Effect of Different Time Step Sizes on Pedestrian Evacuation Time under Emergencies Such as Fires Using an Extended Cellular Automata Model

Abstract

The cellular automata (CA) model has been a meaningful way to study pedestrian evacuation during emergencies, such as fires, for many years. Although the time step used in the CA model is one of the most essential elements, there is a lack of research on its impact on evacuation time. In this paper, we set different time step sizes in an extended cellular automaton model and discuss the effect of time step size on the overall evacuation time under different emergency types and levels. For a fixed step time mode, the larger the time step, the longer the evacuation time. In each time step size, the evacuation time gradually increases with the increase of emergency level, and there is a sharp increase when the time for pedestrians to move one step is exactly an integer multiple of the time step. When there is no friction between pedestrians, the evacuation time at each time step first decreases slightly with the increase of emergency level and then remains unchanged; the larger the time step, when the evacuation time remains unchanged, the lower the emergency level and the greater the evacuation time. For the variable time step model, when the friction between pedestrians approaches infinity, the total evacuation time does not change with the emergency level; when the friction between pedestrians is reduced, the total evacuation time slightly decreases with the increase of the emergency level. The less friction there is, the more significant the reduction. The results of previous actual experiments are also reflected in the simulation at a lower emergency level. The result shows that the time step size significantly impacts the evacuation simulation results of the CA model, and researchers should choose carefully to obtain more realistic simulation results.