Modifications of the Helbing-Molnár-Farkas-Vicsek Social Force Model for Pedestrian Evolution

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Abstract
A model of crowd motion that considers each pedestrian as a Newtonian particle subject to both physical and social forces was reported by Helbing, Farkas, and Vicsek in 2000. Subsequent numerical simulations of this model, performed by its authors, showed that it exhibits realistic crowd behavior. In this article, the authors point out that numerical values of certain parameters in that model may produce counterintuitive results when applied to the motion of an isolated pedestrian or a small number of pedestrians. They have considered modifications of the original model, which allow them to use parameter values that, in the aforementioned sense, are more realistic. However, this is achieved by introducing more features and parameters into the original model. These features are described, and some results of the numerical simulations of the modified model are presented. Two major results of their study need to be mentioned. First, they developed an algorithm, based on an explicit numerical integration scheme, which prevents simulated pedestrians from overlapping with one another in physical space. Second, they demonstrated how the form of the social repulsive force between two pedestrians may be deduced from certain measured characteristics of pedestrian flows.

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