Performance Bounds in Coupled Processor Systems

Abstract

We consider queuing systems with coupled processors, where the service rate at each queue depends on the set of active queues in the system. The coupled-processors model arises naturally in the study of systems where a resource is shared by several classes of customers. For instance, its application has been suggested to model the complex interdependence that is present in wireless scenarios. In general, the queue lengths of such systems, that we call Coupled Processor Systems (CPSs), are modelled through complex Markov Chains whose steady state distributions are known only for two-queue systems. In this paper we propose a new approach for the study of the performance of the CPSs, based on worst case analysis. Our method exploits Network Calculus results over a set of networks whose stability implies the stability of the CPS, and allows to derive sufficient conditions for the stability of a CPS, as well as to compute bounds to queue size and packet delay. We also apply the CPS model to an ad-hoc IEEE 802:11 scenario, where we present a method to derive practical results, and where we show numerically that considering the characteristics of the incoming flows at the nodes improves substantially the resource allocation in the system.