Residence time in presence of moving defects and obstacles

TL;DR

This paper analyzes how moving defects or obstacles affect the residence time of a particle performing a one-dimensional random walk, providing explicit formulas and discussing practical applications like pedestrian movement and water flow.

Contribution

It introduces explicit formulas for residence time in the presence of moving obstacles and explores how stochastic obstacle motion influences local residence time profiles.

Findings

Explicit residence time formulas derived for various obstacle models

Stochastic obstacle motion smoothens residence time profiles

Connections established with pedestrian dynamics and water runoff applications

Abstract

We discuss the properties of the residence time in presence of moving defects or obstacles for a particle performing a one dimensional random walk. More precisely, for a particle conditioned to exit through the right endpoint, we measure the typical time needed to cross the entire lattice in presence of defects. We find explicit formulae for the residence time and discuss several models of moving obstacles. The presence of a stochastic updating rule for the motion of the obstacle smoothens the local residence time profiles found in the case of a static obstacle. We finally discuss connections with applicative problems, such as the pedestrian motion in presence of queues and the residence time of water flows in runoff ponds.