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

  • Emmanuelle Anceaume
  • François Castella
  • Romaric Ludinard
  • Bruno Sericola
Article

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.

Keywords

Asymptotic analysis Competing Markov chains Large-scale distributed systems Markov chains 

AMS 2000 Subject Classifications

60J10 65C40 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Emmanuelle Anceaume
    • 1
  • François Castella
    • 2
  • Romaric Ludinard
    • 3
  • Bruno Sericola
    • 3
  1. 1.IRISA - CNRSRennes cedexFrance
  2. 2.Université de Rennes 1Rennes cedexFrance
  3. 3.INRIA Rennes - Bretagne AtlantiqueRennes cedexFrance

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