A Scaling Analysis of a Transient Stochastic Network

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.