Stochasticity and fractality of Pedestrian flows

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Abstract
In an increasingly urbanized world, understanding pedestrian dynamics during evacuations is critical for ensuring safety and efficiency, for cases like evacuations or venue exiting. This study explores the stochasticity and fractality of pedestrian flows by implementing a simulation strategy that combines both agent-based modeling and cellular automata. We study five distinct movement strategies were the agent will try to follow towards the exit, and each model incorporates three stress levels based on the Yerkes-Dodson Law, which states that optimal performance occurs at a moderate level of arousal. that optimal performance occurs at a moderate level of arousal. Our simulations reveal that stress significantly influences agent behavior, with optimal stress levels enhancing evacuation efficiency while excessive stress leads to erratic movement. Notably, models employing geodesic paths demonstrate more structured movement and fewer collisions. The fractal analysis of trajectories highlights sub-diffusive behavior in constrained environments, while agents with greater spatial flexibility exhibit broader, more variable paths. These findings accentuate the importance of psychological factors and the differences produced by the diversity of movement strategies, in designing safer evacuation protocols. We hope that this type of studies would eventually permit to determine the effective pedestrian strategies, for example through the observed path of individuals.