مدل سازی مدت زمان تغییر مسیر Modeling Duration of Lane Changes

Only a limited number of studies that address the question of duration of lane changes have been presented in the literature. Worrall and Bullen (5) used aerial photographs to estimate lane-change durations, which split into two parts: the time in the initial lane and the time in the target lane. The mean durations were 1.25 and 1.95 s, respectively. The respective standard deviations were 0.4 and 0.5 s. However, later research (6) suggested that lane-change durations were underestimated in this study because of the limitations of the technology that was used. Finnegan and Green (7) reviewed relevant research conducted in the 1970s and 1980s. They report that lane changes, including visual search time, took between 4.9 and 7.6 s depending on the presence of traffic and the direction of change. However, they point out that the use of obtrusive equipment, such as eye markers and helmets, may have interfered with drivers’ behavior. Tijerina et al. (8) used observers who accompanied the driver in the vehicle. The observers gave driving instructions and recorded drivers’ actions. The study included 39 drivers who drove both on highways and on urban streets. For the urban streets, lane-change durations were between 3.5 and 6.5 s, with a mean of 5.0 s. For highways the duration ranged from 3.5 s to 8.5 s with a mean of 5.8 s. Hetrick (9) also used observers to collect data in the vehicle. Sixteen participants drove an instrumented vehicle with an observer for 1.5 h on urban streets and on highways. Lane-change durations ranged from 3.4 s to 13.6 s. Young drivers tended to have short lane-change durations, whereas elderly drivers took longer times to change lanes. The mean lane-change duration was 6.0 s. Lee et al. (10) point out that the presence of the observer in these studies may have influenced drivers’ behavior, resulting in a lack of natural driving behavior. Hanowski (11) used instrumented short-haul trucks to record, among other things, the durations of lane changes in a study designed to evaluate the impact of fatigue. He found that for the 42 drivers who participated in the experiment, lane-change durations ranged from 1.1 s to 16.5 s. The mean and standard deviation were 4.52 s and 1.71 s, respectively [results reported by Lee et al. (10)]. The lanechange initiation was defined by the time when the wheel crossed the lane line. Lee et al. (10) point out that this definition differs from earlier results and that on the basis of the study by Worrall and Bullen (5), 1.25 s should be added to these durations. Lee et al. (10) conducted another experiment with instrumented vehicles that were equipped to automatically gather data on lane changing, and so the presence of an observer was not required. Two vehicles were used: a sedan and a sport utility vehicle. Sixteen drivers who normally commuted more than 40 km every day drove each vehicle for 10 days. The initiation of lane changes was defined by the point in time when vehicles began to move laterally. The completion of lane changes was defined by the points in time when the centers of the vehicles were in the destination lane. With these definitions, the mean duration of single-lane changes observed in the experiment was 6.3 s with a standard deviation of 2.0 s. They also found that lane changes to the left took longer to complete compared with lane changes to the right but found no significant differences between lane changes taken in the two vehicles. A different approach was applied by Salvucci and Liu (12), who used a driving simulator to evaluate drivers’ lane-changing behavior. The 11 participants in the experiment were asked to drive through a multilane highway in a fixed-base medium-fidelity driving simulator. Subjects were asked to report the intention to make a lane change and also the completion of a lane change. On the basis of these observations, the mean duration of lane changes was estimated at 5.14 s with a standard deviation of 0.86 s. The limited realism of the driving simulator may have biased the results. In addition, obtrusive equipment was used, which may have made the driving task unnatural. Although the methods used in the studies just reviewed vary, they all demonstrate that lane changes are not instantaneous events but make take up to 16 s, with mean durations in the range of 5 to 6 s. However, there are significant limitations and potential biases in these studies. In most cases, human observers or obtrusive equipment, such as eye markers, were used to collect data. Their presence may have affected driver’s behavior and biased the results. In one case, data were collected by using a driving simulator and not in naturalistic driving, which may negatively affect the realism of the driving experience and the fidelity of the data collected. Another difficulty is that the definitions of the initiation and completion of lane changes differ in the various studies. For example, in some cases it is assumed that lane changes are initiated when the driver decides to change lanes. This ambiguous definition may be interpreted differently by different drivers and lead to larger variability of the lane-changing durations. Moreover, this definition is not appropriate for use in microscopic traffic simulation, in which driving behavior models are mostly based on the observable positions and speeds of vehicles and not on their intentions. Human factors used in some of the studies to explain lane-change durations, such as eye and head movements, are also not applicable in the context of traffic simulation. Finally, the cost associated with the use of driving simulators and equipped vehicles is high. Therefore, only small samples of drivers could be used, which made it difficult to draw statistically significant conclusions from the results. It is therefore not surprising that Chovan et al. (6) and Lee et al. (10) both point out the lack of onroad lane-changing duration data as an important limitation to studies that use these data to develop and evaluate driver assistance systems. Models for the durations of lane changes are developed here that address some of these limitations by using a large set of trajectory data at a high time resolution that was collected by high-mounted video cameras in naturalistic driving conditions and without the use of obtrusive equipment or even the knowledge of the drivers.