The density-speed correlated mesoscopic model for the study of pedestrian flow

In this study, we developed a mesoscopic evacuation model driven by the density-speed correlations. In this model, the evacuation space is discretized into cells of multiple sizes, and the dynamic field method is extended into the mesoscopic scale. Psychological impatience was introduced to calculate the dynamic field. Instead of tracking individual movement, this approach directly computed the dynamic changes of crowd density in cells. To demonstrate the feasibility of this model, we firstly applied it to a typical scenario (i.e., a square room with a single exit) and conducted a parameter sensitivity study of time step and the impatience level of pedestrians. The simulation results indicated that the mesoscopic model is insensitive to the time step variations. Compared with the case without considering congestion degree, the dynamic method could shorten the evacuation time because the entire exit can be fully utilized. The model makes it possible to acquire key information (e.g., bottleneck areas) directly from the dynamic density map. We used commercial software Pathfinder to evaluate the model. Results showed that the mesoscopic model leads to a slower and smoother evacuation process. Moreover, we also conducted evacuation experiments to evaluate this model in a classroom under single exit and two exits condition. The comparisons revealed that the numerical results in low impatience level agree well with the experimental results in terms of evacuation time and the number of pedestrians choosing each exit. This study shows the potential of this model for predicting evacuation processes.