where the vehicle starts to decelerate in the far upstream of the stop line until the traffic stream regains its original speed in the downstream sections.

Preliminary Analysis

Traffic oscillations in the traffic stream are studied using the average speed. Traffic oscillation is a condition of stop-and-go movements caused by congestion from recurring deceleration and acceleration ( 36 ). A signalized intersection also works as a common stationary bottleneck to several traffic streams in the road network and negatively affects traffic operations, safety, and the environment ( 37 ). Figure 2 shows speed oscillation observed at the Surat study intersection as an example; similar trends were observed at all the study intersections. When the vehicles approach the stop line or end of the queue during the red phase at a signalized intersection, the driver slows down to an idle position. When the signal turns green, the vehicles start discharging through the intersection stop line by accelerating. During this process, the disturbance to vehicle movement in terms of individual speeds, relative speed, or headway between succeeding vehicles is averaged, and the fluctuations are observed (Figure 2) at every 40 m interval.

Figure 2.

Speed oscillation at the study intersection of Surat.

On observing the fluctuation in speeds over several cycles, an oscillatory trend is observed. The fluctuation is observed to propagate upstream of the signalized intersection as the queue length increases and replicates a backward forming shockwave. The smooth movement of traffic starts to show an increase in congestion proportional to the intensity of fluctuations. The fluctuations are found in the range of 5 to 15 m/s at the stop line when averaged at an interval of 10 s. The distance over which the fluctuation propagates upstream before diffusing is proportional to the saturation ratio and shockwave area, as observed between 450 and 600 s in Figure 2. But the intensity of disturbance during the higher saturation ratio signal cycle is less than that of signal cycles with a lower saturation ratio. These observations are found to be similar to those observed for ordered traffic conditions ( 38 ). However, the percolation effect of smaller vehicle classes is challenging to assess through these observations. Different vehicle classes have specific preferences for lateral position on the carriageway ( 16 ). Therefore, the study of microscopic aspects considering vehicle-to-vehicle interactions is pertinent in disordered traffic conditions.

Traffic State Classification

From Figure 2, the signalized intersection observes three distinct traffic conditions. The boundary conditions separated by forming or dissipating shockwaves reflect these conditions. The behavior of a vehicle depends on the surrounding environment and the vehicles it interacts with ( 6 ). Therefore, the traffic data is divided into three traffic flow conditions as described below and depicted in Figure 3.

Stopped flow condition: Exists because of the red phase of the signal cycle. Vehicles arriving at their desired speed are forced to decelerate to a stationary position because of the red phase or the existing queue in the upstream section of the stop line.

Saturated flow condition: After the onset of green, vehicles discharge from the stop line at the roadway section’s capacity limit in a congested state. Because of forward-moving dissipating shockwaves, some vehicles face congested conditions in the downstream section of the stop line.

Unaffected flow condition: Occurs during the green phase, after the queue in the upstream section of the stop line and the congested conditions in the influence area dissipates completely. Vehicles arriving at the intersections during this time do not face any congestion or control delay and traverse at almost their desired speed.

Figure 3.

Space–time plot for vehicles classified in three flow conditions at study intersections in (a) Jaipur, (b) Delhi, and (c) Surat.

Traffic Behavior Parameters

Lane Preference and Composition

After the segregation of the data into specified flow types, the data is analyzed for various parameters to gain insights into traffic and vehicle driving behavior. Desired lateral positioning (lane preference) of vehicles at the signalized intersection in all three flow conditions is studied. Figure 4 shows lane preference at the study intersection of Surat as an example. At all the study locations, the bigger (physical size) vehicle classes prefer far-side (median-side) lanes, followed by the smaller vehicles proceeding toward acquiring the near-side (curb-side) lanes, similar to lane preference behavior at midblock ( 16 ). The vehicle classes of Bus and LCV are observed to be very similar in their preference for far-side and intermediate lanes. The presence of these vehicle classes in near-side lanes occurs in Figure 4 because the LCV and Bus data has been merged. However, from the videographic data, it is verified that the Bus never occupied or traversed through the near-side or near-side intermediate lane. Cars mostly tend to move in the far-side lanes. The 2W vehicle class is observed to have a significant presence in all the lanes, except in the far-side lane during unaffected flow conditions. However, from the far-side intermediate lane toward the near-side lane, the 2W proportion dominates (>58%). Overall the 2Ws prefer near-side lanes, especially during unaffected flow conditions. But in stopped or saturated flow conditions, the proportion of 2W in the near-side lane is lower than in the far-side and far-side intermediate lanes (Figure 4, I and II). During stopped and saturated flow conditions, the 2W vehicle class seeps through the available lateral gaps to achieve a longitudinally advantageous position to facilitate faster traversing through the intersection. 3Ws mostly prefer intermediate lanes. However, to achieve the fastest travel time, 3Ws use the far-side lane in the unaffected flow condition and near-side lane during the stopped flow condition. Since the combined proportion of Bus and LCV at all three study intersection is significantly less (<4%), further analysis in the study is focused on the dominant vehicle classes of 2W, 3W, and Car.

Figure 4.

Traffic composition for each lane in (a) stopped flow, (b) saturated flow, and (c) unaffected flow at Surat.

