Poly-Symmetry in Processor-Sharing Networks.

We consider a network of processor-sharing queues with state-dependent service rates. These are allocated according to balanced fairness within a polymatroid capacity set. Balanced fairness is known to be both insensitive and Pareto-efficient in such networks, which ensures that the performance metrics, when computable, will provide robust insights into the real performance of the system considered. We first show that these performance metrics can be evaluated with a complexity that is polynomial in the system size when we allow for some controlled asymmetry, in the sense that the network contains a fixed number of parts wherein all queues are `exchangeableu0027. This in turn allows us to derive stochastic bounds for a larger class of networks which satisfy less restrictive symmetry assumptions. These results are applied to practical examples of tree data networks and computer clusters.