Poly-Symmetry in Processor-Sharing Systems

TL;DR

This paper analyzes processor-sharing queue systems with state-dependent rates, demonstrating polynomial complexity in performance evaluation for systems with certain symmetries, and deriving bounds for less symmetric systems, with applications to network and computing clusters.

Contribution

It introduces a polynomial-time method for evaluating performance metrics in symmetric processor-sharing systems and extends bounds to less symmetric systems, enhancing practical applicability.

Findings

Performance metrics are polynomial-time computable under certain symmetry conditions.

Stochastic bounds are derived for systems with relaxed symmetry assumptions.

Applications include network backhaul and computer clusters.

Abstract

We consider a system 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 systems, 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 if the system is partitioned into a finite number of parts, so that queues are exchangeable within each part and asymmetric across different parts. This in turn allows us to derive stochastic bounds for a larger class of systems which satisfy less restrictive symmetry assumptions. These results are applied to practical examples of tree data networks, such as backhaul networks of Internet service providers, and computer clusters.