This section describes the major procedures of experimental design and the resulting numerical results to demonstrate the feasibility of the proposed methodology in characterizing incident-induced dynamic driving maneuvers. Considering the intricate nature of incident-induced driving maneuvers and difficulties in the corresponding data acquisition, the current effort devoted in this scenario mainly aims at calibrating and validating the proposed model in the car-following aspect. The main techniques utilized for performance evaluation include the Paramics microscopic traffic simulator and a specific microscopic traffic simulation program, which was coded with the Turbo C++ computer language, developed particularly for this study. Herein, the proposed incident-induced intra-lane traffic model including the quantum mechanics-based glancing-around and rubbernecking-driven car-following models were embedded into the developed traffic simulation program. Evaluation measures were based mainly on comparison of the simulation data generated from the developed traffic simulation program with both video-based real incident data and simulation data output from Paramics, which is a well-known microscopic traffic simulator.
The procedure of data acquisition adopted in this study, involves two scenarios: (1) video-based data processing for model calibration and testing, and (2) simulation data generation for model validation.
The database generated in the first scenario was primarily processed from the video-based data, which were collected with the aid of Taiwan Area National Freeway Bureau (TANFB). The study site was aimed at 3-km 2-lane mainline segment of the northbound N-1 freeway in Taiwan, where two probe vehicles were artificially placed across the shoulder and outside lane of the study site to mimic a rear-end collision event, as illustrated in Fig. 5. Two cameras were installed, respectively, at the upstream and downstream sections of the incident site to videotape the lane traffic movements for fifteen minutes during the incident period. Based on the videotapes, Traffic data including lane traffic arrival rates, densities, approaching speeds, flows, and the corresponding arrival and departure times of these sampled vehicles were generated.
Fig. 5. Scheme of the study site
The generated video-based data were then used to calibrate the parameters of the Paramics microscopic traffic simulator. The primary input data and the calibrated parameters set used for simulation are summarized in Table 1. Here, certain key parameters, e.g., the physical size, the average reaction time, the maximum acceleration and deceleration rates, and the minimum allowable vehicular headway embedded in Paramics were specified. In addition, we also examined the distributions in terms of the arrival rate and the arrival speed, yielding the related test results presented in Table 1.
Table 1. Summary of the static characteristics of vehicles and calibrated traffic parameters
In the second scenario, the Paramics microscopic traffic simulator was utilized for the calibration and validation of the proposed model. Based on the processed video-based data, a simulation network mimicking the study site was constructed using Paramics. Furthermore, the function of vehicular dashboard tracer embedded in Paramics was actuated. Here, using such a function, a Paramics user is allowed to trace any given simulated vehicle, and manipulate the traced vehicle with lane changing as well as acceleration and deceleration maneuvers during simulation, mimicking the mechanisms of a driving simulator.
To calibrate the key parameters of the proposed model, we randomly drew 52 samples as volunteers with driver licenses from the staff and graduate students of a university in northern Taiwan. In each simulation event, simulated vehicles were set to run in real time, where one of the simulated vehicles present in the adjacent lane was randomly selected to trace as it entered into the simulated study site. Meanwhile, one sampled volunteer was asked to manipulate the given traced vehicle at will via the aforementioned dashboard tracer function, as illustrated in Fig. 6, to pass by the simulated incident. The corresponding traffic characteristics, including the types and locations of the traced vehicle and the corresponding surrounding vehicles as well as their instantaneous speeds and accelerations/decelerations were collected to calibrate the parameter, including h , α1, α2, andα3, particularly embedded in the quantum mechanics-based glancing-around and rubbernecking-driven car-following models.
