Title: Modeling Crossing Behavior of Drivers and Pedestrians at Uncontrolled Intersections and Mid-block Crossings

Transcription

1 Title: Modeling Crossing Behavior of Drivers and Pedestrians at Uncontrolled Intersections and Mid-block Crossings Objectives The goal of this study is to advance the state of the art in understanding traffic characteristics and modeling drivers and pedestrians behavior at uncontrolled intersections and mid-block crossings respectively. Based upon the existing research needs and the potential for utilizing data collected at various locations, the following research objectives are established to address goals of this research initiative: Research Objective 1 Traffic Characterization To study the microscopic traffic characteristics at the functional area of unsignalized intersections, such as, vehicle category wise speeds on the major and minor legs, relative speed between the inner lane and outer lane of major road, conflict point study and vehicle trajectories study. Research Objective 2 Drivers and Pedestrian Gap Acceptance Analysis Analyzing the driver and pedestrian behavior while crossing uncontrolled intersections and midblock crossings respectively, which involves quantifying driver and pedestrian gap acceptance and gap rejection behavior, identification of the factors that affect drivers and pedestrians crossing behavior. Research Objective 3 Dilemma Zone for Low Priority Streams Studying the dilemma of crossing vehicles and pedestrians. Finding location and length of the dilemma zone using probabilistic approach at uncontrolled intersections for vehicles and at uncontrolled mid-block crossings for pedestrians. Summary of previous work. Understanding traffic parameters such as speed, traffic composition, gap acceptance, and conflict points at microscopic level is necessary for developing performance evaluation models. These parameters also help to evaluate facilities with respect to safety. Many studies are found in the literature that focus on microscopic traffic characteristics at various transportation facilities in developed countries where traffic is disciplined. Very few studies are found that analyze traffic behavior at unsignalized intersections and mid-block crossings in India. The traffic behaves significantly different at unsignalized intersections and mid-block crossings in developing countries like India than at the intersections and crossings in developed countries which are controlled by stop and yield signs. The situation is more severe in India, because drivers and pedestrians do not follow the traffic rules strictly; major road drivers usually do not yield to minor 1

2 road traffic even in the presence of yield sign. This condition further makes more challenging task to analyze the traffic characteristics. The identified research gaps after doing through literature review are outlined below. Gap acceptance theory is limited to finding Capacity and LOS of the intersections and midblock crossings, only few studies have used gap acceptance theory for highway safety considerations. Many gap acceptance studies are reported for homogenous traffic conditions where lane discipline and priorities are respected. Modeling heterogeneous traffic conditions is more challenging and complex task. A majority of the research used time based gap/lag data for modeling driver and pedestrian gap acceptance behavior. Spatial gap acceptance behavior of drivers and pedestrians at uncontrolled intersections and mid-block crossings is not comprehensively studied. Dilemma behavior of drivers at uncontrolled intersections and pedestrians at mid-block crossings is not yet studied. A few studies have examined the effect of night time on drivers behavior. For the most part, data collected in these studies have not included speed, distance, and vehicle type of conflicting vehicle. Thus, only a very few of these studies have been able to use and study detailed traffic characteristics. Methodology Overview The methodology presented in this research rests on the assumption that driver and pedestrian behavior can be modeled through a set of descriptive parameters, which can be calibrated from filed data. The research presented in this study involves several tasks, as follows: Selection of Intersections and Mid-block Crossings Seven uncontrolled road intersections and two mid-block crossings with their approach segments are identified for data collection. Each intersection having different vehicle composition is studied. One intersection from town, two typical inner-city intersections, three intersections from outer suburban road and one intersection on rural fast road are studied Classification of Intersections Selected intersections are classified/labeled as Type-I, Type-II, and Type-III intersections. Type-I intersections are located at the city centre; Type-II intersections are located on outer link road while Type-III intersections on rural national highway. Snapshots of three intersections, one in main city, one in a suburb, and one in the outskirt of city are shown in Figure 1. 2

