Bounds on Average Delays and Queue Size Averages and Variances in Input-Queued Cell-Based Switches

Ab.rcracf-In this paper we develop a general methodology, mainly based upon Lyapunov functions, to derive bounds on average delays, and on queue size averages and variances of complexsystemsof queues.We then apply this methodologyto input-buffered, cell-basedswitch and router architectures. These architectures require a scheduling algorithm to select at each slot a subset of input-buffered cells wbicb can be transferred towards output ports. Although the stabitity properties (i.e., the limit throughput) of input-buffered, cell-based switches was already studied for several classes of scheduling algorithms, no analytical results concerning cell delays or queue sizes are yet available in the technical literature. We concentrate on purely input-buffered switches that adopt a Maximum Weight Matching scheduling algorithm, that was proved to be the scheduling algorithm providing the best performance. The derived bounds proved to be rather tight, when compared to simulation results.