Refining Square-Root Safety Staffing by Expanding Erlang C

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

doi:10.1287/opre.1110.0991

Cited by 55 publications

(60 citation statements)

References 21 publications

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“…However, we take a different approach, aiming for new asymptotic expansions for the probability of delay and the probability of rejection. The first terms of these expansions are the QED limits, and the higherorder terms are refinements to these QED limits for finite s. This generalizes earlier results on the Erlang B, C and A models [JvLZ08,JvLZ11,ZvLZ12].…”

Section: Introductionsupporting

confidence: 82%

Scaled control in the QED regime

Janssen

Leeuwaarden

Sanders

2013

Performance Evaluation

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We develop many-server asymptotics in the Quality-and-Efficiency-Driven (QED) regime for models with admission control. The admission control, designed to reduce the incoming traffic in periods of congestion, scales with the size of the system. For a class of Markovian models with this scaled control, we identify the QED limits for two stationary performance measures. We also derive corrected QED approximations, generalizing earlier results for the Erlang B, C and A models. These results are useful for the dimensioning of large systems equipped with an active control policy. In particular, the corrected approximations can be leveraged to establish the optimality gaps related to square-root staffing and asymptotic dimensioning with admission control.

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Section: Introductionsupporting

confidence: 82%

Scaled control in the QED regime

Janssen

Leeuwaarden

Sanders

2013

Performance Evaluation

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“…Observe that even for very small values of λ, the capacity function s QED ( ) coincides with the exact solution for almost all ∈ (0, 1) and differs no more than by one server for all . Borst et al [20] recognized this in their numerical experiments too, and [74] later confirmed this theoretically (see Section 4). One can easily formulate other constraint satisfaction problems and reformulate them in the QED regime.…”

Section: Constraint Satisfactionmentioning

confidence: 70%

“…In the context of M /M /s + M queues, Zhang et al [157] obtained similar results on optimality gaps. Motivated by the results in [74,157], Randhawa [124] takes a more abstract approach to quantify optimality gaps of asymptotic optimization problems. He shows under generally assumptions that when the approximation to the objective function is accurate up to O(1), the prescriptions that are derived from this approximation are o(1)-optimal.…”

Section: Optimality Gapsmentioning

confidence: 99%

Economies-of-Scale in Many-Server Queueing Systems: Tutorial and Partial Review of the QED Halfin--Whitt Heavy-Traffic Regime

Leeuwaarden¹,

Mathijsen²,

Zwart³

2019

SIAM Rev.

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Resource sharing systems describe situations in which users compete for service from scarce resources. Examples include check-in lines at airports, waiting rooms in hospitals or queues in contact centers, data buffers in wireless networks, and delayed service in cloud data centers. These are all situations with jobs (clients, patients, tasks) and servers (agents, beds, processors) that have large capacity levels, ranging from the order of tens (checkouts) to thousands (processors). This survey investigates how to design such systems to exploit resource pooling and economies-of-scale. In particular, we review the mathematics behind the Quality-and-Efficiency Driven (QED) regime, which lets the system operate close to full utilization, while the number of servers grows simultaneously large and delays remain manageable. We also discuss emerging research directions related to load balancing, overdispersion and model uncertainty.arXiv:1706.05397v1 [math.PR]

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“…We analyze this system in the Halfin-Whitt regime, in a similar spirit as was done for the M/M/s queue [7], [10], the M/M/s/s queue [9], and the Erlang A model (M/M/s queue with abandonments) [12]. Compared to these earlier studies, the system with retrials brings about additional mathematical challenges, mainly because the retrial rate of returning customers is given implicitly as the solution of what we call Cohen's equation; cf.…”

Section: Introductionmentioning

confidence: 99%

Loss Systems with Slow Retrials in the Halfin–Whitt Regime

2013

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The Halfin-Whitt regime, or the quality-and-efficiency-driven (QED) regime, for multiserver systems refers to a situation with many servers, a critical load, and yet favorable system performance. We apply this regime to the classical multiserver loss system with slow retrials. We derive nondegenerate limiting expressions for the main steady-state performance measures, including the retrial rate and the blocking probability. It is shown that the economies of scale associated with the QED regime persist for systems with retrials, although in situations when the load becomes extremely critical the retrials cause deteriorated performance. Most of our results are obtained by a detailed analysis of Cohen's equation that defines the retrial rate in an implicit way. The limiting expressions are established by studying prelimit behavior and exploiting the connection between Cohen's equation and Mills' ratio for the Gaussian and Poisson distributions.

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Refining Square-Root Safety Staffing by Expanding Erlang C

Cited by 55 publications

References 21 publications

Scaled control in the QED regime

Scaled control in the QED regime

Economies-of-Scale in Many-Server Queueing Systems: Tutorial and Partial Review of the QED Halfin--Whitt Heavy-Traffic Regime

Loss Systems with Slow Retrials in the Halfin–Whitt Regime

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