Advances in Applied Probability

A scaling analysis of a transient stochastic network

Mathieu Feuillet and Philippe Robert

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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.

Article information

Source
Adv. in Appl. Probab., Volume 46, Number 2 (2014), 516-535.

Dates
First available in Project Euclid: 29 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.aap/1401369705

Digital Object Identifier
doi:10.1239/aap/1401369705

Mathematical Reviews number (MathSciNet)
MR3215544

Zentralblatt MATH identifier
1303.60085

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22] 60F05: Central limit and other weak theorems
Secondary: 68M14: Distributed systems 90B05: Inventory, storage, reservoirs

Keywords
Distributed system with breakdown time scale transient Markov chain with absorbing state Skorokhod problem

Citation

Feuillet, Mathieu; Robert, Philippe. A scaling analysis of a transient stochastic network. Adv. in Appl. Probab. 46 (2014), no. 2, 516--535. doi:10.1239/aap/1401369705. https://projecteuclid.org/euclid.aap/1401369705


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