An optimal scheduling policy for the 2 2 input-queued switch with symmetric arrival rates

We investigate a cannonical input-queued switch scheduling problem in which the objective is to minimize the infinite horizon discounted queue length under symmetric arrivals, for which we derive an optimal scheduling policy and establish its theoretical properties with respect to delay. We then compare via simulation these theoretical properties of our optimal policy with those of the well-known MaxWeight scheduling algorithm in order to gain insights on the delay optimality of the MaxWeight scheduling policy.