STEADY-STATE GI/GI/n QUEUE IN THE HALFIN-WHITT REGIME

• 成果类型: Article
• 署名作者: Gamarnik, David; Goldberg, David A.
• 署名单位: Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); University System of Georgia; Georgia Institute of Technology
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/12-AAP905
• 发表日期: 2013
• 页码: 2382-2419
• 关键词: heavy-traffic limits; many-server queues; waiting-time; superposition; CONVERGENCE; THEOREMS; supremum; service

摘要

We consider the FCFS GI/GI/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(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/GI/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].