Stochastic networks with multiple stable points
Abstract
This paper analyzes stochastic networks consisting of a set of finite capacity sites where different classes of individuals move according to some routing policy. The associated Markov jump processes are analyzed under a thermodynamic limit regime, that is, when the networks have some symmetry properties and when the number of nodes goes to infinity. An intriguing stability property is proved: under some conditions on the parameters, it is shown that, in the limit, several stable equilibrium points coexist for the empirical distribution. The key ingredient of the proof of this property is a dimension reduction achieved by the introduction of two energy functions and a convenient mapping of their local minima and saddle points. Networks with a unique equilibrium point are also presented.
Cite
@article{arxiv.math/0601296,
title = {Stochastic networks with multiple stable points},
author = {Nelson Antunes and Christine Fricker and Philippe Robert and Danielle Tibi},
journal= {arXiv preprint arXiv:math/0601296},
year = {2009}
}
Comments
Published in at http://dx.doi.org/10.1214/009117907000000105 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)