  The behavior of pedestrians shows certain regularities, which can be
described by quantitative (partly stochastic) models. The models are based on
the behavior of individual pedestrians, which depends on the pedestrian
intentions and on the aspects of movement. The pedestrian intentions concerning
a sequence of destinations are influenced by the demand for certain kinds of
commodities, by the location of stores selling these, and by the expenditures
to get the required commodities. The actual pedestrian movement starts and ends
at special city entry points like parking lots. It is guided by the pedestrian
intentions, but is subject to deceleration processes and avoidance maneuvers
due to obstacles. As a consequence, the pedestrians have to speed up to reach
the next destination well-timed. In addition, the pedestrian behavior is
influenced by unexpected attractions (e.g. street artists). The model for the
behavior of individual pedestrians is an ideal starting point for computer
simulations of pedestrian crowds. Such simulations take into account the
limited capacity of pedestrian ways and places, and allow to determine an
optimal design of pedestrian areas and an optimal arrangement of store
locations. Therefore, they can be applied for town- and traffic-planning. The
model for the behavior of individual pedestrians also allows the derivation of
mathematical equations for pedestrian crowds and for pedestrian groups.
Pedestrian crowds can be described by a stochastic formulation, by a gaskinetic
formulation or by a fluiddynamic formulation. The gaskinetic formulation
(mezoscopic level) can be derived from the stochastic formulation (microscopic
level), and the fluiddynamic formulation (macroscopic level) from the
gaskinetic formulation.
