A Stable Random-Contact Algorithm for Peer-to-Peer File Sharing

We consider a BitTorrent type file sharing algorithm with randomized chunk copying process. The system functions in completely distributed way without any `Tracker', just relying on randomness. In such case the stability becomes an issue. It may happen, say, that some chunk becomes rare. This problem can persist and cause accumulation of peers in the system, resulting in unstable system. The considered algorithms result in processes similar to urn-processes. The rare chunk phenomenon corresponds to Polya-urn type process, where common chunks are favored. However, some urn-processes like the Friedman-urn can provide good balance by favoring rare chunks in copying process. Recently, we showed that an algorithm based on Friedman-urn is efficient in two chunk case. We generalize this algorithm for the more realistic case of many chunks. It shows good performance in terms of balance of chunks in an open system with constant flow of incoming peers. Further, the system is able to cope with instances like `flash crowd', with large burst of incoming peers. The open system can also quickly reach equilibrium after an initial imbalance, when the system starts from a state with one rare chunk. We constructed a simplified model, assuming a good balance of chunks, and get results surprisingly close to simulations for Friedman-urn based random process.