A Class of Non-Local Models for Pedestrian Traffic

We present a new class of macroscopic models for pedestrian flows. Each individual is
assumed to move towards a fixed target, deviating from the best path according to the
instantaneous crowd distribution. The resulting equation is a conservation law with a
nonlocal flux. Each equation in this class generates a Lipschitz semigroup of solutions
and is stable with respect to the functions and parameters defining it. Moreover, key
qualitative properties such as the boundedness of the crowd density are proved. Specific
models are presented and their qualitative properties are shown through numerical inte-
grations. In particular, the present model accounts for the possibility of reducing the
exit time from a room by carefully positioning obstacles that direct the crowd flow.