Scaling Analysis of a Transient Stochastic Network (TREC seminar)

Speaker : Mathieu Feuillet
Date: 07/06/2012
Time: 2:00 pm - 3:00 pm
Location: LINCS Meeting Room 40


In this talk, we consider a simple transient Markov process with an absorbing point 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 we show 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, we prove that, with  convenient time scales, the evolution of the network towards the absorbing state can be described via a stochastic averaging principle. Some extensions of this model will be discussed.