Fundamental diagram of a one-dimensional cellular automaton model for pedestrian flow — the ASEP with shuffled update

Abstract

A one-dimensional cellular automaton model for pedestrian flow that describes the movement of pedestrians in a long narrow corridor is investigated. The model is equivalent to the asymmetric simple exclusion process (ASEP) with periodic boundary conditions and shuffled dynamics. In this type of update, the positions of the pedestrians are updated in a random order during one discrete time step. We derive expressions for the fundamental diagrams that are in very good agreement with simulation data. Finally we make a generalization to higher velocities and to two dimensions without lane-changing of the pedestrians.