Content dynamics in P2P networks from queueing and fluid perspectives

In this paper we analyze the dynamics of P2P file exchange networks, considering both queueing and fluid models. In such systems, the service rate 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. It is shown that, under a law of large numbers scaling, the system behaves as a M/G/1 or a shifted M/G/∞ queue, depending on whether the server or peer contribution becomes dominant. We also consider fluid models for populations and residual workloads in the form of a partial differential equation, and establish connections with the queueing approach. This method provides broadly applicable results on stability, variability and transient performance, which we validate against packet simulations, showing improvement with respect to earlier models.