Investigating traffic safety reckoning hyperbolic driving following behavior using trajectory data

Using vehicle trajectory datasets developed over a study section for three traffic flow levels, a rectangular hyperbolic relation between  time-to-collision and relative speeds in vehicle-following behavior were observed. A new methodology for estimating the probable rear-end collisions in the given traffic stream is developed based on this relation. The vehicle-following behavior is examined in terms of the hysteresis phenomenon concerning the distance gap (DG) and relative speed (RS). Further, based on the follower’s attention toward towards the leader vehicle, a novel surrogate safety measure, called Instantaneous Heeding Time (IHT), was conceptualized. This measure represents the time gap available based on the positions of the leader and follower vehicles. After exploring vehicle-following behavior, IHT, DG, and RS were used to estimate the rear-end collision probability. The applicability of the proposed methodology is tested using different thresholds (IHT, DG, and RS) and applied to the study section at the three traffic flow levels.