On a loss storage network with finite capacity

Our goal in this paper is to investigate the fluid picture associated with an open large scale storage network of non-reliable file servers with finite capacity. In this storage system, new files can be added and a file with only one copy can be lost or duplicated. The Skorokhod problem with oblique...

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Bibliographic Details
Main Authors Kharroubi, Ahmed El, Masmari, Soukaina El
Format Journal Article
LanguageEnglish
Published 10.02.2023
Subjects
Mathematics - Probability
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Summary:Our goal in this paper is to investigate the fluid picture associated with an open large scale storage network of non-reliable file servers with finite capacity. In this storage system, new files can be added and a file with only one copy can be lost or duplicated. The Skorokhod problem with oblique reflection in a bounded convex domain is used to identify the fluid limits. Such analysis involves the study of three different regimes, the under-loaded, the critical and the overloaded regime. The overloaded regime is of particular importance. To identify the fluid limits, new martingales are obtained and an averaging property is established.
DOI:10.48550/arxiv.2302.05237