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

Emmanuelle Anceaume (), François Castella (), Romaric Ludinard () and Bruno Sericola ()
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Emmanuelle Anceaume: IRISA - CNRS
François Castella: Université de Rennes 1
Romaric Ludinard: INRIA Rennes - Bretagne Atlantique
Bruno Sericola: INRIA Rennes - Bretagne Atlantique

Methodology and Computing in Applied Probability, 2013, vol. 15, issue 2, 305-332

Abstract: 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; 60J10; 65C40 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s11009-011-9239-6

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