The increased availability of detailed trajectory data sets from naturalistic, observational, and simulation-based studies, is a key source for potential improvements in the development of detailed safety models that explicitly account for vehicle conflict interactions and various driving maneuvers. Despite the well-recognized research findings on both crash frequency estimation and traffic conflict analysis carried out over the last decades, only recently researchers have started to study and model the link between the two. This link is typically made by statistical association between aggregated conflicts and crashes, which still relies on crash data and ignores heterogeneity in the estimation procedure. More recently, an extreme value (EV) approach has been used to link the probability of a crash occurrence to the frequency of conflicts estimated from observed variability of crash proximity, using a probabilistic framework and without using crash records. In this study the Generalized Extreme Value distribution used in the block maxima (BM) approach and the Generalized Pareto Distribution used in the peak over threshold approach (POT), are tested and compared for the estimation of head-on collisions in passing maneuvers. The minimum time-to-collision with the opposite vehicle is used in both EV methods. Detailed trajectory data of the passing, passed and opposite vehicles from a fixed-based driving simulator experiment was used in this study. One hundred experienced drivers from different demographic strata participated in this experiment on a voluntary basis. Several two-lane rural highway layouts and traffic conditions were considered in the design of the driving simulator scenarios. Raw data was collected at a resolution of 0.1 s and included the longitudinal and lateral positions, speeds and accelerations of all vehicles in the scenario. From this raw data, both methods were tested for stationary and non-stationary models. The latter allowed not-only for a better modeling performance in estimating the number of expected crashes, but also for a quantified analysis of the detailed driving choices affecting the head-on crash probability during passing maneuvers. The estimation results showed that the BM approach yielded more stable results compared to the POT approach, but the latter was able to produce crash rate estimates more consistently sensitive to the covariates of interest. Finally, the estimated distributions were validated using a second set of data extracted from an additional driving simulator experiment. The results indicate that this is a promising approach for safety evaluation. On-going work of the authors will attempt to generalize this method to other safety measures related to passing maneuvers, test it for the detailed analysis of the effect of demographic factors on passing maneuvers' crash probability and for its usefulness in a traffic simulation environment.
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