Longitudinal Speed

Average longitudinal speed during the stopped condition at each study intersection observes a similar speed profile trend for lane-based or vehicle class along the longitudinal section (Figures 5 and 6). During stopped flow conditions, the 2W vehicle class is observed to be more aggressive against decelerating while approaching the intersection stop line, followed by 3W and Cars. Based on the lane preference results, the speed profile observed in the lanes is directly proportional to the speed profile of the dominating vehicle class proportion present in the lane. The deceleration zone is dependent on the end of the queue location but is observed to vary in the range of 50 to 120 m upstream of the stop line. For saturated flow conditions (Delhi), though the initial speed in the far upstream section is different in all the study locations, in the close vicinity of the stop line, the average speeds observed in all the lanes and for all the vehicle classes range between 3 and 6 m/s. During stopped and saturated flow conditions, near-side lanes and the 2W vehicle class show a higher speed profile. This may be because of the higher maneuverability and smaller size of this vehicle class. The far-side lanes or Cars are observed to travel at comparatively higher speeds (Delhi and Surat) during the unaffected flow conditions. However, it should be noted that at the stop line, the longitudinal speed in all the lanes converges to harmony in all flow conditions (varying between 0 and 1.5 m/s). This may be because of space restrictions created by channelizing islands, the median, or the added pressure of driving through the common area shared by the traffic from all the approach roads, where a non-compliant vehicle might be attempting to cross over during low flow situations. Variation in longitudinal speed can also affect dilemma zone length at the signalized intersections. During the transition of the amber to red phase change, vehicles often experience the dilemma of either decelerating to stop or continue to cross the intersection. The dilemma zone exists upstream of the stop line and can spread over a considerable distance. Dilemma zone length at signalized intersections is highly dependent on the speed of the approaching vehicle and vehicle type ( 39 – 41 ). Therefore, the dilemma zone boundaries could vary for different vehicle classes and lanes considering the longitudinal speed profile during unaffected flow conditions (Figures 5 and 6) for each study intersection.

Figure 5.

Lane-wise average longitudinal speed profile over the study intersection: (a) stopped flow, (b) saturated flow, and (c) unaffected flow.

Figure 6.

Vehicle-class-wise average longitudinal speed profile over the study intersection: (a) stopped flow, (b) saturated flow, and (c) unaffected flow.

Lateral Speed

Lack of lane discipline and lateral movement is an inherent characteristic of disordered traffic conditions. Figures 7 and 8 show the lateral speed observed for each vehicle class, and the lane averaged over 10 m longitudinally. For the stopped condition, the lateral speed decreases and comes to a bare minimum as the vehicle approaches a stationary position at the stop line of the intersection (Figures 7a and 8a). As for the vehicle-class-wise situation, the trait of higher lateral speed by 2W can be observed and could very well be because of the vehicles’ higher maneuverability, smaller size, and good mechanical performance. Similarly, in the 2W-dominated near-side lane, lateral speeds are higher than in the far-side lane. During saturated flow conditions, fluctuations are to be observed in the lateral speed after the stop line. After crossing the stop line, the vehicles start traversing laterally to overtake vehicles, gain longitudinally desired position/speeds, and break free from the saturated platoon. Accordingly, lateral movement by vehicle class and corresponding lanes should also be higher as a result of higher lateral speeds, resulting in more vehicular interactions.

Figure 7.

Lane-wise average lateral speed profile over the study intersection: (a) stopped flow, (b) saturated flow, and (c) unaffected flow.

Figure 8.

Vehicle-class-wise average lateral speed profile over the study intersection: (a) stopped flow, (b) saturated flow, and (c) unaffected flow conditions.

Lateral Movement

Each vehicle’s absolute lateral movement between every consecutive time frame is calculated from the trajectory data and cumulated to determine the respective vehicle’s total lateral movement while traversing through the intersection (Figure 9). Owing to higher lateral speeds, the 2W vehicle class shows the most lateral movement for any flow condition, followed by 3W and Cars at all the respective study intersections and in all flow conditions. This may be attributed to the earlier points raised about them traversing laterally for securing better positions or 2W percolating through the lateral gaps available between bigger vehicles. The size and maneuverability of smaller vehicle classes also facilitate such behavior ( 19 ).

Figure 9.

Lateral movement of each vehicle class for different flow conditions.

In addition, the specific behavior of 2Ws and 3Ws occupying some part of the auxiliary lane and trying to cut diagonally into the near-side (immediately upstream of a channelizing island) might be the cause as they are the only ones partaking in such movement and actions. Among the study intersections, the lateral movement in Surat is highest, followed by Jaipur and then Delhi. A critical fact that supports the trend of change in lateral movement is the proportion of 2W and 3W vehicle classes. The Delhi study intersection shows the highest proportion of Cars (33%) and the lowest proportion of 2W and 3W (63%) vehicle classes. For the Surat study intersection, the composition emphasis is reversed, with the lowest proportion of Cars (21%) and the highest proportion of 2W and 3W vehicle classes (76%). The higher concentration of laterally moving vehicles also results in a proportionally higher degree of lateral movement in Surat, followed by Jaipur and then the Delhi study intersection. For different flow conditions, the lateral movement for other vehicle classes overall is at its minimum during unaffected flow conditions, followed by stopped flow conditions, and highest for saturated flow conditions. Being restricted or in a stationary position during the red time should result in the minimum lateral movement, but that is not observed. Drivers traverse diagonally to cross over the dense section to achieve a longitudinally advantageous position while joining the queue’s end, resulting in higher lateral movement during stopped conditions. The fluctuations or comparatively higher lateral speeds (Figures 7 and 8) are also observed in the deceleration zone (Figures 5 and 6). For unaffected flow conditions, vehicles are moving mostly at their desired speed and position; lateral movement is undertaken only for overtaking purposes or if the driver wishes to perform a left or right turn at the intersection. But for all vehicle classes, the lateral movement is greatest during saturated flow. So, in general, it can be said that lateral movement is proportional to the density of vehicles in the section up to a certain point, beyond which the lateral movement decreases because of lack of space for movement.

