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Markov Chains Competing for Transitions: Application to Large-Scale Distributed Systems

Emmanuelle Anceaume 1, François Castella 2, 3, Romaric Ludinard 1, Bruno Sericola 4

(21/05/2010)

We consider the behavior of a stochastic system composed of several identically distributed, but non independent, discrete-time absorbing Markov chains competing at each instant for a transition. The competition consists in determining at each instant, using a given probability distribution, the only Markov chain allowed to make a transition. We analyze the first time at which one of the Markov chains reaches its absorbing state. We obtain its distribution and its expectation and we propose an algorithm to compute these quantities. We also exhibit the asymptotic behavior of the system when the number of Markov chains goes to infinity. Actually, this problem comes from the analysis of large-scale distributed systems and we show how our results apply to this domain.

1 :	ADEPT (INRIA - IRISA)
	CNRS : UMR6074 – INRIA – Université de Rennes 1
2 :	Institut de Recherche Mathématique de Rennes (IRMAR)
	CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne
3 :	IPSO (INRIA - IRMAR)
	CNRS : UMR6074 – INRIA – Université de Rennes 1
4 :	DIONYSOS (INRIA - IRISA)
	INRIA – Université de Rennes 1 – CNRS : UMR6074

Domaine

:

Informatique/Modélisation et simulation Informatique/Performance et fiabilité Informatique/Recherche opérationnelle

Mots-clés : Markov Chains – Competing Markov Chains – Asymptotic Analysis – Large-Scale Distributed Systems

inria-00485667, version 1

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Contributeur : Bruno Sericola <>

Soumis le : Mardi 25 Mai 2010, 16:44:51

Dernière modification le : Mercredi 26 Janvier 2011, 10:20:06