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Fluid limits of a loss storage network

Abstract

Our goal in this paper is to investigate the fluid picture associated with an open large-scale storage system with infinite size. We consider a large-scale storage network of non-reliable file servers in which new files can be added and a file with only one copy can be lost or duplicated. The Skorokhod problem with oblique reflection in an orthant is used to identify the fluid limits of this system which describe its qualitative behaviour and give an idea about a good choice of parameters that guarantees reliability. The fluctuations around the fluid limits are investigated.

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El Kharroubi, A., El Masmari, S. Fluid limits of a loss storage network. Queueing Syst 101, 137–164 (2022). https://doi.org/10.1007/s11134-022-09738-x

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  • DOI: https://doi.org/10.1007/s11134-022-09738-x

Keywords

  • Continuous time Markov process
  • Skorokhod problem
  • Loss network
  • Functional law of large number
  • Functional central limit theorem
  • Ornstein–Uhlenbeck process

Mathematics Subject Classification

  • 60J25
  • 60F05