Totally asymmetric simple exclusion process with one or two shortcuts

TL;DR

This paper analyzes a variant of the asymmetric simple exclusion process with shortcuts, using mathematical and numerical methods to understand how bifurcation choices affect flow, with applications in road network design.

Contribution

It introduces a model with one or two shortcuts in ASEP and explores how bifurcation choices influence system behavior, providing insights for traffic flow management.

Findings

Different bifurcation choices lead to distinct system behaviors.

Mathematical analysis and simulations reveal the impact of shortcuts.

Results have practical implications for road bifurcation design.

Abstract

In this paper, the operation of totally asymmetric simple exclusion process with one or two shortcuts under open boundary conditions is discussed. Using both mathematical analysis and numerical simulations, we have found that, according to the method chosen by the particle at the bifurcation, the model can be separated into two different situations which lead to different results. The results obtained in this paper would be very useful in the road building, especially at the bifurcation of the road.