Crowd Management Services In Hajj: A Mean-Field Game Theory Approach

The problem of managing congestion and overcrowding in a critical situation has largely been studied over the last decades. The problem is how to safely direct pedestrians with suitable velocity to the nearest floor in order to avoid the bottleneck. For example, in Hajj there is a ritual practice where millions of pilgrims arrive in a certain area and we should indicate the nearest and lowest congestion path that leads to the ritual. In this paper, we address this problem during the Hajj season and propose a crowd management service based on the game theory model. We modeled the problem as a Mean-Field-Game (MFG) where the solution is a system composed of a Backward Hamilton-Jacobi-Bellman equation and a Forward Transport (Kolmogorov) equation. Simulation results show the efficiency of the MFG solution on the total time out of the pilgrims to reach the ritual.