Fig. 6. Illustration of the simulated-vehicle manipulation function
Utilizing the calibrated parameters and models proposed, a specific microscopic traffic simulation program was developed in the Turbo C++ computer language. The framework of the proposed simulation program is shown in Fig. 7, involving five major subroutines (termed mode-1 to
mode-5), where mode-2 to mode-4 embed the proposed models particularly to deal with the vehicles approaching the incident site via the adjacent lane. In contrast with mode-4, mode-5 aims at the vehicles moving in the blocked lane upstream to the incident site, embedding the respective lane traffic models developed previously. The details about the model formulation and evaluation can be found elsewhere (Sheu, 2006). Note that the focus of this scenario is on verifying the validity of the proposed incident-induced adjacent-lane traffic behavior models using the developed simulation tool.
Also, calibration of the proposed traffic simulation tool is needed, which was conducted previously to the model tests.
Fig. 7. Framework of the proposed microscopic traffic simulation program
To evaluate the proposed models, we compared the simulation data generated from the proposed incident-induced traffic simulation program with both the video-based real incident data and the Paramics simulation data in the following test scenario. Herein, four types of traffic measures are utilized, including: (1) the aggregate arrival volume, (2) the aggregate departure volume, (3) the average link travel time, and (4) the lane usage. Herein, both the arrival and departure volumes were used to test the acceptability of the simulated lane traffic flows entering into and exiting from the study site; in contrast, the average link travel time and lane usage were used to evaluate the system performance of the proposed models in characterizing the incident-induced lane traffic maneuvers. The comparison results are summarized in Tables 2 to 6, where all the simulated values shown in this table were the aggregated measurements via 10-run simulations for each event.
A discussion on the comparison results is provided in the following.
Table 2. Summary of the comparison results (arrival volume)
Table 3. Summary of the comparison results (departure volume) Table 4. Summary of the comparison results (average link travel time)
Table 5. Summary of the comparison results (lane usage)
Overall, the numerical results shown in the above tables may reveal the validity of the proposed approach in characterizing the incident-induced driving maneuvers. Here, all the estimated errors of the proposed method relative to the video-based data fall within the range of
%
−10 and 10%. In addition, several generalizations are further provided for explication.
(1) Given the same traffic arrival patterns, the resulting traffic flows leaving the incident site yielded from the proposed model may fit in with the corresponding video-based data, compared to the simulated data obtained from Paramics. Relative to the video-based data, both proposed model and Paramics may be able to capture the traffic arrival patterns to a certain extent; however, the proposed model appears to outperform Paramics in characterizing the incident-induced driving maneuvers, thus resulting in a relatively lower estimation error in either 5-min. or 15-min. data sampling cases.
(2) In the aspect of the average link travel time, the result of the proposed model may remain valid since the simulation error relative to the video-based data is -5.7%, which is significantly lower than that of Paramcis (i.e., 19.1%). This may imply the significance of respective incident-induced driving behavior models in improving incident traffic characterization and simulation.
(3) The simulated lane traffic distribution and the resulting traffic densities generated by the proposed model are greatly acceptable, compared to the output from Paramics. According to our observations from simulations, such a generalization should also rely, to a certain extent,
on the integration of the proposed models with the respective incident-induced lane-changing model embedded in model-5, which was previously developed to deal particularly with the incident-induced traffic maneuvers in blocked lanes. Therefore, the resulting multi-lane traffic usage yielded from the proposed method is almost consistent with the video-based data.
Furthermore, the potential advantages of the proposed models with respect to depicting incident-induced lane traffic maneuvers have also been revealed in comparison with the Paramics microscopic traffic simulator. This generalization may support our claim, in this paper, on the urgent need of developing respective driving behavior models to characterize the incident-induced lane traffic phenomena.
Despite the acceptability of the proposed model’s capability, demonstrated above, in macroscopic traffic flow characterization, the model’s potential in reproducing the reality of the corresponding microscopic traffic maneuvers should also need to be examined. For this reason, the consistency of the inter-vehicle headway distributions generated by the proposed model and the video-based data was examined as follows.
First, the inter-vehicle headways measured at certain locations of the study site were collected from the video-based data, where ten locations upstream from the incident site were randomly selected to measure the corresponding headways of vehicles moving in adjacent lanes.