Microscopic Traffic Parameters

To study the microscopic behavior of traffic flow and the intricacies involved in the interactions between the vehicles, parameters including vehicle following behavior, vehicle following time, minimum stopping distance, acceleration from the idle position, time headway between vehicles, relative velocity, and spacing during vehicle following are explored in this section. The observations and results also highlight the complexity in the driving behavior of disordered traffic. However, it is imperative to identify the leader–follower vehicle interactions to assess these parameters.

Identifying Leader–Follower Pairs

Studying the vehicle following behavior based on lane may not yield acceptable results because of weak lane discipline. There might also exist a condition when there are multiple leaders and followers. The identification of the leading and the following vehicle is made using the concepts of lateral thresholds (LT) and lateral clearance (LC) ( 18 , 42 ). The lateral threshold is the minimum lateral distance between the centerline of two subject vehicles, including width and lateral clearance, with which the vehicles can travel parallel to each other comfortably (Equation 1) without experiencing a sideswipe collision. And lateral clearance is the minimum acceptable sidewise safety spacing maintained by a vehicle with neighboring vehicles or objects when it travels through a traffic stream. It is assumed that a vehicle will not move into the desired position if the lateral gap available is less than the LT and will aim to maintain its trajectory until the desired conditions are met. Lateral gap (LG) is the lateral distance between the centerline of two subject vehicles (Equation 2). Figure 10 supplements the explanation for the identification of leader and follower vehicles.

Figure 10.

Leader–follower pair identification.

From Figure 10,

The leader–follower pair of A–C is usually observed for lane-based traffic.

For disordered traffic conditions, vehicles occupy any lateral position on the carriageway (Figure 1b, c , and d). Staggered vehicle movements are observed (Vehicles B, C, and D).

Vehicle D overlaps within the width zone of both vehicles B and C. However, DG_CD <DG_BD (where DG = the distance gap, as shown in Figure 10); therefore the movement of vehicle D will be primarily influenced by the maneuvers of vehicle C, making the leader–follower pair of C–D. If vehicle D shifts laterally and moves out of vehicle C’s width zone while staying in the width zone of vehicle B, then the leader–follower pair will be B–C.

Vehicle F exists between the widths of vehicle D and E, but vehicle F’s width does not overlap with D or E’s width zone. However, minimum lateral clearance is maintained by the vehicles while traversing (else there would be a sideswipe collision).

LT = 0.5^{*} (w_{Lv} + w_{Tv}) + L C_{Tv}

(1)

LG = Y_{Lv} - Y_{Tv}

(2)

where

LT = lateral threshold;

Y_i = lateral position of vehicle i on the carriageway;

w = width of the vehicle;

Lv and Tv = leading vehicle and trailing vehicle, respectively;

LC_i = lateral clearance; and

LG = lateral gap.

A vehicle’s lateral clearance depends on the other interacting vehicles’ classes and speeds ( 18 ). For this study, the individual vehicle class’s minimum lateral clearance at different speeds is considered from the existing literature ( 18 , 42 ). If the vehicle’s width zones are not overlapping and sufficient lateral clearance is available, vehicles are not going to interact as leaders or followers. Only if the LG is less than the LT will the vehicles be in each other’s width zone.

\begin{matrix} Leader - follower pair : T_{i} f {\begin{matrix} (X_{Lv} + l_{Lv} > XTv \\ LG < LT \\ D G_{ij} is minimum \end{matrix} \end{matrix}

(3)

where

X_i = longitudinal position of vehicle i on the carriageway; and

l _Lv = length of the leading vehicle.

Leader–follower pairs at the time interval “i” are identified when all the conditions of Equation 2 are fulfilled. The first two conditions of Equation 3 help to find the leading and following vehicles, while the third condition covers the issue of multiple leading vehicles being present in the lateral threshold zone (e.g., Vehicles B and C for trailing vehicle D in Figure 10). A MATLAB script is developed to identify all the leader–follower pairs from the trajectory data and obtain their corresponding temporal positions, speeds, and acceleration values. Accordingly, several parameters are computed to study and assess the interactions between different vehicle classes.

