The repulsive force in continous space models of pedestrian movement

Pedestrian movements can be modeled at different degrees of detail. While flux models (Predeshensky/Milinski 1971) and cellular automata models (Schreckenberg 2002) give answers to some important questions and are fast and easy to use, continuous space modeling has the potential of full flexibility in geometry and realistic description of individual movements in arbitrary fine resolution. While the acceleration forces in these models are known with good reliability, there is no agreement on the repulsive forces, not even on the functional form of these forces (Lakoba 2005, Molnar 1996, Parisi 2005, Yu 2005). We give some basic consideration to define the minimal complexity of the functional form of the repulsive forces together with some estimates of the values of parameters. From these considerations it becomes obvious that the repulsive forces have to depend not only on the relative position of persons, but also on the speeds and speed differences. The parameters of these forces will be situation dependant. They can in principle be derived from video observations of people moving, although the large scatter of data and the complexity involved makes for large uncertainties