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 (non-reversible) Markov jump processes are analyzed under a thermodynamic limit regime, i.e. when the networks have some symmetry properties and when the number of nodes goes to infinity. A metastability property is proved: under some conditions on the parameters, it is shown that, in the limit, several 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. Cases with a unique equilibrium point are also presented.
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https://hal.inria.fr/inria-00000997
Contributor : Philippe Robert <>
Submitted on : Wednesday, January 24, 2007 - 10:09:45 AM
Last modification on : Sunday, March 31, 2019 - 1:23:31 AM
Long-term archiving on : Thursday, September 23, 2010 - 4:41:55 PM

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Nelson Antunes, Christine Fricker, Philippe Robert, Danielle Tibi. Stochastic Networks with Multiple Stable Points. 2007. ⟨inria-00000997v3⟩

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