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June 2014 A scaling analysis of a transient stochastic network
Mathieu Feuillet, Philippe Robert
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Adv. in Appl. Probab. 46(2): 516-535 (June 2014). DOI: 10.1239/aap/1401369705

Abstract

In this paper we use a simple transient Markov process with an absorbing point to investigate the qualitative behavior of a large-scale storage network of nonreliable file servers across which files can be duplicated. When the size of the system goes to ∞, we show that there is a critical value for the maximum number of files per server such that, below this quantity, most files have a maximum number of copies. Above this value, the network loses a significant number of files until some equilibrium is reached. When the network is stable, we show that, with convenient time scales, the evolution of the network towards the absorbing state can be described via a stochastic averaging principle.

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Mathieu Feuillet. Philippe Robert. "A scaling analysis of a transient stochastic network." Adv. in Appl. Probab. 46 (2) 516 - 535, June 2014. https://doi.org/10.1239/aap/1401369705

Information

Published: June 2014
First available in Project Euclid: 29 May 2014

zbMATH: 1303.60085
MathSciNet: MR3215544
Digital Object Identifier: 10.1239/aap/1401369705

Subjects:
Primary: 60F05, 60K25
Secondary: 68M14, 90B05

Rights: Copyright © 2014 Applied Probability Trust

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Vol.46 • No. 2 • June 2014
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