Residence time estimates for asymmetric simple exclusion dynamics on stripes

TL;DR

This paper investigates how asymmetric simple exclusion processes on stripes affect particle residence times, considering boundary conditions and anisotropy, with implications for pedestrian and biological transport efficiency.

Contribution

It provides numerical and analytical estimates of residence times under asymmetric exclusion dynamics with boundary and anisotropic effects.

Findings

Residence time depends on boundary conditions and anisotropy.

Asymmetry influences the asymptotic behavior of residence times.

Results are relevant for modeling pedestrian and biological transport.

Abstract

The target of our study is to approximate numerically and, in some particular physically relevant cases, also analytically, the residence time of particles undergoing an asymmetric simple exclusion dynamics on a stripe. The source of asymmetry is twofold: (i) the choice of boundary conditions (different reservoir levels) and (ii) the strong anisotropy from a nonlinear drift with prescribed directionality. We focus on the effect of the choice of anisotropy in the flux on the asymptotic behavior of the residence time with respect to the length of the stripe. The topic is relevant for situations occurring in pedestrian flows or biological transport in crowded environments, where lateral displacements of the particles occur predominantly affecting therefore in an essentially way the efficiency of the overall transport mechanism.