Vehicle Following Behavior

Vehicle following behavior is assessed considering the relative speed and distance gap maintained between the identified leader and follower vehicles for different flow conditions at each study intersection. Since different vehicles are observed for each flow condition and at the various study locations, the observations are independent. A Mann-U Whitney non-parametric test is performed at a 95% confidence interval to test the statistical difference in the distribution of relative velocity and distance gap of two different groups. Table 2 details the p-value from the non-parametric test for different combinations of flow conditions and leading–following vehicles. The results show that the vehicle following behavior is different and statistically significant for different study locations, flow conditions, and vehicle classes in most cases. The result for the distance gap maintained by vehicles during the stopped flow condition is not statistically significant for Delhi–Jaipur (p-value = 0.613), Jaipur–Delhi (p-value = 0.127), or Delhi–Surat (p-value 0.173). Similarly, no statistical difference is observed in the following distance distribution during the unaffected flow in Jaipur–Surat (p-value = 0.058). However, the results for relative speed observed at each study location are statistically significant.

Table 2.

P-value from Non-Parametric Test Results for the Difference in Following Velocity and Following Distance Maintained Observed between Two Groups of Flow Condition and Vehicle Class at Different Study Locations

		Jaipur			Delhi		Surat
Study intersection	Vehicle class	ST	SF	UF	ST	SF	ST	SF	UF
Flow conditions
Jaipur	ST		<0.001	<0.001	<0.001	0.011	0.043	<0.001	<0.001
	SF	0.001		<0.001	<0.001	0.104	<0.001	<0.001	<0.001
	UF	<0.001	<0.001		<0.001	<0.001	<0.001	<0.001	<0.001
Delhi	ST	0.613	<0.001	<0.001		<0.001	0.381	<0.001	<0.001
Delhi	SF	<0.001	<0.001	<0.001	<0.001		0.021	0.654	0.03
Surat	ST	0.127	<0.001	<0.001	0.173	<0.001		0.001	<0.001
	SF	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001		<0.001
	UF	0.827	<0.001	0.098	<0.001	<0.001	<0.001	<0.001
Vehicle class
		Jaipur			Delhi			Surat
Study intersection	Vehicle class	2W	3W	Car	2W	3W	Car	2W	3W	Car
Jaipur	2W		<0.001	<0.001	0.164	<0.001	<0.001	<0.001	<0.001	<0.001
	3W	0.000		<0.001	<0.001	<0.001	<0.001	<0.001	0.609	<0.001
	Car	<0.001	0.007		<0.001	<0.001	<0.001	<0.001	<0.001	<0.001
Delhi	2W	0.072	<0.001	<0.001		<0.001	<0.001	<0.001	<0.001	<0.001
	3W	<0.001	0.241	<0.001	<0.001		<0.001	<0.001	0.283	<0.001
	Car	<0.001	0.006	0.872	<0.001	<0.001		<0.001	<0.001	0.091
Surat	2W	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001		<0.001	<0.001
	3W	<0.001	<0.001	<0.001	<0.001	0.084	<0.001	<0.001		<0.001
	Car	<0.001	<0.001	0.087	<0.001	<0.001	<0.273	<0.001	<0.001

Note: ST = stopped flow; SF = saturated flow; UF = unaffected flow; 2W = motorized two-wheeler; 3W = motorized three-wheeler; Car = passenger car.

Values in bold represent statistically insignificant results

Red Triangle with dashed boundary: p-value for the statistical test of relative velocity between two respective categories.

Blue triangle with solid boundary line: p-value for the statistical test of distance gap between two respective categories.

No significant difference was observed among vehicle classes for the distance gap maintained as a following vehicle in Delhi–Jaipur (2W: 0.072; 3W: 0.241; Cars: 0.871). Similarly, results are observed for Cars (Surat–Jaipur), and 3W and Car (Delhi–Surat). But the results for relative speeds show a significant difference for most of the vehicle classes between cities. This shows that the vehicle following behavior is significantly different among different vehicle classes and study locations. The only similarity observed is for the vehicle class of 3W and Cars in Delhi and Surat study intersections.

The driving behavior is observed to influence the safety aspects involved in vehicular interactions and road traffic ( 1 , 4 ). The hysteresis phenomenon between relative speed and distance gap between leader and follower vehicles has been used for driving behavior studies. Additionally, the hysteresis relation also supplements observing the proactive (surrogate) safety aspects of a vehicle following operation. According to the hysteresis phenomenon, the relationship between relative speed (Δv) should reduce as the distance gap (Δx). Theoretically, the variation in Δv should reduce as Δx between the leader and follower decreases, forming an inverted conical shape. Conversely, if Δv remains positive (i.e., v_f > v_l) and unchanged, a rear-end collision between the leader and follower vehicle can occur. Therefore, the hysteresis phenomenon helps to study the nature of driving behavior and safety aspects. Since actual collisions during data collection are hard to observe, safety aspects can also be studied in terms of rear-end conflicts that occur more frequently. Conflict is defined as “an observable situation in which two or more road users approach each other in space and time for such an extent that there is a risk of collision if their movements remain unchanged” ( 43 ). Time to collision (TTC), a time-proximal surrogate safety measure at any time instance, is denoted as the ratio of the observed Δx and Δv. The interaction between the leader and follower vehicle can be termed as a conflict or a normal interaction, using a predefined threshold value. TTC is also used for rear-end conflict assessment at signalized intersections. In addition, the TTC at time “i” is represented by the slope of the line between the origin (zero Δx & Δv) and a specific point in individual hysteresis (Figure 11a). For TTC to exist, Δv should be positive. At the same Δx, higher Δv results in a lower value of TTC, reflecting a higher degree of risk associated with a potential rear-end conflict. A general trend line for the hysteresis phenomenon at all the study intersections is shown in Figure 11b. It is observed that variation in Δv at the same Δx is highest at the Surat intersection, followed by Jaipur, and is smallest for the intersection in Delhi. Therefore, in general, the expected TTC value at the Surat study intersection should be lower than that at Jaipur and Delhi, suggesting a higher probability of rear-end conflicts in Surat. These observations suggest that a higher degree of aggressive vehicle following behavior prevails at the study intersection of Surat. The study intersection of Surat also shows the highest traffic composition of small vehicles with significant lateral movements. Based on the observations of difference in driving behavior (Table 2) and variations in hysteresis plot (Figure 11b), the difference in traffic behavior and safety aspects between varying traffic conditions, vehicle classes, and locations can be explored, therefore also providing an avenue for future research.

