Time-evolving measures and macroscopic modeling of pedestrian flow

TL;DR

This paper introduces a measure-theoretical macroscopic model for pedestrian flow that effectively captures nonlocal interactions and boundary effects, providing a new framework for analysis and numerical approximation.

Contribution

It develops a novel measure-theoretical approach for modeling pedestrian dynamics, enabling better handling of nonlocal interactions and boundary conditions compared to traditional methods.

Findings

Model successfully captures pedestrian interactions and boundary effects.

Framework simplifies analysis and numerical approximation.

Provides early results indicating promising applicability.

Abstract

This paper deals with the early results of a new model of pedestrian flow, conceived within a measure-theoretical framework. The modeling approach consists in a discrete-time Eulerian macroscopic representation of the system via a family of measures which, pushed forward by some motion mappings, provide an estimate of the space occupancy by pedestrians at successive time steps. From the modeling point of view, this setting is particularly suitable to treat nonlocal interactions among pedestrians, obstacles, and wall boundary conditions. In addition, analysis and numerical approximation of the resulting mathematical structures, which is the main target of this work, follow more easily and straightforwardly than in case of standard hyperbolic conservation laws, also used in the specialized literature by some Authors to address analogous problems.