## The Annals of Applied Probability

- Ann. Appl. Probab.
- Volume 27, Number 5 (2017), 2862-2906.

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

Rami Atar and Asaf Cohen

#### 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.

#### Article information

**Source**

Ann. Appl. Probab., Volume 27, Number 5 (2017), 2862-2906.

**Dates**

Received: October 2015

Revised: September 2016

First available in Project Euclid: 3 November 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.aoap/1509696036

**Digital Object Identifier**

doi:10.1214/16-AAP1269

**Mathematical Reviews number (MathSciNet)**

MR3719948

**Zentralblatt MATH identifier**

06822207

**Subjects**

Primary: 49N70: Differential games 60F10: Large deviations 60K25: Queueing theory [See also 68M20, 90B22] 93E20: Optimal stochastic control

**Keywords**

Moderate deviations heavy traffic risk-sensitive cost differential games

#### Citation

Atar, Rami; Cohen, Asaf. Asymptotically optimal control for a multiclass queueing model in the moderate deviation heavy traffic regime. Ann. Appl. Probab. 27 (2017), no. 5, 2862--2906. doi:10.1214/16-AAP1269. https://projecteuclid.org/euclid.aoap/1509696036