Achievable catalog size in peer-to-peer video-on-demand systems

We analyze a system where n set-top boxes with same upload and storage capacities collaborate to serve r videos simultaneously (a typical value is r = n). We give upper and lower bounds on the catalog size of the system, i.e. the maximal number of distinct videos that can be stored in such a system so that any demand of at most r videos can be served. Besides r/n, the catalog size is constrained by the storage capacity, the upload capacity, and the maximum number of simultaneous connections a box can open. We show that the achievable catalog size drastically increases when the upload capacity of the boxes becomes strictly greater than the playback rate of videos.