It is well-known that live multimedia streaming applications operate more efficiently when organized in peer-to-peer (P2P) topologies, since peer upload capacities are utilized to support other peers, and to alleviate the load and operating costs on the streaming servers. To date, there have been a number of existing experimental proposals with respect to how such peer-to-peer topologies are organized to support live streaming sessions. However, most of the existing proposals resort to intuition and heuristics when it comes to the design of such topology construction (i.e., neighbor selection) protocols. In this paper, we investigate the scaling laws of live P2P multimedia streaming, by quantitatively studying the asymptotic effects and tradeoffs among three key parameters in P2P streaming: server bandwidth cost, the maximum number of peers that can be supported, and the maximum number of streaming hops experienced by a peer. To further generalize our studies, we do not make restrictive assumptions in our theoretical analysis of such scaling laws: both peer upload capacities and peer lifetimes in a session may come from arbitrary distributions. With the theoretical insights we have developed, we propose Affinity, a simple and realistic heuristic to demonstrate the key benefits of our theoretical analysis in dynamic P2P networks, as compared to the topology construction algorithms in existing work.
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