Figure 11.

Hysteresis phenomenon of vehicles at all the study intersection.

Vehicle Following Time

Vehicle following time is the total time spent by a particular vehicle following the leading vehicle. In other words, it denotes the total time duration of a longitudinal interaction between the leader and follower vehicles ( 20 ). The time during which both the leading and following vehicles are at a stationary position (idle conditions) in the queue during the red phase is not considered for vehicle following time calculation. The vehicle following time also denotes cumulative measurement over space. To some degree, the vehicle following time is observed to be inversely proportional to the lateral movement of the vehicles. Lateral movement of a vehicle and disordered traffic conditions result in continuously changing leader–follower pairs. Delhi’s study intersection, which shows the least lateral movement (Figure 9), displays the highest vehicle following time (Figure 12). And vice versa for the study intersection of Surat, while the Jaipur study intersection shows intermediate readings. Still, the variation in the vehicle following time is not significant, probably because the 2W and 3W vehicle classes shift laterally, terminating a leader–follower interaction and starting a new one. Because of this, even for the vehicle class of Cars, which exhibits the least lateral movement (Figure 9), the following time of Car or by Car is not high, as the leader or follower might be terminating the leader–follower relation. Therefore a definitive or reliable trend for vehicle following time, based on vehicle classes or size of vehicles at signalized intersections in disordered traffic conditions, might be difficult to establish. Consequently, the Car–Car leader–follower following time is found to be the highest. During unaffected flow conditions, the overall vehicle following time is higher than during stopped and saturated flow conditions. The lateral movement and low vehicle following time are observed as short-lived vehicle interactions observed at the Surat study intersection. In saturated flow conditions, relative velocity for all distance gap ranges shows maximum average variation compared with stopped flow followed by unaffected flow with the least variation in relative velocity. Considering the average vehicle following time, Cars show the most stable following behavior, and the vehicle class of 2W the least stable.

Figure 12.

Vehicle following time for the leader (upper row of X-axis) and the follower (lower row) vehicle class pairs during: (a) stopped conditions (b) saturated flow (c) unaffected flow

Headway, Distance Gap, and Relative Velocity during Vehicle Following

With significant differences in traffic operation and driving behavior parameters of different vehicle classes, study locations, and traffic flow conditions, a specific set of representative values cannot be used to model the traffic at the signalized intersection with disordered traffic conditions. Therefore additional parameters observed during vehicle following for different pairs of leader–follower combinations are studied. Figure 13, a and b , details the point measure values of time headway and vehicle following variation (distance) values throughout the vehicle following. Time headway is the time difference between the leading and following vehicles when they arrive at or cross a specific point on the carriageway, and following variation is the distance gap maintained between the vehicles at a particular time interval during vehicle following. Results in Figure 13b for stopped flow conditions (during the red phase) are derived when both the leader and follower vehicles are moving or at least the following vehicle is approaching the leading stationary vehicle. Results for distance gap when both the vehicles are at a stationary position (idle conditions) in the queue during stopped flow conditions are presented separately in a later section.

Figure 13.

Parameters of (a) headway and (b) following distance maintained by vehicle classes at respective study intersections during different flow conditions.

Follower vehicles in Jaipur and Delhi maintain very similar time headways with the leader during stopped flow conditions, with Delhi showing slightly lower headway values. In contrast, the Surat study intersection shows very low headway values. As the traffic condition shifts from stopped flow to saturated flow and then to unaffected flow, the average headway value trend stays the same, but the difference increases. Though the mean headway values range is 1 ± 0.5 (s), the speed of operations is significantly different in all the traffic flow conditions (Figures 5 and 6).

Figure 13b shows that the vehicle’s following distance is dependent on the average speed and density of the study intersection. Proximal following distance is observed during the stopped flow condition, with increasing values in saturated and unaffected flow conditions. As a follower, every vehicle class maintains almost equal spacing from the leader, on average, during stopped flow and saturated flow conditions at respective study locations (Figure 13b). But the spacing increases significantly during the unaffected flow condition. The average vehicle following distance during unaffected flow conditions is highest at the Jaipur and lowest at the Surat study intersection. The Jaipur study intersection is more undersaturated than Surat, and therefore more arriving vehicles traverse in unaffected flow conditions. As a follower, Cars are found to maintain the maximum average spacing from the leader, and 2W maintain the smallest distance gap from the leading vehicle.

