Gas-Kinetic Modeling and Simulation of Pedestrian Flows

Abstract

Insight into pedestrian flow operations is important in both planning and geometric design of infrastructure facilities such as railway stations as well as in the management of pedestrian flows in such facilities. Lack of empirical knowledge regarding the characteristics of pedestrian flows under varying circumstances and designs motivates using a model-based approach. In this study, a new pedestrian flow model based on the gaskinetic modeling paradigm is established. The mesoscopic equations describe the dynamics of so-called pedestrian phase-space density, which can be considered as a two-dimensional generalization of the phase-space density used in gas-kinetic vehicular traffic flow. Convection, acceleration, and noncontinuum transition terms govern the dynamics. The latter terms reflect the dynamic influence of pedestrians decelerating and the changing angle of movement due to pedestrians interacting. Numerical solutions of the resulting gas-kinetic equations are established by using a novel particle discretization approach. Essentially, this approach upgrades the mesoscopic equations to a microscopic pedestrian flow simulation model. Using the particle discretization approach, the model’s behavior is tested for different test-case scenarios. The model is shown to produce plausible speed-density functions from which walking speeds and travel times can be derived for a variety of conditions.