On optimality gaps in the Halfin--Whitt regime

TL;DR

This paper improves the understanding of control optimality in large multi-class queueing systems by constructing controls with smaller, logarithmic optimality gaps in the Halfin--Whitt regime.

Contribution

It introduces a new sequence of asymptotically optimal controls with logarithmic optimality gaps, refining previous results that had gaps of smaller order.

Findings

Optimality gaps grow logarithmically with system size.

Refined Brownian control problems enable improved optimality analysis.

Constructed controls outperform previous asymptotic bounds.

Abstract

We consider optimal control of a multi-class queue in the Halfin--Whitt regime, and revisit the notion of asymptotic optimality and the associated optimality gaps. The existing results in the literature for such systems provide asymptotically optimal controls with optimality gaps of $o(\sqrt{n})$ where $n$ is the system size, for example, the number of servers. We construct a sequence of asymptotically optimal controls where the optimality gap grows logarithmically with the system size. Our analysis relies on a sequence of Brownian control problems, whose refined structure helps us achieve the improved optimality gaps.