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

TL;DR

This paper introduces a p-species asymmetric simple exclusion process using matrix product formalism, analyzing its steady states and phase transitions related to particle velocities and traffic flow dynamics.

Contribution

It generalizes the ASEP to multiple species with overtaking, providing algebraic structures and steady state analysis for complex traffic-like systems.

Findings

Steady state characterized for open systems.

Density of slow particles increases abruptly at critical rates.

Dependence of system behavior on velocity distribution.

Abstract

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.