  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. The parameters 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.
This is inpart due to 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 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. A second problem
is the additive combination of binary interactions. It is shown that combining
only a few relevant interactions gives better model performance.