Table 3 details the descriptive parameters of relative speed for different leader–follower combinations. The relative speed is measured as the difference between the speed of leading and following vehicles. Therefore, the results in Table 3 only consider the speed of vehicles involved in a leader–follower interaction for calculating relative speeds. Cars while traversing are focused on far-side lanes, where 2W and 3W composition is less. It can be said that Cars interact with fewer laterally moving vehicles. Consequently, the number of leader–follower relations for Cars is smaller. Therefore, this class exhibits the lowest standard deviation in relative velocities as a follower and the highest following time for all the flow conditions. This implies that Cars traverse in a more stable manner than other vehicle classes, although without any lane discipline, with a minimal lateral movement. 2W and 3W vehicle classes, with the highest degree of lateral movement and lateral speeds, often interact with a vehicle at close proximity before shifting laterally and interacting with another vehicle afterward. In such scenarios, they exhibit the least following time, and therefore lower distance gaps and higher standard deviations are observed during vehicle following behavior.

Table 3.

Descriptive Parameters for Relative Velocities between Leader–Follower Vehicle Pairs

Study intersection	Traffic condition	Leader–follower	3W			2W			Car
Study intersection	Traffic condition	Des. stats	3W	2W	Car	3W	2W	Car	3W	2W	Car
Jaipur	Stopped flow	Average (m/s)	–0.85	1.51	0.92	–0.72	0.07	–0.15	–0.64	0.36	0.08
		Std dev. (m/s)	1.57	1.49	1.28	1.85	1.58	1.79	2.57	1.7	1.41
		Range (m/s)	6.58	5.81	6.13	11.19	15.55	15.38	12.44	10.42	15.12
	Saturated flow	Average (m/s)	–0.1	1.53	–0.07	–1.25	0.01	–0.68	–0.48	0.26	–0.04
		Std dev. (m/s)	1.28	1.82	1.63	1.61	1.46	1.9	1.83	1.28	1.4
		Range (m/s)	7.98	7.98	10.04	8.69	11.3	15.48	9.37	8.04	12.09
	Unaffected flow	Average (m/s)	–0.14	0.93	–0.39	–0.9	–0.38	–1.79	–2.85	–0.68	–0.23
		Std dev. (m/s)	1.71	1.65	1.77	2.36	2.26	2.07	2.18	1.46	1.45
		Range (m/s)	9.45	6.74	4.86	12.71	12.27	8.1	8.39	9.67	14.69
Delhi	Stopped flow	Average (m/s)	0.09	1.21	0.11	–0.01	0.03	0.2	0	0.29	1.7
		Std dev. (m/s)	2.15	2.5	2.51	2.1	1.71	2.62	1.98	3.15	4.02
		Range (m/s)	12.4	7.39	13.58	15.51	19.09	14.62	16.78	12.73	25.35
	Saturated flow	Average (m/s)	–0.02	1.34	0.14	–0.55	0.1	–0.11	–0.04	1.17	0.49
		Std dev. (m/s)	1.45	3.25	1.31	1.26	1.67	1.17	0.78	2.04	1.96
		Range (m/s)	11.83	17.61	8.11	10.06	14.87	18.26	15.02	12.61	9.67
Surat	Stopped flow	Average (m/s)	0.34	0.55	–0.19	–0.53	0.1	–1.05	0.36	1.15	0.01
		Std dev. (m/s)	1.06	1.43	2.38	1.58	0.81	2.3	2.32	2.4	0.27
		Range (m/s)	8.45	13.06	20.28	26.63	11.56	14.39	17.03	18.47	11.49
	Saturated flow	Average (m/s)	0.02	0.08	0.36	–0.28	–0.05	–0.67	–0.42	0.44	–0.01
		Std dev. (m/s)	0.78	1.65	0.98	0.66	0.61	1.51	1.26	1.34	0.95
		Range (m/s)	8.18	11.05	4.37	12.36	13.9	15.44	2.88	15.33	0.14
	Unaffected flow	Average (m/s)	1.04	0.52	–1.21	–0.17	–0.39	0.74	1.71	0.5	0.96
		Std dev. (m/s)	3.02	3.03	2.07	2.93	2.5	5.14	1.65	5	2.1
		Range (m/s)	12.01	17	14.11	12.68	22.17	16.28	8.82	19.19	7.56

Note: 3W = motorized three-wheeler; 2W = motorized two-wheeler; Car = passenger car; des. stats = descriptive statistics; std dev. = standard deviation.

Standstill Conditions

A minimum space headway is maintained by the vehicles even when stationary. This distance is called standstill distance. Traffic data from the stopped flow condition was filtered spatially and temporally for data pertaining to vehicles at idle during the red phase. Based on the observations from three study intersections (Figure 14a), the minimum longitudinal standstill distance is found to be very low (0.05 m for 2W–2W interaction). The median standstill distance is observed to vary as vehicle size increases. The vehicle classes of 2W and 3W tend to maintain lower standstill distance from other leading vehicle classes. However, for the Car vehicle class, as a follower, the median standstill distance is lower for another Car as the leader and comparatively higher for the smaller vehicle classes of 2W and 3W.

Figure 14.

Under standstill conditions: (a) minimum stopping distance for different leader–follower pairs; (b) initial acceleration of the subject vehicle.

