Peer-assisted file distribution: The minimum distribution time

With the emergence of BitTorrent, Swarm-cast, and CDNs, peer-assisted file distribution has become a prominent Internet application, both in terms of user popularity and traffic volumes. We consider the following fundamental problem for peer-assisted file distribution. There are seed nodes, each of which has a copy of the file, and leecher nodes, each of which wants a copy the file. The goal is to distribute the file to all the leechers - with the assistance of the upload capacity of the leechers - in order to minimize the time to get the file to all the leechers (the distribution time). We obtain explicit expressions for the minimum distribution time of a general heterogeneous peer-assisted file distribution system. Derived with fluid-flow arguments, the expressions are in terms of the file size, the seeds' upload rates and the leechers' upload and download rates. We demonstrate the utility of the result by comparing the optimal distribution time with the measured distribution time when BitTorrent is used to distribute a file from a seed to ten leechers.