A Microscopic-To-Macroscopic Crowd Dynamic Model

This paper presents a model for a two-dimensional pedestrian movement flow. The model is derived by extending a one-dimensional vehicle traffic flow model that uses two coupled partial differential equations (PDEs) to govern vehicular motion. This model modifies the vehicular traffic model so that bidirectional flow is possible, and also the pedestrian movement can be controlled to model different behaviors. The model satisfies the conservation principle and is classified as a hyperbolic PDE system. Analysis of the model is drawn based on the theoretical aspects as well as the numerical simulation results achieved using the finite volume method. The original vehicular macroscopic model was derived by extending a corresponding microscopic model. This paper follows the same strategy and shows how microscopic pedestrian behavior can be used to derive the macroscopic behavior