Mean-field theory for car accidents

We study analytically the occurrence of car accidents in the Nagel-Schreckenberg traffic model. We obtain exact results for the occurrence of car accidents P-ac as a function of the car density rho and the degree of stochastic braking p(1) in the case of speed limit v(max) = 1. Various quantities are calculated analytically. The nontrivial limit p(1) --> 0 is discussed.