For acceleration of vehicles when starting from a standstill distance, data from saturated flow conditions was filtered, and vehicles starting to accelerate at the start of green were considered. Vehicles in Jaipur show lower values of acceleration (0.58 m/s²) from a standstill position than those in Delhi (0.99 m/s²) and Surat (0.96 m/s²). Longitudinal speed lane-wise (Figure 5c) and vehicle-class-wise (Figure 6c) shows lower operating speeds during the unaffected flow conditions in Jaipur. It might be possible that the Jaipur study intersection’s operating conditions or driving behaviors are least aggressive compared with the other two study intersections. Therefore, the vehicle drivers observe a gradual acceleration. However, the standstill position’s acceleration values are an average of observed values and taken under the saturated flow condition (high density). A vehicle’s desired acceleration rate from standstill might be higher, and therefore the distribution of acceleration rates is provided for better reference (Figure 14b).

Implications for Traffic Behavior Modeling

The present study explored various microscopic traffic parameters, found to be critical in modeling the traffic behavior in disordered traffic conditions. The results show that statistically significant behavior is exhibited by different vehicle classes across flow conditions and locations in disordered traffic conditions. The difference in driving and vehicle following behavior combined with the vehicles’ significant lateral movements means that the vehicular interactions are very complex, longitudinally and laterally. This study primarily focuses on the longitudinal aspects of vehicular interactions while incorporating lateral positional aspects in identifying leader–follower pairs. Apart from exploring the actual field behavior at signalized intersections with disordered traffic, this study also aims to supplement modeling and calibrate the driving behavior. Various results showcased in the plots and tables throughout the manuscript are aimed at providing various DBRPs in a quantified format. As discussed initially, a DBRP from one study intersection might not be applicable to another. The available literature exploring the traffic behavior of disordered traffic at signalized intersections has derived the DBRP using optimization techniques considering a specific range as constraints. However, the range for specific DBRPs is observed to vary among the available studies. The reason for selecting the ranges is based on theoretical measures or values representing under- and overestimation of field conditions.

The present study provides distribution of several DBRPs at signalized intersections; the vehicle following variation (relative velocity, together with time and space headways), and standstill distance and acceleration from standstill position are provided for dominant vehicle classes and combinations of leader–follower vehicle classes during different flow conditions. Table 4 compares some DBRP values proposed in different studies, and obtained from optimization using assumed ranges, with the empirically derived range in this study. The available DBRP values are observed to be well within the observed range. This study provides a similar range of DBRPs for several combinations that can be used as constraints during the optimization process and therefore make the achievement of DBRP values possible and enable them to be observed in the field with a higher degree of reliability.

Table 4.

Comparison of Calibration Values of Traffic Behavior Models at the Signalized Intersection with Disordered Traffic

Study	Category	Standstill distance (m)	Headway time (m)	Following variation (m)	Acceleration from standstill (m/s²)
Bhattacharyya, et al. ( 21 )	Car	0.8	0.58	0.5	2.64
	2W	0.38	0.33	3	1.66
	3W	1.01	0.38	5.91	4
Mathew and Radhakrishnan ( 26 )	Study section 1	0.27	3.47	6.451	NA
	Study section 2	0.8	0.8	0.32	NA
	Study section 3	1.28	2	12.97	NA
Mondal and Gupta ( 27 )	Average values	0.652	0.11	NA	NA
Present study	Car	0.08–1.96	0–3.8	0.25–21	0.1–4.3
	2W	0.02–1.87	0–3	0.1–15	0.2–4.4
	3W	0.04–2.16	0.1–4.5	0.2–19.5	0.1–2.6

Note: Car = passenger car; 2W = motorized two-wheeler; 3W = motorized three-wheeler; NA= not available.

Conclusion and Way Forward

Mixed traffic and non-lane-based driving habits of drivers in developing countries like India pose a significant challenge to a precise analysis of traffic conditions and behavior. Several factors limit the applicability or accuracy of the existing vehicle traffic behavior models. This study aims to supplement the efforts in tackling these limitations. The present study analyzes traffic stream behavior at signalized intersections for non-lane-based mixed traffic conditions using empirical vehicular trajectory data. The results showcase added variability and complexities observed in traffic behavior at the signalized intersection for disordered traffic conditions, implying the importance of study based on microscopic parameters for traffic behavior assessment of disordered traffic. The study also highlights the need to develop a detailed and rich dataset of vehicular trajectories in disordered traffic conditions.

The study of speed oscillations at signalized intersections with disordered traffic shows results similar to those observed for ordered traffic conditions ( 37 , 38 ). The average longitudinal speed profile of different vehicle classes, different lanes, and different traffic flow conditions displays significant variations (Figures 5 and 6), suggesting different queue buildup and discharge characteristics. Dilemma zone length is dependent on the speed of the approaching vehicle and vehicle type ( 39 – 41 ). Also, the behavior of each vehicle class is statistically different in disordered traffic conditions ( 16 ). Therefore, the dilemma zone boundaries at signalized intersections could vary for different vehicle classes and lanes considering the longitudinal speed profile during unaffected flow conditions (Figures 5 and 6) for each study intersection.

