An upload bandwidth threshold for peer-to-peer Video-on-Demand scalability

We consider the fully distributed video-on-demand problem, where n nodes called boxes store a large set of videos and collaborate to serve simultaneously n videos or less between them. It is said to be scalable when Omega (n) videos can be distributively stored under the condition that any sequence of demands for these videos can always be satisfied. Our main result consists in establishing a threshold on the average upload bandwidth of a box, above which the system becomes scalable. We are thus interested in the normalized upload capacity u = upload bandwidth/video bitrate of a box. The number m of distinct videos stored in the system is called its catalog size. We show an upload capacity threshold of 1 for scalability in a homogeneous system, where all boxes have the same upload capacity. More precisely, a system with u < 1 has constant catalog size m = O (1) (every box must store some data of every video). On the other hand, for u > 1, an homogeneous system where all boxes have same upload capacity at least u admits a static allocation of m = Omega (n) videos into the boxes such that any adversarial sequence of video demands can be satisfied. Moreover, such an allocation can be obtained randomly with high probability. This result is generalized to a system of boxes that have heterogeneous upload capacities under some balancing conditions.