PDE models for population and residual work applied to peer-to-peer networks

This paper studies partial differential equations that have recently been proposed as fluid models for queueing networks, where both populations and residual workloads must be accounted for. After reviewing these models in general, we focus on an application to peer-to-peer networks, where the dynamics must keep track of the download progress of a population of peers as content propagates among them through file sharing. Applying control-theoretic methods to this PDE yields a series of analytical results, in particular: local stability analysis of the equilibrium is proved through a small-gain argument on an appropriate feedback loop; variability around this equilibrium in the presence of random noise is analyzed through the frequency domain; and transient studies are performed to compute completion times.