On a loss storage network with finite capacity

TL;DR

This paper models a large-scale storage network with finite capacity using fluid limits and Skorokhod problems, analyzing different operational regimes and establishing new martingales for the overloaded case.

Contribution

It introduces a novel fluid limit analysis for storage networks with finite capacity, employing Skorokhod problems and martingales to handle complex regimes.

Findings

Fluid limits characterized for different regimes

New martingales developed for overloaded regime

Averaging property established for the system

Abstract

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.