Mass Evacuation Planning Based on Mean Field Games Theory

Abstract

This study proposes a dynamic framework for a mass evacuation in a large-scale urban area. The evacuation plan includes three main decisions: shelter (destination), departure time, and route. The first decision can be formulated as a shelter allocation problem, while the two latter decisions can be addressed by traffic assignment models. Unlike previously proposed dynamic models that solve shelter allocation and traffic assignment problems separately at the microscopic level, the proposed model addresses the population evacuation at the network level for a large but finite population of agents. We formulate the model based on an extension of infinite population game theory called Mean Field Games. The proposed dynamical system has two sets of equations: conservation equations for the traffic flow dynamics and Hamilton-Jacobi-Bellman (HJB) equation for the trajectory of the particles. The solution of the model is derived by solving the corresponding HJB with respect to the conservation equations, which is equivalent to solving a fixed-point problem. A heuristic algorithm is proposed to find the fixed point.