A Heterogeneous Visual Imaging Model for Analyzing the Impact of Vehicle Type on Car-Following Dynamics

1 Heterogeneity is an essential characteristic in car-following behaviors, which can be defined 2 as the differences between the car following behaviors of driver/vehicle combination under 3 comparable conditions. This paper proposes a Visual Imaging Model (VIM) with relaxed 4 assumption on a driver’s perfect perception for 3-D traffic information and uniform reaction 5 to vehicles with different sizes in most existing car following models. The proposed model 6 can generate greater stimuli to the followers from the leading vehicles with larger back sizes 7 (i.e. defined as vehicle width×vehicle height) and short distance to the following vehicles, but 8 less changes in stimuli for the distant leading vehicles under various back sizes. The US101 9 NGSIM data set containing vehicle type/size information is used to evaluate the proposed 10 model at the levels of single trajectory pair and vehicle types. The calibration and validation 11 results show the promising performance of the proposed model in describing heterogeneous 12 car-following behavior. In this study, it is also found from US101 NGSIM data set that in 13 relatively high velocity range, the following gap distance for car following truck (C-T) is 14 greater than that for car following car (C-C), while in low velocity range, C-T has a smaller 15 spacing than C-C. The phenomenon can also be reproduced by the proposed model. 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 TRB 2013 Annual Meeting Paper revised from original submittal. Zheng, Jin, Cheng, Ma and Ran 4 INTRODUCTION 1 Heterogeneity is an essential characteristic in car following behaviors and can be defined as 2 the differences between the car following behaviors of driver/vehicle combination under 3 comparable conditions (1). The heterogeneous driving behavior studies usually include three 4 aspects of the general problem: different driving styles within a vehicle group of the same 5 vehicle type, different driving styles related to the different vehicle types, different driving 6 styles of the follower because of the leader’s different vehicle type. Ossen and Hoogendoorn 7 (1) gained insights into the level of heterogeneity in car following behaviors in real traffic 8 under different types of heterogeneity. In another study (2), they pointed out the highly 9 different driving styles in car following behavior observed in a vehicle trajectory dataset 10 collected from a helicopter and also explored the feasibility of incorporating different types 11 and degree of heterogeneity in car following models. Ranjitkar et al.(3) investigated the 12 performance of some well-known microscopic traffic flow concepts based on different GPS 13 data and found that interpersonal variation are relatively higher than the intermodal variations. 14 Punzo and Tripodi (4) extend the single-class models to multiclass traffic scenario and 15 developed a calibration procedure for multiclass GIPPS car-following model. Meanwhile, 16 several researchers have concentrated on the following distance with respect to the vehicle 17 type. The following distance for car following truck (C-T) was found to be smaller than that 18 for car following car (C-C) in several different data sets (5,6,7). However, Yoo and Green (8) 19 obtained different conclusions that the following distance of C-C was 10% less than that C-T. 20 Ravishankar and Mathew (9) also concluded that the mean following distance varied across 21 vehicle-type combinations with smaller sized vehicles following at a closer spacing. The 22 contradicting results obtained by previous researchers about the following gap distances for 23 C-C and C-T indicate the necessity of studying the problem from a different viewpoint. 24 However, most existing car-following models were postulated for drivers’ perfect 25 perception about 3-D traffic information (velocity, distance or acceleration) and homogenous 26 vehicle types. For example, the well-known General Motors (GM) model, firstly proposed by 27 Chandler et al. (10), utilizes the relative velocity between the leader and the follower as the 28 stimulus. Safe distance (SD) models pursue a safe following distance so as to avoid the 29 rear-end collision, one representative of which is Gipps’ model (11). Optimal Velocity Model 30 (OVM) employs the difference between the current velocity and ideal velocity dependent on 31 the distance headway as the stimulus (12). Despite their success in describing the motion of 32 TRB 2013 Annual Meeting Paper revised from original submittal. Zheng, Jin, Cheng, Ma and Ran 5 individual vehicles in continuous space and time from different aspects, there are some 1 deviations between the car-following behaviors described in those models and the reality. 1) 2 Car following behavior is a human decision-making and response process, and drivers can 3 not accurately perceive the 3-D traffic information, which violates the basic assumption of 4 those models. 2) Such car-following models do not have built-in mechanism to describe the 5 heterogeneous traffic flow composed of vehicles with different vehicle types. Multiple 6 sub-models with different model parameters need to be developed and calibrated to describe 7 each heterogeneous car-following scenario. However, it should be noted that Action Point 8 (AP) models set some perceptual thresholds of spacing or relative velocity to define the 9 minimum value of the stimulus to which the driver will react (13,14,15,16,17). Especially 10 drivers’ perceiving the relative velocity between two successive vehicles is usually through 11 changes on the visual angle subtended by the vehicle in-front, which is definitely related to 12 the vehicle type/size of the preceding vehicle (15). Therefore, AP models can remedy above 13 two deviations in some degree. 14 Moreover, many other researchers have also considered different kinds of projected 2-D 15 visual information related to the vehicle type/size of the preceding vehicle when modeling the 16 car following behaviors, which can all be utilized to cope with the heterogeneous driving 17 behaviors due to the vehicle type/size. For example, Andersen and Sauer (18) presented 18 Driving by visual angel (DVA) model based on the framework of Helly’s model (19), which 19 can produce more predictive driving performance than other models based on 3-D 20 information. Jin et al.(20) introduced a visual angle car following model by using the visual 21 angle and its change rate, which contributes to the design of more realistic car following 22 models. Lee and Jones (21) proposed a model that determines acceleration by the change rate 23 of the visual angle. On the other hand, Lee (22) showed that the inverse rate of expansion of 24 an approaching object (i.e. Denoted byτ ) was a visual variable that could be used to estimate 25 the time to an impending collision, which was also investigated in the studies of driving 26 performance (23,24). However, when traffic flow is stable, τ usually keeps at an infinite 27 value. Therefore, it has limited usefulness in actual car following. 28 Besides, what worth our attention is that another candidate visual source is the visual 29 image information, which is related to two-dimensional information about the back size of 30 the leading vehicle. Michael (25) suggested that the image size of the preceding vehicle or its 31 TRB 2013 Annual Meeting Paper revised from original submittal. Zheng, Jin, Cheng, Ma and Ran 6 visual extent could be used to model car following. Moreover, Zielke et al.(26) designed a 1 computer algorithm for car following so as to maintain a constant image size of the preceding 2 vehicle. Therefore, inspired by using the image information as the stimulus, in this paper, we 3 utilize the visual imaging size of the leading vehicle and its change rate to replace the gap 4 distance and relative velocity and propose the visual imaging model (abbreviated as VIM) 5 based on the framework of Helly’s model. The proposed VIM can not only relax the 6 unrealistic assumption on a driver’s perfect perception for the 3-D traffic information, but 7 also can describe the heterogeneous driving behaviors caused by the various vehicle-type of 8 the leader. The rest of the paper is organized as follows. First, VIM is proposed and analyzed. 9 Then heterogeneous driving behaviors under different leader-follower compositions and 10 velocity ranges are analyzed based on the US101 NGSIM data. After that, the rationality and 11 performance of VIM in modeling the heterogeneous driving behaviors are evaluated. Finally, 12 some important conclusions are drawn. 13