|Preprint-No.:||< 369 >||Published in:||July 2013||PDF-File:||IGPM369_k.pdf|
|Title:||Flow on Sweeping Networks|
|Authors:||Pierre Degond, Michael Herty, Jian–Guo Liu|
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|
|Publication:||Multiscale modeling & simulation |
12(2), 538-565 (2014)