This paper develops a probabilistic model for analyzing longitudinal collision/safety between an abruptly decelerating vehicle and its immediate follower. The input parameters are the length of the gap between the two vehicles, their common speed prior to the failure, the reaction delay of the following vehicle and a bivariate distribution for the two deceleration rates. The output includes the probability of a collision and the probability distribution of the relative speed at collision time We use this model to compare the safety consequences associated with the platooning and “free-agent” longitudinal-separation rules. We also demonstrate that the free-agent rule implemented with a potential technology of fast and accurate emergency deceleration, under some reasonable conditions, can avoid collisions while offering a high freeway capacity previously thought possible only under the platooning rule. This model has many other applications.
Jacob Tsao and Randolph Hall. "A Probabilistic Model for AVCS Longitudinal Collision/Safety Analysis" Intelligent Vehicle Highway Systems Journal (IVHS Journal) (1994): 261-274.