A Kinetic Theory Approach to Model Pedestrian Dynamics in Bounded Domains with Obstacles

TL;DR

This paper develops a kinetic theory model for pedestrian evacuation in bounded domains with obstacles, capturing behaviors like congestion avoidance and stream following, and validates it against empirical data.

Contribution

It introduces a novel kinetic theory framework incorporating game theory for pedestrian interactions, enabling realistic simulation of evacuation dynamics with obstacles and multiple exits.

Findings

Good agreement with empirical evacuation data for medium groups

Model reproduces lane formation in bidirectional flow

Capable of simulating evacuations with obstacles and variable exit sizes

Abstract

We consider a kinetic theory approach to model the evacuation of a crowd from bounded domains. The interactions of a person with other pedestrians and the environment, which includes walls, exits, and obstacles, are modeled by using tools of game theory and are transferred to the crowd dynamics. The model allows to weight between two competing behaviors: the search for less congested areas and the tendency to follow the stream unconsciously in a panic situation. For the numerical approximation of the solution to our model, we apply an operator splitting scheme which breaks the problem into two pure advection problems and a problem involving the interactions. We compare our numerical results against the data reported in a recent empirical study on evacuation from a room with two exits. For medium and medium-to-large groups of people we achieve good agreement between the computed average people density and flow rate and the respective measured quantities. Through a series of numerical tests we also show that our approach is capable of handling evacuation from a room with one or more exits with variable size, with and without obstacles, and can reproduce lane formation in bidirectional flow in a corridor.