Synchronous Heterogeneous Exclusion Processes on Open Lattice

TL;DR

This paper introduces a traffic model on an open lattice with heterogeneous particles, proposing an approximate method to compute flow and density, which is exact in a specific case.

Contribution

It presents a novel stochastic traffic model with heterogeneous particles and an approximate analytical approach validated as exact in a special case.

Findings

The approach accurately computes flow rate and density.

Exact results are obtained for a particular system case.

The model captures complex particle dynamics on open lattices.

Abstract

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.