A Scaling Analysis of a Transient Stochastic Network (I)
  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. 
Mathieu Feuillet and Philippe Robert
math.PR