Asymptotically optimal control for a multiclass queueing model in the moderate deviation heavy traffic regime

TL;DR

This paper develops an asymptotically optimal control policy for a multi-class queueing system in the moderate deviation heavy traffic regime, extending previous models and providing a stationary feedback policy for large time horizons.

Contribution

It introduces the first control policy for this regime that surpasses pathwise minimality limitations and remains stationary for large T.

Findings

Control policy is asymptotically optimal via a differential game approach.

The policy is stationary feedback for sufficiently large T.

First to address moderate deviation queueing control beyond pathwise minimality.

Abstract

A multi-class single-server queueing model with finite buffers, in which scheduling and admission of customers are subject to control, is studied in the moderate deviation heavy traffic regime. A risk-sensitive cost set over a finite time horizon $[0,T]$ is considered. The main result is the asymptotic optimality of a control policy derived via an underlying differential game. The result is the first to address a queueing control problem at the moderate deviation regime that goes beyond models having the so called pathwise minimality property. Moreover, despite the well known fact that an optimal control over a finite time interval is generically of a nonstationary feedback type, the proposed policy forms a stationary feedback, provided $T$ is sufficiently large.