Implications of peer selection strategies by publishers on the performance of P2P swarming systems

Abstract

In peer-to-peer swarming systems, as peers join a swarm to download a content they bring resources such as bandwidth and memory to the system. That way, the capacity of the system increases with the arrival rate of peers. Furthermore, if publishers are intermittent, increasing the arrival rate of peers can increase content availability [7]. In the presence of stable publishers that have enough service capacity for peers to smoothly complete their download [6], increasing the arrival rate of peers decreases the probability that a piece will be unavailable among peers. However, if the capacity of the stable publisher, U pieces/second, is not large enough, it has been shown that the system might be unstable [3, 5, 14]. Hajek and Zhou [3, 14], following up work by Mathieu and Reynier [5], have shown that if the arrival rate of peers, λ, is greater than U , the number of peers increases unboundedly with time. It has also been shown that simple strategies can alleviate, and in some cases resolve, the instability problem. For instance, if peers reside in the system after completing their downloads, on average, the same time that they take to download a piece, then the system is always stable [14]. Nevertheless, as peers have no incentive to stay in the system after completing their downloads, it is important to investigate whether other simple strategies that do not depend on providing incentives for peers to remain online after the download completion can improve system performance and stability. In a peer to peer system, each peer has to make two decisions before transmitting each piece: 1) which piece to transmit and 2) to whom to transmit it. Although the former question has received some attention in previous works (for instance, it has been shown that rarest-first piece selection and random useful piece selection yield the same stability region [3]), to the best of our knowledge the implications of the peer selection strategy have not been discussed yet (previous works assumed random peer selection [3, 9, 14], a notable exception being [5] – see related work section). Let the throughput be the rate at which peers leave the system. The goal of this paper is to evaluate the impact of different peer selection strategies on the throughput (hence, stability) of the system. We pose the following questions: a) how to increase the throughput of the system by letting peers strategically select their neighbors? b) how does throughput scale with the number of peers in a closed peer-to-peer swarming system? We provide the following answers to the above questions. First, we derive an upper bound on the throughput when the stable publisher adopts the most deprived peer selection [1] and rarest-first piece selection, while peers adopt random peer selection and random useful piece selection. The bound is significantly larger than the maximum attainable throughput when both peers and publishers adopt random peer and random useful piece selection. Then, we consider a closed system and we use a simple Markov chain model to study how the throughput of the system scales with the number of peers.