Date: 15 Dec 2009

A Modification of the Social Force Model by Foresight

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Summary

The motion of pedestrian crowds (e.g. for simulation of an evacuation situation) can be modeled as a multi-body system of self driven particles with repulsive interaction. We use a few simple situations to determine the simplest allowed functional form of the force function. More complexity may be necessary to model more complex situations. There are many unknown parameters to such models, which have to be adjusted correctly to give proper predictions of evacuation times, local densities and forces on rails or obstacles.

The parameters of the social force model can be related to quantities that can be measured independently, like step length and frequency. The microscopic behavior is, however, only poorly reproduced in many situations, a person approaching a standing or slow obstacle will e.g. show oscillations in position, and the trajectories of two persons meeting in a corridor in opposite direction will be far from realistic and somewhat erratic.

One of the reasons why these models are not realistic is the assumption of instantaneous reaction on the momentary situation. Obviously, persons react with a small time lag, while on the other hand they will anticipate changing situations for at least a short time. Thus basing the repulsive interaction not on the momentary situation but on a (linear) extrapolation over a short time (e.g. 1 s) eliminates the oscillations at slowing down and smoothes the patterns of giving way to others to a more realistic behavior. The exact extrapolation time is of little importance, but a combination of long time with linear extrapolation may get unstable. One second anticipation seems reasonable, and while the actual anticipation in peoples mind will most likely not be based on linear extrapolation, the differences will be small.

A second reason is the additive combination of binary interactions. It is shown that combining only a few relevant interactions gives better model performance.