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

Emmanuelle Anceaume 1, 2 François Castella 3, 4 Romaric Ludinard 5 Bruno Sericola 5
1 CIDER
IRISA-D1 - SYSTÈMES LARGE ÉCHELLE
2 CIDRE - Confidentialité, Intégrité, Disponibilité et Répartition
CentraleSupélec, Inria Rennes – Bretagne Atlantique , IRISA-D1 - SYSTÈMES LARGE ÉCHELLE
3 IPSO - Invariant Preserving SOlvers
Inria Rennes – Bretagne Atlantique , IRMAR - Institut de Recherche Mathématique de Rennes
5 DIONYSOS - Dependability Interoperability and perfOrmance aNalYsiS Of networkS
IRISA-D2 - RÉSEAUX, TÉLÉCOMMUNICATION ET SERVICES, Inria Rennes – Bretagne Atlantique
Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00650081
Contributor : Emmanuelle Anceaume <>
Submitted on : Friday, December 9, 2011 - 2:32:02 PM
Last modification on : Wednesday, April 8, 2020 - 4:04:28 PM
Document(s) archivé(s) le : Saturday, March 10, 2012 - 2:25:34 AM

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Emmanuelle Anceaume, François Castella, Romaric Ludinard, Bruno Sericola. Markov Chains Competing for Transitions: Application to Large-Scale Distributed Systems. Methodology and Computing in Applied Probability, Springer Verlag, 2013, 15 (2), pp.305--332. ⟨10.1007/s11009-011-9239-6⟩. ⟨hal-00650081⟩

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