Optimal Control in Fluid Models of nxn Input-Queued Switches under Linear Fluid-Flow Costs

We consider a fluid model of n x n input-queued switches with associated fluid-flow costs and derive an optimal scheduling control policy to an infinite horizon discounted control problem with a general linear objective function of fluid cost. Our optimal policy coincides with the cμ-rule in certain parameter domains, but more generally, takes the form of the solution to a flow maximization problem. Computational experiments demonstrate the benefits of our optimal scheduling policy over variants of max-weight scheduling and the cμ-rule.