Simulation of Pedestrian Flow outside a Singleexit Room in Mean-field Approximation Model

Abstract

In this study, a framework model, based on lattice gas model and Mean-Field Approximation model, is proposed to analyze pedestrian evacuation uncertainty. The model is focused on the probability that each grid is occupied by a pedestrian, but not the specific pedestrians. By calculating the evolution of occupancy probabilities, more information about the simulation uncertainty can be gotten. The model is presented in terms of a series of nonlinear equations and complete probability formula. In each time step, the probabilities that pedestrians exist on each site, as well as the transition probabilities to the neighboring sites, are calculated and updated using random sequential update rule. The pedestrian flow going outside a single-exit room is investigated numerically. The cumulative distribution and probability density distribution of the total evacuation time can be obtained by a single simulation using the model. In this case, the uncertainty and reliability of the simulation results can be easily analyzed and improve the calculation efficiency. In addition, the time dependent of mean flow rate and the effect of the width of exit on the total evacuation time are studied. The framework model can be extended using other Cellular Automaton model with different rules to analyze their uncertainty.