A multi-species asymmetric simple exclusion process and its relation to traffic flow

Using the matrix product formalism we formulate a natural p-species generalization of the asymmetric simple exclusion process. In this model particles hop with their own specific rate and fast particles can overtake slow ones with a rate equal to their relative speed. We obtain the algebraic structure and study the properties of the representations in detail. The uncorrelated steady state for the open system is obtained and in the ($p \to \infty)$ limit, the dependence of its characteristics on the distribution of velocities is determined. It is shown that when the total arrival rate of particles exceeds a certain value, the density of the slowest particles rises abroptly.