Hypergeometric solution of a stochastic model for traffic flow(Theory,Applied Integrable Systems,<Special Issue>Joint Symposium of JSIAM Activity Groups 2006)

Abstract

In the present paper, we investigate the asymmetric simple exclusion process with parallel dynamics on a ring of finite sites. We focus on the correspondence between the asymmetric exclusion process and the zero-range process, and exploit the recursion formula for the partition function of the zero-range process. Then, we find that the explicit formulas for the partition function and the average velocity (or the flux) in the steady state are expressed by the Gauss hypergeometric functions.