Synchronous Heterogeneous Exclusion Processes on Open Lattice

A traffic model on an open one-dimensional lattice is considered. At any discrete time moment, with prescribed probability, a particle arrives to the leftmost cell of the lattice, and, with prescribed probability, the arriving particle belongs to one of the types characterized by the probabilities of particle attempts to move at the present time and the probabilities to leave the system. An approximate approach to compute the particle flow rate and density in cells is proposed. It is proven that, for a particular case of the system, the approach gives exact results.