Modeling file-sharing with BitTorrent-like incentives

We propose a new model for file-sharing peer-to-peer (P2P) networks that mimics the incentives provided by the popular BitTorrent system. In it, larger files are split into chunks and a peer can download or swap only one chunk at a time. We propose a Markov chain model in continuous time that resembles a stochastic epidemic/coagulation model. We prove that the Markov chain is approximated by a differential equation which, by itself, can give some rough information about the performance of the system. Finally, using this model, we explore the performance of BitTorrent-like incentives for an open system with peer departures and arrivals and a single file (torrent) with two chunks.