Mean-field theory for pedestrian outflow through an exit.

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