Section: New Results

Scaling Methods: Stochastic Models of peer-to-peer networks

Participants : Philippe Robert, Florian Simatos.

File-sharing networks are distributed systems used to disseminate files among a subset of Internet end nodes. A file is split into several pieces called chunks. The general simple principle is that once a node has retrieved a chunk, it in turn becomes a server for this chunk. In Leskela et al.  [22] , we have considered a stochastic model for chunk arrival times and download durations. We determined the maximal arrival rate that such a network can accommodate, i.e., the conditions under which the Markov process describing this network is ergodic. Technical estimates related to the survival of interacting branching processes are key ingredients to establish the stability of these systems. Several cases are considered: networks with one and two chunks where a complete classification is obtained and several cases of networks with n chunks.