On Optimal Weighted-Delay Scheduling in Input-Queued Switches

Abstract

Motivated by relatively few delay-optimal scheduling results, in comparison to results on throughput optimality, we investigate an input-queued switch scheduling problem in which the objective is to minimize a linear function of the queue-length vector. Theoretical properties of variants of the well-known MaxWeight scheduling algorithm are established within this context, which includes showing that these algorithms exhibit optimal heavy-traffic queue-length scaling. For the case of $2 \times 2$ input-queued switches, we derive an optimal scheduling policy and establish its theoretical properties, demonstrating fundamental differences with the variants of MaxWeight scheduling. Our theoretical results are expected to be of interest more broadly than input-queued switches. Computational experiments demonstrate and quantify the benefits of our optimal scheduling policy