Optimal Weighted-Delay Scheduling in $2\times 2$ Input-Queued Switches

TL;DR

This paper develops an optimal scheduling policy for 2x2 input-queued switches to minimize discounted delay costs, providing theoretical insights and demonstrating significant performance improvements over existing policies.

Contribution

It introduces a novel optimal scheduling policy for input-queued switches focused on delay minimization, extending beyond throughput optimality results.

Findings

Optimal policy minimizes discounted delay costs effectively.

Computational results show significant delay improvements.

Policy outperforms MaxWeight variants in simulations.

Abstract

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.