Eikonal equation based cellular automaton for a pedestrian evacuation problem

We propose a two-dimensional cellular automaton (CA) for the simulation of pedestrian evacuation based on the solution of the Eikonal equation. This approach was inspired by the role of the Eikonal equation in the fluid dynamics model of pedestrian flow presented in [1]. The solution φ of the Eikonal equation represents the shortest time needed for a pedestrian to reach the exit. In the cellular automaton for each pedestrian, the transition probabilities for a move to an unoccupied neighbor cell are determined by the value of the potential φ, which is the novelty of the paper. The shortest time to reach the exit is so taken into account for a pedestrian decision. The fast sweeping method from [2] is used for the numerical solution of the Eikonal equation. As an application we show simulations of the evacuation of a room with an obstacle. The comparison with the fluid dynamics pedestrian model is presented.