369	RWTH Publication No: 230468        2013        IGPM369.pdf
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)