An Optimal Topology for a Static P2P Live Streaming Network with Limited Resources

In this paper we propose a P2P live streaming topology, prove its optimality under common constraints, and match the analytical research with results from a running commercial network. We assume two types of nodes: viewers that consume the entire media, and amplifiers which are non-viewing nodes utilized for their upstream bandwidth. We analytically derive the minimum needed server upload capacity, for any topology, under the following assumptions: the amount of amplifiers and buffer time are limited, dynamics are low, and the total bandwidth required by the viewers exceeds the total upstream bandwidth of all peers. Then, we present a two-level topology and prove that it achieves the minimum possible server upload, up to a small fraction. Finally, the assumptions and derivation are supported by performing several experiments on RayV's real-world commercial system, with varying network parameters. Namely, we show our predictions are valid while varying the viewers to amplifiers ratio, the stream bit-rate, and the country of the peers. These results not only verify the analytical static predictions, but also evaluate the dynamic costs during the `flash crowd', the initial time when peers are joining the system.