3 Data Extraction Figure 1: Typical examples of type I, type II and type III intersections Except geometric data, all required data are extracted from the video recorded. For gap acceptance and dilemma study, vehicle and pedestrian yielding behavior, accepted and rejected gaps, traffic volume data are recorded at study sites and analyzed. The data extracted has total 1234 gap/lag observations at three 4-legged intersections located on outer link road; 1469 and 113 gap/lag observations at one 3-legged intersection located on rural national highway for day and night respectively, and 117 gap/lag observations for pedestrians at two mid-block crossings. Data Analysis The data extracted is then analyzed for studying drivers and pedestrians gap acceptance and understanding their dilemma at uncontrolled intersections and mid-block crossings respectively. Gap acceptance study involves temporal as well as spatial gap analysis. For dilemma analysis, variations in temporal and spatial gap acceptance behavior are analyzed to arrive at dilemma zone boundary values. Summary of Input Data The preliminary analysis is done to understand different traffic parameters at uncontrolled intersections. The preliminary analysis includes understanding of traffic composition, lane preference, speed analysis, traffic conflict points, distribution of gaps, and vehicle trajectories. Traffic Composition and Lane Preference It is observed that Type I intersection is handling much higher traffic compared to others, and Type II intersection traffic is higher than that of Type III. The traffic composition clearly shows that very high proportions of two-wheelers are used in most cities of India. Similar observations are reported in other studies (Sangole, 211). The proportion of two-wheeler is highest at Type I intersections. This is mainly because two-wheelers are preferred for shorter trips and in the areas of high congestion. 3

4 Speed (km/hr) Speed (km/hr) Table 1: 2-Minutes Volume Statistics in % with Type and Lane Choice Inter. Type Lane 2W Car HMV Rickshaw Bicycle Total Outer Type I Inner Total % Outer Type II Inner Total % Outer Type III Inner Total % Speed Analysis Vehicle speeds are calculated at different distances by noting the vehicle crossing time at cross grid lines along a vehicle path. The speed variations of vehicles along its path for a major approach and a minor approach are depicted in Figure 2. The speed values at centre of intersection (- m) are much lower since vehicles have to slow down or stop because of crossing or merging of traffic from other approaches and large number undisciplined pedestrian movements. 5. Major Road (West Bound ) 5. Minor Road (South Bound) Figure 2: Speed variations for major road and minor road at type I intersection Vehicle Conflict Points Good understanding of how and where conflicts occur is required for the proper geometric design and implementing efficient traffic control measures. Vehicle trajectories on the angular view from video and the transferred trajectores on a plan are shown in Figure 3. One important observation from the trajectory path is that the two-wheelers taking turns are not at the centre of the lane. As far as possible the vehicles are on extreme right of an approach; this minimizes the crossing time for a vehicle. Howerver, the standard 32 points conflict diagram is based on the assumption that vehicle move at the center of a lane. Distributions of Gaps and Observed Trajectory Data The histograms for temporal and spatial gap along with the various distributions (Exponential, Lognormal, Gamma and Weibull) fitted for all available gaps (accepted and rejected) are shown 4

5 Speed (km/hr) Speed (km/hr) in Figure 4. Based on Kolmogorov-Smirnov (K-S) test, it is observed that lognormal distribution fits temporal gaps well, whereas the spatial gaps follow Gamma distribution. Figure 3: Plotting of vehicle trajectories and comparison of conflicts between right turning vehicles.5 D e n s i t y Histogram Exponential Lognormal Gamma Weibull D e n s i t y Histogram Exponential Lognormal Gamma Weibull Gap (Sec) Gap (Meter) Figure 4: Distribution fitting for available temporal gaps and spatial gaps at 4-legged intersection The distance of the vehicle and its speed travelling over a major road are plotted when the vehicle on minor road is waiting to accept the gap. Figure 5 depicts the graphical representation of locations and speeds of observed main line stream vehicle either during the acceptance or rejection of gap or lag by minor road vehicle to cross the major road. (a) Accepted Rejected (b) Accepted Rejected Figure 5: Observed speeds and distances of main line stream vehicles while acceptance and rejection of gap by minor road vehicles for (a) 4-Legged intersection, (b) 3-Legged intersection (Day) Analysis Overview and Main Results Modeling Driver and Pedestrian Behaviour Using Binary Logit Models A binary-logit model is recognized as one of the important modelling tool for studying discrete choices. It has two alternative outputs from which an individual can choose. In present case, a minor road vehicle or a pedestrian waiting for a sufficient gap has to choose between the two 5

