Heavy-traffic Analysis of the Generalized Switch under Multidimensional State Space Collapse

Abstract

The drift method was recently developed to study performance of queueing systems in heavy-traffic [1]. It has been used to analyze several queueing systems, including some where the Complete Resource Pooling (CRP) condition is not satisfied, like the input-queued switch [4]. In this paper we study the generalized switch operating under MaxWeight using the drift method. The generalized switch is a queueing system that was first introduced by [5], and can be thought of as extension of several single-hop queueing systems, such as the input-queued switch and ad hoc wireless networks. When the CRP condition is not satisfied, we prove that there is a multidimensional state space collapse to a cone and we compute bounds on a linear combination of the queue lengths that are tight in heavy-traffic. This work generalizes some of the results obtained by [1] and the results from [4], since the queueing systems studied there are particular cases of the generalized switch.