The G/GI/N queue in the Halfin–Whitt regime

By Josh E. Reed. 2009

159 citations recorded by the source corpus.

In this paper, we study the $G/\mathit{GI}/N$ queue in the Halfin--Whitt regime. Our first result is to obtain a deterministic fluid limit for the properly centered and scaled number of customers in the system which may be used to provide a first-order approximation to the queue length process. Our second result is to obtain a second-order stochastic approximation to the number of customers in the system in the Halfin--Whitt regime. This is accomplished by first centering the queue length process by its deterministic fluid limit and then normalizing by an appropriate factor. We then proceed to obtain an alternative but equivalent characterization of our limiting approximation which involves the renewal function associated with the service time distribution. This alternative characterization reduces to the diffusion process obtained by Halfin and Whitt [Oper. Res. 29 (1981) 567--588] in the case of exponentially distributed service times.

Subfields: Management Information Systems, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/286df60be35f666d27f93abc1508f8b8a1cf8c8f

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In Management Information Systems

In Management Science and Operations Research

Citations in the corpus

Martingale proofs of many-server heavy-traffic limits for Markovian queues ∗ (2007, methodology): “Even though we focus on elementary Markov models here, we are motivated by the desire to treat more complicated models, such as the non-Markovian GI/GI/n models in Krichagina and Puhalskii [37], Puhalskii and Reiman [53], Reed [55] and Kaspi and Ramanan [34], and network generalizations of these, su”
Gaussian expansions and bounds for the Poisson distribution applied to the Erlang B formula (2008, background): “The regime where a many-server queue is both in heavy traffic and critically loaded is known as the Halfin-Whitt regime or the Quality and Efficiency Driven (QED) regime and has been the subject of an extensive recent research effort, motivated by agent staffing problems in customer contact centers,”
SPDE Limits of Many Server Queues (2010, methodology): “1 of Reed [30], and a more detailed proof of measurability in the critical case can also be found in the Appendix of [30].”
Law of large numbers limits for many-server queues (2007, methodology): “Concurrently with this work, fluid and central limit theorems for just the number in system were established in the work of Reed [19] using a clever comparison with a G/GI/∞ system.”
Steady-state analysis of a multiserver queue in the Halfin-Whitt regime (2007, background): “Keywords: Multiserver queue; heavy-traffic approximation; Halfin–Whitt (QED) regime 2000 Mathematics Subject Classification: Primary 60K25 Secondary 90B22”
Stein's method for steady-state diffusion approximations: an introduction through the Erlang-A and Erlang-C models (2015, background): “Proving such limit theorems has been an active area of research in the last 50 years; see, for example, [7, 8, 37, 38, 33, 51] for single-class queueing networks, [49, 9, 63] for multiclass queueing networks, [42, 64] for bandwidth sharing networks, [32, 50, 17] for many-server queues.”