Congested Crossing Pedestrian Traffic Flow : Dispersion vs. Transport in Crowded Areas

TL;DR

This paper models and analyzes the interactions between two populations in crowded spaces, using theoretical and numerical methods to evaluate strategies that mitigate congestion during crossing scenarios.

Contribution

It introduces a combined transport and granular diffusion model to study pedestrian crossing dynamics and evaluates various movement strategies for congestion mitigation.

Findings

Directed movement reduces congestion more effectively.

Internal dispersion minimizes overcrowding.

Different strategies significantly impact crowd behavior.

Abstract

This study investigates the complex dynamic interactions between two typed populations coexisting within a shared space. We propose both theoretical and numerical study to analyze scenarios where one population (population $1$) must traverse a territory occupied by another (population $2$), necessitating strategies to mitigate overcrowding caused by spatial limitations. To capture these interactions, we model population $1$ using a linear transport equation, while population $2$ is described by a granular diffusion model a la sandpile to represent its internal dynamics and tendency to decongest. Through numerical simulations, we explore how different movement strategies of the traversing population (population $1$) - including directed motion towards a specific destination, internal dispersion to minimize crowding, and uniform dispersal across the space - affects the behavior of population $2$.