Section: New Results

Analysis of a large number of Markov chains competing for transitions

Participant : François Castella.

This text [41] generalizes the previous one [12] in the following sense.

In the situation on the previous article, we analyze the first time at which one of the Markov chains reaches its absorbing state. When the number of Markov chains goes to infinity, we analyze the asymptotic behavior of the system for an arbitrary probability mass function governing the competition. We give conditions for the existence of the asymptotic distribution and we show how these results apply to cluster-based distributed storage when the competition is handled using a geometric distribution.