6 alternatives from an available gap: accept the gap or reject the gap. A linear-utility expression can be expressed as shown in Equation 1: 1 P k (i) = 1 + e U i (1) U i is a utility of gap i, expressed as: U i = β 1 X 1 + β 2 X 2 + β 3 X β n X n (2) Where, X 1, X 2,, X n are the variables that influences the decision of drivers and β 1, β 2,, β n are the corresponding coefficients. We used software tool NLOGIT to calibrate binary logit model. Various dummy variables tried while developing model along with their definition and share in the total data set are given in Table 2. Dummy Variables Table 2: Definitions of Dummy Variables Definition 1 % observation with value 1 Gender of the subject vehicle driver Female Male 85% Whether Lag or Gap Gap Lag 21% Position of conflicting vehicle Lane1 Lane2 19.6% Conflicting vehicle: two-wheeler No Yes 42% Conflicting vehicle: Auto Rickshaw No Yes 8% Conflicting vehicle: Car No Yes 34% Conflicting vehicle: Truck No Yes 11% Subject vehicle: two-wheeler No Yes 71% Subject vehicle: Auto Rickshaw No Yes 11% Subject vehicle: Car No Yes 17% Subject vehicle: Truck No Yes 1% Separate models for spatial and temporal gaps are developed. We tried various combinations of variables affecting the gap acceptance decision and shortlisted two models each for spatial and temporal gaps. Model 1 and 2 are developed by taking various combination of variables from Table 2. Table 3 gives values of t-statistics for variables used and R 2 for the models developed. Model 1 U i = (T) (LG) (TW_T) (TW_TW).616 (TW_C) (5) Model 2 U i = (S) (D) (LG) (TW T ) (TW_TW).539 (TW_C) (6) The probablity of accepting spatial lag or gap is shown in Figure 6(a). From the figure, it is clearely evident that for a given value of lag/gap, drivers are more willing to accept lag i.e. first gap. Figure 6(b) shows the probability of accepting spatial gap by two wheelers for different types of conflicting vehicles. 6

7 Probablity Probablity (a) Lag (36 km/hr) 6 8 Gap (36 km/hr) Figure 6: (a) Probability of acceptance of spatial gap and lag and (b) Probability of accepting spatial gap by two wheelers for different types of conflicting vehicles Table 3: Results of the Estimation of the Logit Model Variable Description Model 1 Model 2 Model 3 Model 4 t-stat t-stat t-stat t-stat Constant Constant T Time S Speed D Distance LG Lag/Gap TW_T 2Wheller_Truck TW_TW 2Wheller_2Wheller TW_C 2Wheller_Car McFadden Pseudo R-squared Comparison of Critical Gaps Lag Gap As per HCM 2, critical gap is the minimum time between successive major street vehicles where minor street vehicles make a maneuver. Critical gap may differ for different drivers based on driver s characteristics such as driving experience, age, gender, and psychological condition. The summary of temporal and spatial critical gap values for through traffic, right turning, and through and right combined is listed in Table 4. Table 4: Summary of Critical Gap Values Calculated from Different Methods Method Critical Gap Through Traffic Right Turning (Minor Rd. to Minor Rd.) (Minor Rd. to Major Rd.) Combined Traffic Temporal (s) Spatial (m) Temporal (s) Spatial (m) Temporal(s) Spatial(m) Raff's Method Logit Method MLM Lag Method Ashworth 3. n/a 3.7 n/a 3.3 n/a (b).2 Two Wheeler_Two Wheeler Two Wheeler_Car Two Wheeler_Truck 7

8 Critical Gaps for Pedestrians The critical gap values estimated using different methods are shown in Table 5. The probabilistic methods (logit method and maximum likelihood method) are relatively close in their estimation of the mean pedestrian critical gaps. Critical gaps estimated using Raff s and Ashworth s methods are on lower side. Table 5: Critical Gap Comparison by Different Methods Critical gap accepted by pedestrian Temporal critical gap spatial critical gap ( Found using different methods) (Adequate Gap) (Adequate Gap) Temporal Spatial (s) (m) Method (s) (m) Raff's Method Logit Method * 198* MLM ** 148** Ashworth s Method 3.6 N/A N/A not applicable; * Adequate Gap using HCM default values; ** Using observed field values SVM for Classification of Gaps The basic idea of the SVM is to construct a hyperplane as the decision plane, which separates the trajectories of accepted and rejected gap classes with the largest margin. The data are divided into two classes: positive (+1) which are accepted gaps and negative (-1) which are rejected gaps (see Figure 7). The two classes in present situation are linearly non-separable. Figure 7 shows the profiles of both accepted and rejected spatial gaps for various speed ranges for a 4-legged intersection. The 1-fold cross-validation method was used for training and validating. Speed (km/hr) Critical Gap Line (Hyperplane) Accepted Rejected Support Vectors Figure 7: Hyperplane separating two classes accepted and rejected for 4-legged Intersection Dilemma Zone for Low Priority Streams 2 Mean Speed Critical Gap = 3m The study defines Dilemma zone as a roadway segment of a major road over which if a vehicle is present with a certain speed, creates dilemma to minor road vehicle regarding maneuvering. When a conflicting vehicle is in this zone, minor road vehicles may take incorrect decision, and this unsafe behavior may lead to crashes at intersection. This observation leads to the evaluation 8

