Inhomogeneous Discrete‐Time Asymmetric Exclusion or Zero‐Range Processes and Traffic Models

Versions of stochastic discrete‐time totally asymmetric simple exclusion processes (TASEP) and totally asymmetric simple zero‐range processes (TASZPR) are considered. The approach is developed in the frame of microscopic models of vehicular traffic. Known facts of discrete‐time queueing network theory are used to obtain theorems regarding TASEP and TASZRP. The following discrete‐time processes are studied: A TASEP on a closed lattice such that the probability of a particle transition depends on the index of the particle and the number of vacant sites ahead of the particle; a TASZRP inhomogeneous along a closed lattice; a TASEP on an infinite lattice with a finite number of particles such that the probability of a particle transition depends on the number of vacant sites ahead of the particle; and a TASZRP inhomogeneous along an open boundaries lattice. For the processes under consideration, the stationary state distribution is studied.