Bounds on delays and queue lengths in input-queued cell switches

Abstract

In this article, we develop a general methodology, mainly based upon Lyapunov functions, to derive bounds on average delays, and on averages and variances of queue lengths in complex systems of queues. We apply this methodology to cell-based switches and routers, considering first output-queued (OQ) architectures, in order to provide a simple example of our methodology, and then both input-queued (IQ), and combined input/output queued (CIOQ) architectures. These latter switching architectures require a scheduling algorithm to select at each slot a subset of input-buffered cells that can be transferred toward output ports. Although the stability properties (i.e., the limit throughput) of IQ and CIOQ cell-based switches were already studied for several classes of scheduling algorithms, very few analytical results concerning cell delays or queue lengths are available in the technical literature. We concentrate on Maximum Weight Matching (MWM) and Maximal Size Matching (mSM) scheduling algorithms; while the former was proved to maximize throughput, the latter allows simpler implementation. The derived bounds are shown to be rather tight when compared to simulation results.