From microscopic social force models to macroscopic continuum models for pedestrian flow

TL;DR

This paper bridges microscopic social force models and macroscopic continuum models for pedestrian flow, deriving kinetic equations and validating them through numerical examples to better understand multi-scale interactions.

Contribution

It introduces a method to derive continuum models from microscopic social force models, linking different scales of pedestrian flow modeling.

Findings

Derived kinetic equations from social force models.

Developed several continuum models based on interaction force variations.

Validated models through numerical simulations.

Abstract

The pedestrian flow is one of the most complex systems, involving large populations of interacting agents. Models at microscopic and macroscopic scales offer different advantages for studying related problems. In general, microscopic models can describe interaction forces at the individual level. Macroscopic models, on the other hand, provide analytical insights into global interactions and long-term overall dynamics, along with efficient numerical simulations and predictions. However, the relationship between models at different scales has rarely been explored. In this study, based on the original microscopic social force model with a reactive optimal route choice strategy, we first derive kinetic equations at the mesoscopic level. By varying the interaction force in different scenarios, we then derive several continuum models at the macroscopic level. Finally, numerical examples are given to evaluate the behaviors of the social force model and our continuum models.