## 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.