Asymptotically optimal staffing of service systems with joint QoS constraints

Jing Zan; John J. Hasenbein; David P. Morton

doi:10.1007/s11134-014-9406-x

Asymptotically optimal staffing of service systems with joint QoS constraints

Jing Zan, John J. Hasenbein^*, David P. Morton

^*Corresponding author for this work

Industrial Engineering and Management Sciences

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We consider the problem of staffing large-scale service systems with multiple customer classes and multiple dedicated server pools under joint quality-of-service (QoS) constraints. We first analyze the case in which arrival rates are deterministic and the QoS metric is the probability a customer is queued, given by the Erlang-C formula. We use the Janssen–Van Leeuwaarden–Zwart bounds to obtain asymptotically optimal solutions to this problem. The second model considered is one in which the arrival rates are not completely known in advance (before the server staffing levels are chosen), but rather are known via a probability distribution. In this case, we provide asymptotically optimal solutions to the resulting stochastic integer program, leveraging results obtained for the case of deterministic arrivals.

Original language	English (US)
Pages (from-to)	359-386
Number of pages	28
Journal	Queueing Systems
Volume	78
Issue number	4
DOIs	https://doi.org/10.1007/s11134-014-9406-x
State	Published - Oct 16 2014

Funding

Acknowledgments This research was supported by the National Science Foundation Grant CMMI-0800676. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Keywords

Erlang-C formula
Halfin–Whitt regime
Parameter uncertainty

ASJC Scopus subject areas

Statistics and Probability
Computer Science Applications
Management Science and Operations Research
Computational Theory and Mathematics

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10.1007/s11134-014-9406-x

Cite this

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Asymptotically optimal staffing of service systems with joint QoS constraints

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