Title: 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.