Mean Field Theory for Pedestrian Outflow through an Exit

An average pedestrian flow through an exit is one of the most important index in evaluating pedestrian dynamics. In order to study the flow in detail, the floor field model, which is a crowd model by using cellular automaton, is extended by taking into account a realistic behavior of pedestrians around the exit. The model is studied by both numerical simulations and cluster analysis to obtain a theoretical expression of an average pedestrian flow through the exit. It is found quantitatively that the effect of exit door width, a wall, and pedestrian's mood of competition or cooperation significantly influence the average flow. The results show that there is suitable width of the exit and position according to pedestrian's mood.