A Class of Non-Local Models for Pedestrian Traffic

TL;DR

This paper introduces a new class of macroscopic non-local models for pedestrian traffic, capturing how individuals move towards targets while avoiding crowded areas, with proven stability and qualitative properties.

Contribution

It develops a novel mathematical framework for pedestrian flow modeling using nonlocal conservation laws, including stability analysis and numerical validation.

Findings

Models generate Lipschitz semigroups of solutions.

Solutions are stable with respect to initial data and parameters.

Numerical simulations illustrate qualitative properties.

Abstract

We present a new class of macroscopic models for pedestrian flows. Each individual is assumed to move towards a fixed target, deviating from the best path according to the instantaneous crowd distribution. The resulting equation is a conservation law with a nonlocal flux. Each equation in this class generates a Lipschitz semigroup of solutions and is stable with respect to the functions and parameters defining it. Moreover, key qualitative properties such as the boundedness of the crowd density are proved. Specific models are presented and their qualitative properties are shown through numerical integrations.