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
IRISA-D1 - SYSTÈMES LARGE ÉCHELLE, Inria Rennes – Bretagne Atlantique , CentraleSupélec
3 IPSO - Invariant Preserving SOlvers
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique
5 DIONYSOS - Dependability Interoperability and perfOrmance aNalYsiS Of networkS
Inria Rennes – Bretagne Atlantique , IRISA-D2 - RÉSEAUX, TÉLÉCOMMUNICATION ET SERVICES
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.
Type de document :
Article dans une revue
Methodology and Computing in Applied Probability, Springer Verlag, 2013, 15 (2), pp.305--332. 〈10.1007/s11009-011-9239-6〉
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00650081
Contributeur : Emmanuelle Anceaume <>
Soumis le : vendredi 9 décembre 2011 - 14:32:02
Dernière modification le : jeudi 7 février 2019 - 17:34:24
Document(s) archivé(s) le : samedi 10 mars 2012 - 02:25:34

Fichier

RR-1953_1_.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Citation

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〉

Partager

Métriques

Consultations de la notice

945

Téléchargements de fichiers

231