Control of the multiclass $G/G/1$ queue in the moderate deviation regime

TL;DR

This paper investigates optimal control strategies for a multi-class G/G/1 queue in a moderate deviation heavy traffic regime, linking differential game solutions to queue management.

Contribution

It introduces a novel differential game framework for controlling multi-class queues under moderate deviations, bridging heavy traffic diffusion and large deviation analyses.

Findings

Explicit solution to the differential game governing the control problem

Characterization of the queue control in the moderate deviation regime

Connection between large deviation and diffusion scale control analysis

Abstract

A multi-class single-server system with general service time distributions is studied in a moderate deviation heavy traffic regime. In the scaling limit, an optimal control problem associated with the model is shown to be governed by a differential game that can be explicitly solved. While the characterization of the limit by a differential game is akin to results at the large deviation scale, the analysis of the problem is closely related to the much studied area of control in heavy traffic at the diffusion scale.