Ergodic control of multi-class M/M/N + M queues in the Halfin-Whitt regime

Ari Arapostathis, Anup Biswas, Guodong Pang

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We study a dynamic scheduling problem for a multi-class queueing network with a large pool of statistically identical servers. The arrival processes are Poisson, and service times and patience times are assumed to be exponentially distributed and class dependent. The optimization criterion is the expected long time average (ergodic) of a general (nonlinear) running cost function of the queue lengths. We consider this control problem in the Halfin-Whitt (QED) regime, that is, the number of servers n and the total offered load r scale like n ≈ r + ρ√r for some constant ρ. This problem was proposed in [Ann. Appl. Probab. 14 (2004) 1084-1134, Section 5.2]. The optimal solution of this control problem can be approximated by that of the corresponding ergodic diffusion control problem in the limit. We introduce a broad class of ergodic control problems for controlled diffusions, which includes a large class of queueing models in the diffusion approximation, and establish a complete characterization of optimality via the study of the associated HJB equation. We also prove the asymptotic convergence of the values for the multi-class queueing control problem to the value of the associated ergodic diffusion control problem. The proof relies on an approximation method by spatial truncation for the ergodic control of diffusion processes, where the Markov policies follow a fixed priority policy outside a fixed compact set.

Original languageEnglish (US)
Pages (from-to)3511-3570
Number of pages60
JournalAnnals of Applied Probability
Volume25
Issue number6
DOIs
StatePublished - Dec 1 2015

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Ergodic Control
Multi-class
Queue
Control Problem
Diffusion Problem
Server
Multiclass Queueing Networks
HJB Equation
Controlled Diffusions
Dynamic Scheduling
Diffusion Approximation
Asymptotic Convergence
Queueing Model
Queueing
Queue Length
Time-average
Dynamic Problem
Compact Set
Nonlinear Function
Approximation Methods

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Arapostathis, Ari ; Biswas, Anup ; Pang, Guodong. / Ergodic control of multi-class M/M/N + M queues in the Halfin-Whitt regime. In: Annals of Applied Probability. 2015 ; Vol. 25, No. 6. pp. 3511-3570.
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Ergodic control of multi-class M/M/N + M queues in the Halfin-Whitt regime. / Arapostathis, Ari; Biswas, Anup; Pang, Guodong.

In: Annals of Applied Probability, Vol. 25, No. 6, 01.12.2015, p. 3511-3570.

Research output: Contribution to journalArticle

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