369 IGPM369.pdf        July 2013
TITLE Flow on Sweeping Networks
AUTHORS Pierre Degond, Michael Herty, Jian-Guo Liu
ABSTRACT We introduce a cellular automaton model coupled with a transport equation for flows on graphs. The direction of the flow is described by a switching process where the switching probability dynamically changes according to the value of the transported quantity in the neighboring cells. A motivation is pedestrian dynamics in a small corridor where the propagation of people in a part of the corridor can be either left or rightgoing. Under the assumptions of propagation of chaos and mean- field limit, we derive a master equation and the corresponding meanfield kinetic and macroscopic models. Steady–states are computed and analyzed analytically and exhibit the possibility of multiple meta-stable states and hysteresis.
KEYWORDS Master equation, cellular automata, pedestrian dynamics, networks
DOI 10.1137/130927061
PUBLICATION Multiscale modeling & simulation
12(2), 538-565 (2014)