A stochastic epidemiological model and a deterministic limit for BitTorrent-like peer-to-peer file-sharing networks

In this paper, we propose a stochastic model for a file-sharing peer-to-peer network which resembles the popular BitTorrent system: large files are split into chunks and a peer can download or swap from another peer only one chunk at a time. We prove that the fluid limits of a scaled Markov model of this system are of the coagulation form, special cases of which are well-known epidemiological (SIR) models. In addition, Lyapunov stability and settling-time results are explored. We derive conditions under which the BitTorrent incentives under consideration result in shorter mean file-acquisition times for peers compared to client-server (single chunk) systems. Finally, a diffusion approximation is given and some open questions are discussed.