Generalized Collision-free Velocity Model for Pedestrian Dynamics

The collision-free velocity model is a microscopic pedestrian model, which despite its simplicity, reproduces fairly well several self-organization phenomena in pedestrian dynamics The model is composed of two components: a direction sub-model which combines individual desired direction and neighbor’s influence to imitate the process of navigating in a two-dimensional space, and an intrinsically collision-free speed sub-model which controls the speed of the agents based on the distance to their surroundings.

Although the model performs well is many scenarios, its minimal character can be improved by further extensions Firstly, the model definition is shape specific Circles are used to express the projection of a pedestrian’s body on the two-dimensional plane, however many references and researches indicate that dynamical ellipses can represent a pedestrian’s shape more accurately Secondly, the change of the direction is per definition performed instantaneously in every time step, which leads to an unnatural “shaking” of pedestrians during simulations.

This paper generalizes the collision-free velocity model by extending the distance calculations to velocity-based ellipses Besides, we introduce an enhancement to the direction sub-module of the model, which smooths the direction changes of pedestrians in the simulation; a shortcoming that was not visible in the original model due to the symmetry of the circular shapes Furthermore, we study the effects of the pedestrian’s shape on the simulation’s result.

We validate our enhancements by comparing the simulation results with the flow through a bottleneck for different widths of the exit The model is implemented within the open source software JuPedSim.