Assuming that the collected ten groups of video-based headway measurements follow respective Pearson Type-III distributions, according to the previous literature (May, 1990), we tested if the simulated data yielded from the proposed model follow a consistent distribution for each sampling location. Here, the primary procedures for testing the hypothesis are presented in Fig.
8, and considering the space limit, these procedures as well as the corresponding interim output
data are not presented in this paper. Through 10-run simulations, which are the same as the above test scenario, the final test results of the simulated data groups are summarized in Table 6.
Fig. 8. Primary procedures for examining simulated headway distributions
Table 6. Test results of simulated headway distributions
As can be seen in Table 6, the test results of simulated headway distributions are overall accepted expect for the data group 9, which is located 0.2km upstream from the incident site.
Several important findings from the tests are provided in the following.
First, the corresponding lower values of the chi-square statistics shown in this table imply that the headway patterns measured beyond 1.5km upstream from the incident site were captured pretty well using the proposed quantum mechanics-based glancing-around car-following model.
It is also induced that the glancing-around car-following behavior reproduced by the proposed model appears to exist upstream from the incident site before the occurrence of drivers’
perception of the incident.
Second, due to the increase in the incident-induced lane-changing effects from the blocked lane, the headway patterns of the adjacent lane may turn out to be more anomalous as collected towards the incident site. Such an argument may be true particularly as the continuity of intra-lane traffic flow is significantly and frequently disturbed by the lane-changing vehicles from the blocked lane, as revealed by the chi-square statistics associated with data groups 7, 8, and 9, which were collected within 1.0km upstream from the incident site.
Third, despite the fact that the test result associated with data group 9 is not acceptable, there is no strong reason of denying the validity of the proposed model in characterizing the
incident-induced rubbernecking-driven car-following maneuvers. According to our observation from the videotape, it was found that a certain number of lane-changing vehicles from the blocked lane appeared to significantly interrupt the continuity of the adjacent-lane traffic flow near the incident site, thus contributing to the unexpected variations of headways exhibited in data group 9. Correspondingly, the headways measured at the adjacent lane near the incident site may no longer be fully composed of the pairs of remaining vehicles moving in the adjacent lane; under certain conditions, they may be composed of the mixed traffic flow or the vehicles unexpectedly conducting lane changing from the blocked to the adjacent lane very close to the incident site. This is why we still accept the overall performance of the proposed model in characterizing the incident-induced lane traffic maneuvers near the incident site.
Fourth, compared to data group 9, the headways exhibited in data group 10 appear to be relatively consistent with those measured from video-based data. It is worth mentioning that the measurements of data group 10 were collected just at the location right adjoining to the incident event, where the corresponding lane-changing effect might not be as significant as what happened upstream from the incident site. In the test scenario (i.e., a medium-volume incident case), it was observed that most of the drivers present in the blocked lane appeared to be able to complete changing maneuvers before reaching the incident site. Thus, the resulting lane-changing effect on data group 10 turned out to be less significant than that on data group 9, leading to such a generalization.
Despite the above test results, which may help to prove the feasibility of the proposed model in characterizing microscopic traffic maneuvers, several limitations of this study are summarized in the following for future consideration.
(1) The queuing and lane-changing effects oriented from the blocked lane may remain as significant factors influencing the drivers’ maneuvers of the adjacent lane while they are approaching to the incident site. Furthermore, such effects may also vary with time and space, as well as the instantaneous traffic flow conditions, as illustrated in the previous literature (Sheu et al., 2001a; Sheu, 2003). However, testing the proposed model under diverse lane-changing and queuing scenarios has not yet been taken into account in the present experimental design.
(2) The present study case is limited to the lane blockage in a two-lane mainline freeway segment such that the proposed model serving to deal with incident-induced lane-changing maneuvers from the adjacent lane to the other farther adjacent lanes has not been tested.
(3) Due to the limitations of advanced instruments in collecting enough real incident data and the potential drivers’ responses to the resulting incident-induced traffic flows, the prototype of the proposed quantum mechanics-based approach to incident-induced driving maneuvers may not be effectively calibrated and tested in the present preliminary tests.