This paper develops a probabilistic model and a software tool for analyzing longitudinal collision/safety between two automated vehicles. The input parameters are the length of the gap between the two vehicles, the common speed prior to the failure, the reaction delay of the following vehicle and a bivariate pint distribution of the deceleration rates of the two vehicles. The output includes the probability of a collision and also the probability distribution of the relative speed at collision time.We will use this model to compare the safety consequences associated with the platooning and "free-agent" vehicle-following rules. We will also demonstrate that the free-agent vehicle following rule implemented with a potential technology of fast and accurate emergency deceleration, under some reasonable conditions, can virtually avoid collisions while offering a high freeway capacity previously thought possible only under the platooning rule.
H.-S. Jacob Tsao and Randolph Hall. "A Probabilistic Model and a Software Tool for AVCS Longitudinal Collision/Safety Analysis" PATH Working Paper (1993).