Steady-state GI/G/n queue in the Halfin–Whitt regime
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Gamarnik-2013-Steady-state GI.pdf
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Author(s)
Gamarnik, David
Goldberg, David A.
Date Issued
December 2013
Journal
The Annals of Applied Probability
Publisher
Institute of Mathematical Statistics
Citation
Gamarnik, David, and David A. Goldberg. “Steady-state $GI/G/n$ queue in the Halfin–Whitt regime.” The Annals of Applied Probability 23, no. 6 (December 2013): 2382-2419. © Institute of Mathematical Statistics
Version
Final published version
Abstract
We consider the FCFS GI/G/n queue in the so-called Halfin–Whitt heavy traffic regime. We prove that under minor technical conditions the associated sequence of steady-state queue length distributions, normalized by n[superscript 1/2], is tight. We derive an upper bound on the large deviation exponent of the limiting steady-state queue length matching that conjectured by Gamarnik and Momcilovic [Adv. in Appl. Probab. 40 (2008) 548–577]. We also prove a matching lower bound when the arrival process is Poisson.
Our main proof technique is the derivation of new and simple bounds for the FCFS GI/G/n queue. Our bounds are of a structural nature, hold for all n and all times t ≥ 0, and have intuitive closed-form representations as the suprema of certain natural processes which converge weakly to Gaussian processes. We further illustrate the utility of this methodology by deriving the first nontrivial bounds for the weak limit process studied in [Ann. Appl. Probab. 19 (2009) 2211–2269].
MIT Department
Sloan School of Management
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1214/12-AAP905
