A Stochastic Model for Chain Collisions of Vehicles Equipped With Vehicular Communications

Improvement of traffic safety by cooperative vehicular applications is one of the most promising benefits of vehicular ad hoc networks (VANETs). However, to properly develop such applications, the influence of different driving parameters on the event of vehicle collision must be assessed at an early design stage. In this paper, we derive a stochastic model for the number of accidents in a platoon of vehicles equipped with a warning collision notification system, which is able to inform all the vehicles about an emergency event. In fact, the assumption of communications being used is key to simplify the derivation of a stochastic model. The model enables the computation of the average number of collisions that occur in the platoon, the probabilities of the different ways in which the collisions may take place, as well as other statistics of interest. Although an exponential distribution has been used for the traffic density, it is also valid for different probability distributions for traffic densities, as well as for other significant parameters of the model. Moreover, the actual communication system employed is independent of the model since it is abstracted by a message delay variable, which allows it to be used to evaluate different communication technologies. We validate the proposed model with Monte Carlo simulations. With this model, one can quickly evaluate numerically the influence of different model parameters (vehicle density, velocities, decelerations, and delays) on the collision process and draw conclusions that shed relevant guidelines for the design of vehicular communication systems, as well as chain collision avoidance applications. Illustrative examples of application are provided, although a systematic characterization and evaluation of different scenarios is left as future work.