Stability and capacity of peer-to-peer assisted video-on-demand applications

We propose a mathematical framework for the optimal design of a video on-demand (VoD) application under regime. Peers join the network following a Poissonian process, download progressively one or possibly many concurrent video contents, and abort the system when they wish. The system is supported by static servers managed by the operator, called super-peers, and the altruism of peers, that upload resources and might stay online even after completing downloading. Our goal is to minimize the expected download time perceived by end-users under regime. We propose a general fluid model, and show that it is stable, reaching its regime. Via the Little´s law, we find closed expressions for the expected waiting time under regime in terms of the popularity of different contents, file sharing efficiency and other network parameters. We state theoretically that this system outperforms traditional Content Delivery Networks (CDN). The operator can decide only the number of video replicas stored in each super-peer, a fact that has a direct impact on the mean waiting times. Hence, a combinatorial optimization problem is introduced, whose nature is similar to the multi-knapsack problem (i.e. the items are video contents, and the knapsacks are the super-peers storage). A greedy randomized resolution is here designed, and a comparison between traditional content distribution systems promotes the deployment of peer-to-peer video on-demand services. Finally, real-life scenarios are studied based on traces taken from YouTube. The results confirm that the peer-to-peer model can outperform five times the throughput of traditional CDN under flash-crowded scenarios.