The Asymptotic Behavior of Minimum Buffer Size Requirements in Large P2P Streaming Networks

The growth of real-time content streaming over the Internet has resulted in the use of peer-to-peer (P2P) approaches for scalable content delivery. In such P2P streaming systems, each peer maintains a playout buffer of content chunks which it attempts to fill by contacting other peers in the network. The objective is to ensure that the chunk to be played out is available with high probability while keeping the buffer size small. A small playout buffer means that the playout delay is small. Thus, the objective is to study the tradeoff between two measures of QoS, chunk playout rate and delay. A policy is a rule that suggests which chunks should be requested by the peer from other peers. We consider consider a number of recently suggested policies consistent with buffer minimization for a given target of skip-free playout. We first study a rarest-first policy that attempts to obtain chunks farthest from playout, and a greedy policy that attempts to obtain chunks nearest to playout. We show that they both have similar buffer scalings (as a function of the number of peers of target probability of skip-free probability). We then study a hybrid policy which achieves order sense improvements over both policies and can achieve order optimal performance. We validate our results using simulations.