Stochastic traffic model with random deceleration probabilities: queueing and power-law gap distribution

Abstract

We extend the Nagel - Schreckenberg stochastic cellular automata model for single-lane vehicular traffic to incorporate quenched random deceleration probabilities. We show, by computer simulations, that at low densities this model displays queueing of cars with a power-law probability distribution of gaps between the cars while at high densities the behaviour of the model is similar to the jammed phase of the standard Nagel - Schreckenberg model. The approach to the steady state is characterized by the same critical exponents as for the coarsening process in the simple exclusion processes with random rates, recently investigated independently by Krug and Ferrari, and Evans. The numerical values of the exponents for gap distributions are in agreement with the analytical conjecture of Krug and Ferrari, which implies that the models belong to the same universality class.