A Multiscale Examination of Two-Dimensional Agent-Based Pedestrian Flow Models with Slowdown Interactions



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Cellular automata models and agent-based models have been areas of significant research over the last few decades. These models have been of particular use in the study of traffic and pedestrian flow, and many models have been proposed to study such problems as highway traffic, evacuation time, and proper placement of exits for optimal evacuation strategy. Because these models are difficult and resource intensive to simulate, however, macroscopic models that examine only gross properties of such flows have been preferred.

Building on recent attempts to derive macroscopic models for traffic and pedestrian flow, such as [14], [21], and [29], the present work, after examining a simple pedestrian model, presents an agent-based model for two groups of pedestrians moving on a two-dimensional lattice with a slowdown interaction. From this microscopic model, we derive a mesoscopic system of differential equations and a macroscopic system of inviscid conservation laws for the model. This macroscopic model is then simulated and compared to a simulation of the microscopic model.

Noting some differences between the microscopic and macroscopic results, we then derive a second-order diffusive system of partial differential equations. Additionally, the hyperbolicity of the inviscid macroscopic model is analyzed in some general cases, as well as one of the simulated specific cases. Finally, we discuss potential directions of future research in the area.



Cellular automata, Agent based modeling, Pedestrian flow, Traffic flow, Multiscale modeling