Queueing analysis of peer-to-peer swarms: Stationary distributions and their scaling limits

In this paper we analyze the dynamics of a P2P file exchange swarm from a queueing standpoint. In such systems, the service rate a peer receives depends on one mostly fixed component (servers or seeders), and another that scales with the number of peers present. We analyze a class of M / G Processor Sharing queues that describe populations and residual workloads in this situation, characterizing its stationary regime in the case of a fixed population of servers; the result behaves like a combination of M / G / 1 and M / G / ∞ queues. We apply scaling limits to this queue and identify two limiting regimes, depending on whether the server or peer contribution becomes dominant. For the latter, more important case we refine the fluid limit description of the download profile with a suitable functional Gaussian approximation. We also analyze the case of a slowly varying population of servers, extending the fixed case through a quasi-stationary analysis. For practical validation we offer comparisons with detailed packet simulations.