Stochastic differential games for crowd evacuation problems: A paradox

Abstract

We examine the crowd evacuation problem by following a stochastic receding-horizon differential game. We study two main different directions. First, we only consider local aggregated congestion terms that penalize the magnitude of the decision-makers’ strategies allowing us to avoid the formation of congestion. Second, we consider both local and global (population-like) aggregated congestion terms to perform crowd aversion during the evacuation procedure. We present the solution for these proposed problems in a semi-explicit way by solving the corresponding Hamilton–Jacobi–Bellman (HJB) backward Partial Differential Equation (PDE). Afterward, we discuss an evacuation Braess paradox stating that enabling a new path to the exits may lead to a worse evacuation performance. We propose a concrete example where a Braess paradox can emerge and we formally find the required conditions. Finally, we present some numerical examples corresponding to a case study with multiple rooms and either one or two exits. We implement the two aforementioned stochastic differential-game approaches and compare the results.