Theoretical investigation of synchronous totally asymmetric exclusion processes on lattices with multiple-input-single-output junctions

TL;DR

This paper provides a theoretical analysis of synchronous totally asymmetric exclusion processes on lattices with multiple-input-single-output junctions, revealing how the number of subchains influences phase boundaries and stationary states.

Contribution

It introduces a mean-field approach to analyze complex MISO junctions in TASEP models, extending understanding of phase behavior in such systems.

Findings

Phase boundary shifts with increasing subchains

Stationary states depend on boundary conditions and subchain number

Simulation results agree with theoretical predictions

Abstract

In this paper, we investigate the dynamics of synchronous totally asymmetric exclusion processes on lattices with a multiple-input single-output (MISO) junction, which consists of m subchains for the input and one main chain for the output. A MISO junction is a type of complex geometry that is relevant to many biological processes as well as vehicular and pedestrian traffic flow. A mean-field approach is developed to deal with the junction that connects the subchains and the main chain. Theoretical results for stationary particle currents, density profiles, and a phase diagram have been obtained. It is found that the phase boundary moves toward the left in the phase diagram with an increase of the number of subchains. The nonequilibrium stationary states, stationary-state phases, and phase boundaries are determined by the boundary conditions of the system as well as by the number of subchains. The density profiles obtained from computer simulations show very good agreement with our theoretical analysis.