  Motivated by few delay-optimal scheduling results, in comparison to results
on throughput optimality, we investigate a canonical input-queued switch
scheduling problem in which the objective is to minimize the discounted delay
cost over an infinite time horizon. We derive an optimal scheduling policy and
establish corresponding theoretical properties, which are expected to be of
interest more broadly than input-queued switches. Computational experiments
demonstrate and quantify the benefits of our optimal scheduling policy over
alternative policies such as variants of MaxWeight scheduling, well-known to be
throughput optimal and more recently shown to be delay optimal in the
heavy-traffic regime limit.
