Analysis of P2P file transferring system by stochastic queue models

Distributed protocols for peer-to-peer (P2P) file sharing over the Internet have been highly successful in recent years. The idea is that files to be shared are broken into pieces. As new peers enter the system, they strive to obtain a complete collection from other peers and from a seed. In this thesis we focus on studying a P2P file transferring network by a stochastic queue model. After presenting a general stochastic model, we discuss three cases obtained by specializing the general model using three different choices of parameter values and selection strategies. In the first case, we deal with a simple model under a fixed peer selection strategy, and identify a problem that might occur when the rate of distribution of pieces is not large enough. The similar problem exists when we consider the second and the third cases where the uniform random peer selection strategy is applied. The problem is that, when the distribution of pieces from either the seed or external arrivals is not large enough, the system will work poorly. There may be symmetry breaking --- with one piece becoming very rare --- that makes the system unstable