Risk-sensitive control for the multi-class many server queue in the moderate deviation regime

TL;DR

This paper investigates risk-sensitive control strategies for multi-class G/M/N queues in the moderate deviation heavy traffic regime, linking the control problem to a differential game framework and deriving the rate function for the single class model.

Contribution

It introduces a novel risk-sensitive control approach for multi-class queues under moderate deviation scaling, connecting it to differential game theory.

Findings

Derived the rate function for the single class G/M/N queue.

Formulated the multi-class control problem as a differential game.

Established the connection between risk-sensitive control and differential games.

Abstract

A G/M/N queue is considered in the moderate deviation heavy traffic regime. The rate function for the customers-in-system process is obtained for the single class model. A risk-sensitive type control problem is considered for multi-class G/M/N model under the moderate deviation scaling and shown that the optimal control problem is related to a differential game problem.