A Fractional Micro-Macro Model for Crowds of Pedestrians based on Fractional Mean Field Games

TL;DR

This paper introduces a novel fractional micro-macro modeling framework for pedestrian crowds, integrating fractional mean field games and conservation laws to better capture complex interactions and dynamics.

Contribution

It develops a fractional micro-macro model for pedestrian crowds using fractional mean field games and conservation laws, advancing the modeling of crowd behavior.

Findings

Fractional models better capture real pedestrian dynamics.

Simulation results validate the effectiveness of the fractional models.

The approach integrates micro and macro scales seamlessly.

Abstract

Modeling of crowds of pedestrians has been considered in this paper from different aspects. Based on fractional microscopic model that may be much more close to reality, a fractional macroscopic model has been proposed using conservation law of mass. Then in order to characterize the competitive and cooperative interactions among pedestrians, fractional mean field games are utilized in the modeling problem when the number of pedestrians goes to infinity and fractional dynamic model composed of fractional backward and fractional forward equations are constructed in macro scale. Fractional micro-macro model for crowds of pedestrians are obtained in the end. Simulation results are also included to illustrate the proposed fractional microscopic model and fractional macroscopic model respectively.