File-sharing networks are distributed systems used to disseminate files among nodes of a communication network. The general simple principle of these systems is that once a node has retrieved a file, it may become a server for this file. In this paper, the capacity of these networks is analyzed with a stochastic model when there is a constant flow of incoming requests for a given file. It is shown that the problem can be solved by analyzing the asymptotic behavior of a class of interacting branching processes. Several results of independent interest concerning these branching processes are derived and then used to study the file-sharing systems.
Leskelä, L., Robert, P., & Simatos, F. (2010). Interacting branching processes and linear file-sharing networks. Advances in Applied Probability, 42(3), 834-854. https://doi.org/10.1239/aap/1282924065