Corrected asymptotics for a multi-server queue in the Halfin-Whitt regime

Janssen, Ajem Guido; Leeuwaarden, Johan S. H. van; Zwart, Bert

doi:10.1007/s11134-008-9070-0

Cited by 22 publications

(29 citation statements)

References 30 publications

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“…For this, we derive a lower bound on the delay probability that is explicit in β, using the lower bound in Theorem 1, and using that γ < β and also α < β, cf. [12], Lemma 7. Combining these bounds yields…”

Section: A Corrected Optimization Problemmentioning

confidence: 99%

Refining Square-Root Safety Staffing by Expanding Erlang C

Janssen

Leeuwaarden

Zwart

2011

Operations Research

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We apply a new corrected diffusion approximation for the Erlang C formula to determine staffing levels in cost minimization and constraint satisfaction problems. These problems are motivated by large customer contact centers that are modeled as an M/M/s queue with s the number of servers or agents. The proposed staffing levels are refinements of the celebrated square root safety staffing rule, and have the appealing property that they are as simple as the conventional square root safety staffing rule. In addition, we provide theoretical support for the empirical fact that square root safety staffing works well for moderate-sized systems.

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Section: A Corrected Optimization Problemmentioning

confidence: 99%

Refining Square-Root Safety Staffing by Expanding Erlang C

Janssen

Leeuwaarden

Zwart

2011

Operations Research

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“…Indeed, if λ → ∞, then proportional capacity growth results in W = 0, see e.g. Janssen et al (2008) for the asymptotic analysis of a similar slotted model with S equal to a constant.…”

Section: Two-moment Approximationmentioning

confidence: 99%

Efficiency evaluation for pooling resources in health care

et al. 2010

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Hospitals traditionally segregate resources into centralized functional departments such as diagnostic departments, ambulatory care centers, and nursing wards. In recent years this organizational model has been challenged by the idea that higher quality of care and efficiency in service delivery can be achieved when services are organized around patient groups. Examples include specialized clinics for breast cancer patients and clinical pathways for diabetes patients. Hospitals are struggling with the question of whether to become more centralized to achieve economies of scale or more decentralized to achieve economies of focus. In this paper we examine service and patient group characteristics to study the conditions where a centralized model is more efficient, and conversely, where a decentralized model is more efficient. This relationship is examined analytically with a queuing model to determine the most influential factors and then with simulation to fine-tune the results. The tradeoffs between economies of scale and economies of focus measured by these models are used to derive general management guidelines.

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“…The idea of bringing P(A λ ≤ s) into quasi-Gaussian form has been introduced by the authors in their recent paper [15] on corrected asymptotics in the Halfin-Whitt regime for the delay probability in the M/D/s queue. In [15] a detailed analysis of y was presented for the case λ < s. The present setting requires additional analysis for the case λ ≥ s. Moreover, in the present paper we fully exploit the fact that the quasi-Gaussian form permits us to derive bounds on P(A λ ≤ s) by deriving bounds on y and its derivative y ′ .…”

Section: Introductionmentioning

confidence: 99%

“…In [15] a detailed analysis of y was presented for the case λ < s. The present setting requires additional analysis for the case λ ≥ s. Moreover, in the present paper we fully exploit the fact that the quasi-Gaussian form permits us to derive bounds on P(A λ ≤ s) by deriving bounds on y and its derivative y ′ . The bounds on P(A λ ≤ s) are of the Berry-Esséen type except that we again express our approximation in terms of α instead of β.…”

Section: Introductionmentioning

confidence: 99%

Gaussian expansions and bounds for the Poisson distribution applied to the Erlang B formula

2008

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This paper presents new Gaussian approximations for the cumulative distribution function P(A λ ≤ s) of a Poisson random variable A λ with mean λ. Using an integral transformation, we first bring the Poisson distribution into quasiGaussian form, which permits evaluation in terms of the normal distribution function Φ. The quasi-Gaussian form contains an implicitly defined function y, which is closely related to the Lambert W function. A detailed analysis of y leads to a powerful asymptotic expansion and sharp bounds on P(A λ ≤ s).The results for P(A λ ≤ s) differ from most classical results related to the central limit theorem in that the leading term Φ(β), with β = (s − λ)/ √ λ, is replaced by Φ(α), where α is a simple function of s that converges to β as s → ∞. Changing β into α turns out to increase precision for small and moderately large values of s.The results for P(A λ ≤ s) lead to similar results related to the Erlang B formula. The asymptotic expansion for Erlang's B is shown to give rise to accurate approximations; the obtained bounds seem to be the sharpest in the literature thus far.

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Corrected asymptotics for a multi-server queue in the Halfin-Whitt regime

Cited by 22 publications

References 30 publications

Refining Square-Root Safety Staffing by Expanding Erlang C

Refining Square-Root Safety Staffing by Expanding Erlang C

Efficiency evaluation for pooling resources in health care

Gaussian expansions and bounds for the Poisson distribution applied to the Erlang B formula

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