Optimality of the generalized c\mu- rule in the moderate deviation regime

TL;DR

This paper demonstrates that the generalized cμ-rule remains asymptotically optimal for multiclass queueing systems with risk-sensitive costs in heavy traffic at the moderate deviation scale, extending its applicability beyond diffusion approximations.

Contribution

It proves the asymptotic optimality of the generalized cμ-rule in the moderate deviation regime for risk-sensitive multiclass queueing systems, a novel extension of existing heavy traffic results.

Findings

Generalized cμ-rule is asymptotically optimal in the moderate deviation regime.

The study extends the rule's optimality beyond diffusion scale approximations.

Results apply to systems with convex queue length penalties.

Abstract

This paper studies a multiclass queueing system with an associated risk- sensitive cost observed in heavy traffic at the moderate deviation scale, accounting for convex queue length penalties. The main result is the asymptotic optimality of a dynamic index policy known from the diffusion scale heavy traffic literature as the generalized c\mu- rule.