Lateral movement of the vehicles is a significant factor in governing the exhibited driving behavior in disordered conditions. Lateral movements are primarily performed to occupy the desired lateral position (lane preference) that might support a beneficial longitudinal position (possibly less delay). The smaller vehicles (2W and 3W) are distinct in their longitudinal and lateral behavior compared with the bigger vehicle class of Cars. Therefore, these vehicle classes are most susceptible to exhibiting non-lane-discipline driving behavior. Because of their high maneuverability and dynamic properties, these vehicle classes exhibit higher traffic speed during congested conditions. Simultaneously, the lateral movement and lateral moving speeds (Figures 7 and 8) of these vehicles are also significant. But during unaffected flows with lower vehicular densities, the average speed of Cars and far-side lanes is observed to be higher, followed by speeds of 2Ws, and then 3W.

During unaffected flow conditions, the lateral movement of vehicles is lowest (Figure 9c), as vehicles can traverse at desired speeds, resulting in stable traffic movement and longer vehicle following behavior. Therefore, a comparatively higher range is observed in the time headway and distance gap (following variations) values for all leader–follower pairs at all the study locations (Figure 13). Consequently, the vehicle following time is high in unaffected flow conditions, at the Delhi study intersection, and for bigger vehicle classes (Car) that show the lowest lateral movement in their respective categories.

Conversely, as the traffic conditions change to stopped or saturated flow conditions, variations in traffic behavior are observed. High fluctuations in lateral speed before the stop line in stopped flow conditions (Figures 7a and 8a) and after the stop line in saturated flow conditions (Figures 7b and 8b) result in increased lateral movements (Figure 9a and b ). Consequently, the number of longitudinal and lateral interactions between the vehicles in the downstream section is higher than the number upstream of the stop line. However, these leader–follower pairs or vehicular interactions are very short-lived. Because of short-lived interactions between vehicles as leader or follower, no specific trend in the vehicle following time can be expected at signalized intersections as either the leader or the follower, or both, might be undergoing a lateral shift terminating an existing longitudinal interaction and creating a new one. Because of this, the variations in range values of time headway and following (Figure 13) are lower than observed during unaffected flow conditions. Signalized intersections with more heterogeneity in traffic composition, especially a higher composition of 2W and 3W vehicle classes, exhibit higher lateral movement with more fluctuation in longitudinal and lateral speed and accelerations at lower distance gap, which could result in more aggressive driving behavior that might lower the safety standards.

The resulting short-lived leader following interactions also result in vehicle following behavior that somewhat compromises safety. Many of the interactions involve higher positive relative speeds at a lower distance gap. This would lead to a need to observe the extreme values (closer to threshold levels of defining conflicts) of different surrogate safety measures, denoting most vehicular interactions as rear-end conflicts (44). It can also be inferred that the signalized intersections with disordered traffic might have aggressive driving behavior present, especially downstream of the stop line, considering the comparatively congested conditions and fluctuation in lateral movement there. From Figure 11, the study intersection of Surat, with its higher composition of laterally moving vehicles, can be said to display more aggressive driving behavior and conflicting traffic than the other two study intersections. The vehicular interactions and conflicts at signalized intersections might be high compared with midblock sections (congested conditions + lateral movements). Still, considering the vehicles’ speeds, the severity of the conflicts should be lower than at the midblock section, but that requires another detailed study.

Because of the variability in traffic behavior associated with different study sections, flow conditions, and vehicle classes, specific trends in the vehicle following parameters are difficult to establish, especially at signalized intersections with disordered traffic conditions. Because of staggered vehicle following and the presence of multiple leader or follower vehicles, it is difficult to conclude that the use of traditional car following models for traffic analysis will yield favorable results. Additionally, the vehicle following behavior of each vehicle class is observed to be statically different in every traffic flow condition and for all the study locations (Table 2). Each vehicle class’s distinct characteristics demand the study of vehicle–vehicle interactions using microscopic traffic behavior models to assess the traffic operations’ safety aspect. Therefore, calibration parameters used to model a particular study intersection might not be useful for another study section, even if similar flow conditions are observed. The present study analyzes driving behavior at signalized intersections operating under disordered traffic conditions. The variation in different DBRPs such as lateral movement, lane preference, relative spacing, relative velocity, acceleration, and deceleration characteristics of different vehicle classes is investigated in detail. As a practical outcome, the ranges of different DBRPs are suggested and compared with those reported in the past literature. The authors anticipate that the values of DBRP can help in calibrating more robust driving behavior models for signalized intersections operating under disordered traffic conditions and this, therefore, forms the novelty of the present study. Moreover, further research can be conducted to modify existing driving behavior models by incorporating lateral shifting behavior to replicate disordered traffic conditions.

Footnotes

Acknowledgements

The authors acknowledge the anonymous reviewers’ efforts and suggestions that helped to modify and enhance the manuscript qualitatively. The authors also acknowledge the help of Mr Yawar Ali and Mr Vattsal Shah during data collection.

Author Contributions

The authors confirm contribution to the paper as follows: study conception and design: all authors; data collection and extraction: Chauhan; analysis of data: Chauhan; interpretation of results and manuscript preparation: all authors. All authors reviewed the results and approved the final version of the manuscript.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The data collection process for this study was supported by the Third Phase of Technical Education Quality Improvement Programme (TEQIP III) of SVNIT-Surat chapter under Grant CED/AD/TEQIP-III/4183/2019.

ORCID iDs

Ritvik Chauhan

Ashish Dhamaniya

Shriniwas Arkatkar

Data Accessibility Statement

Some or all data, models, or code that support the findings of this study are available from the corresponding author on reasonable request.

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