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Modeling chunk availability in P2P swarming systems

Peer-to-peer swarming systems a la BitTorrent are usually deployed for the dissemination of popular content. Popular content naturally gets highly replicated in the network and capacity scales with demand ensuring high performance for peers requesting popular content. Nevertheless, the behavior of swarming systems in the face of unpopular content and small populations of users also deserves attention. First, it is important to understand what is the popularity threshold above which the use of swarming systems is most beneficial for a publisher. The second reason is economic. With the monetization of BitTorrent clients such as Vuze (previously known as Azureus), and surveys showing a huge demand for legal P2P content [2], publishers need to identify how to best allocate their resources across multiple swarms. For that purpose, it is imperative to identify whether a swarm is self sustaining or not. This is particularly evident in a market where enterprises that can make “everything available, with small costs”, thrive [1]. Third, models focusing on small user populations may provide insight on when and if coding, bundling [6] or other techniques can help to make unpopular swarms last longer without the support of a publisher. For large populations, Massoulie and Vojnovic [5] used a coupon collector model to show that rarest-first guarantees almost uniform distribution of chunks across the population leading to a robust system. Fan et al. [4] considered the large population regime, and used fluid approximations and stochastic differential equations to model the dynamics of a population of users. Qiu and Srikant [8], also considered large populations and concluded that the efficiency of the system is always high. For small populations we have Markov Chain (MC) models [10] that provide insights on the performance of the system but that do not consider the problem of chunk availability. In comparison, the goal of this paper is to analyze, especially for a small population of users, how chunk availability varies as a function of different system parameters such as arrival rate of peers and download capacity.