On a loss storage network with finite capacity
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916844083871744 |
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| author | Kharroubi, Ahmed El Masmari, Soukaina El |
| author_facet | Kharroubi, Ahmed El Masmari, Soukaina El |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_05237 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On a loss storage network with finite capacity Kharroubi, Ahmed El Masmari, Soukaina El Probability 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. |
| title | On a loss storage network with finite capacity |
| topic | Probability |
| url | https://arxiv.org/abs/2302.05237 |