A Scaling Analysis of a Transient Stochastic Network (I)

TL;DR

This paper analyzes a large-scale storage network using a transient Markov process, identifying critical thresholds for file retention and describing the network's evolution towards failure with stochastic averaging.

Contribution

It introduces a simple Markov model to study the behavior of large storage networks and characterizes the critical file duplication threshold affecting system stability.

Findings

Existence of a critical file number per server for system stability

Below the threshold, the network maintains most files in a quasi-stationary state

Above the threshold, the network rapidly loses files until equilibrium

Abstract

In this paper, a simple transient Markov process with an absorbing point is used to investigate the qualitative behavior of a large scale storage network of non reliable file servers where files can be duplicated. When the size of the system goes to infinity it is shown that there is a critical value for the maximum number of files per server such that below this quantity, the system stays away from the absorbing state, all files lost, in a quasi-stationary state where most files have a maximum number of copies. Above this value, the network looses a significant number of files until some equilibrium is reached. When the network is stable, it is shown that, with convenient time scales, the evolution of the network towards the absorbing state can be described via a stochastic averaging principle.