A discrete Hughes' model for pedestrian flow on graphs

TL;DR

This paper presents a new discrete model for pedestrian flow on graphs, combining conservation laws and eikonal equations to simulate route choice and movement, validated through numerical examples.

Contribution

It introduces a novel discrete Hughes' model on graphs that integrates route optimization with pedestrian density evolution.

Findings

Model is mathematically well-posed

Numerical simulations confirm model validity

Demonstrates realistic pedestrian flow behavior

Abstract

In this paper, we introduce a discrete time-finite state model for pedestrian flow on a graph in the spirit of the Hughes dynamic continuum model. The pedestrians, represented by a density function, move on the graph choosing a route to minimize the instantaneous travel cost to the destination. The density is governed by a conservation law while the minimization principle is described by a graph eikonal equation. We show that the model is well posed and we implement some numerical examples to demonstrate the validity of the proposed model.