9 of upper and lower limit of accepted/rejected gaps which are stated as outer (D) and inner (Di) boundaries of dilemma zone. Using probabilistic approach, we have found the dilemma zone which is modeled as the road segment or a zone where more than 1% and less than 9% of the drivers would choose to reject the gap. Binary discrete choice models are developed to determine the probability of rejection of gap for a given distance and speed of the conflicting vehicle. Table 6 depicts parameter estimates and statistical significance of the logit models for selected intersections. Table 7 shows the dilemma zone boundaries for probability of 1% and 9% stopping for 4-legged intersection. Table 6: Parameter Estimates and Statistical Significance of the Logit Model for Selected Intersections Variable Description 3-legged inter. 4-legged inter. 3-legged inter. (Day) (Night) Coefficient t-stat Coefficient t-stat Coefficient t-stat Constant Constant S Speed D Distance McFadden R Table 7: Dilemma Zone Boundaries for Probability of 1% and 9% Stopping for 4-legged Intersection Approach Speed (km/hr) 4-legged intersection 9% 1% m 4 m m 48 m m 58 m Effect of Vehicle Type on Dilemma Zone Boundaries The distribution of the dilemma zones are found varying with different type of vehicles. Vehicle types such as truck, car and two wheeler were found to have statically significant effect on length and location of dilemma zone boundaries. Analysis result indicated that the dilemma zone distribution shifts away from the intersection as vehicle size increases. Time of the day (i.e., day vs night) had a statically significant effect on both length and the location of dilemma zone. Main Conclusions Preliminary Data Analysis It is well know that two-wheelers form a major component of the traffic in India. At one intersection, the proportion of two-wheelers is more than 7% and at two intersections, it is close to 5%. It is also observed that the traffic speed on inner lane is higher than that on outer lane. Vehicles at type II and type III intersections maintain much higher speed than the posted speed limit. From the vehicle trajectories analysis, it is concluded that the conflict points of right turning 9

10 two-wheelers are located significantly away from the conflict points arrived assuming vehicles move at the center of a lane. Gap Acceptance Analysis It is observed that, approach speed of major stream affects the spatial gap acceptance but not the temporal gap acceptance. Type of conflicting vehicle also has a major impact on crossing vehicle and pedestrian gap acceptance behaviour. It was found that, as size of conflicting vehicle increases, the probability of accepting the available gap decreases. At 4-legged intersection, the temporal critical gap values for through movement vary from 3. sec by Ashworth method to 3.7 sec by Raff s method. The values for right turning movement vary from 3.4 to 3.8 seconds. This study also demonstrates the feasibility of SVM to classify and predict gap acceptance/rejection for uncontrolled intersections and midblock crossing. Dilemma Zone for Low Priority Streams The empirical results have clearly indicated that the existence of dilemma zone vary with the traffic and geometric characteristic. Separate dilemma zones for trucks, cars and two wheelers are analyzed. The start and end point of dilemma zone for medium speed intersection for different conditions varies from 1 to 4 m and 32 to 62 m, whereas for high speed intersection these values vary from 12 to 88 m and 76 to 148 m. Suggested Further Research The aggressive behavior of drivers and pedestrians reported could be partly due to the poor enforcement of the priority rules. The study can be extended to analyze the variations in gap acceptance for different traffic volumes at different time periods. The effect of driver/pedestrian age, and education level can also be studied. Gap acceptance depends upon various traffic and geometric factors. The selected intersections had level approaches, central refuge area and 9 degree intersecting approaches. Intersections having peculiar traffic and geometric characteristics (traffic encroachment, speed breakers etc.) can also be analyzed. Selected pedestrian crosswalks in this study were on high speed arterials. Thus, the transferability of behavioral models for different locations needs to be checked. Dilemma zone and prediction of gap acceptance at uncontrolled road sections can be important to develop real time applications such as Advanced Warning and Safety System (AWSS) and Advanced Traffic Management Systems (ATMS). These systems will help drivers and pedestrians to make an appropriate choice of action during crossing at intersections and midblock crossings. Future studies should apply the SVM technique to data from different cities and check the applicability of the models developed. 1