Hostname: page-component-cb9f654ff-9knnw Total loading time: 0 Render date: 2025-08-23T17:15:54.650Z Has data issue: false hasContentIssue false
  • English
  • Français

Staffing Many-Server Systems with Admission Control and Retrials

Part of: Special processes Approximations and expansions Computer system organization

Published online by Cambridge University Press:  22 February 2016

A. J. E. M. Janssen  and
J. S. H. van Leeuwaarden
A. J. E. M. Janssen*
Affiliation:
Eindhoven University of Technology and Eurandom
J. S. H. van Leeuwaarden*
Affiliation:
Eindhoven University of Technology
*
∗ Postal address: Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands.
∗ Postal address: Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In many-server systems it is crucial to staff the right number of servers so that targeted service levels are met. These staffing problems typically lead to constraint satisfaction problems that are difficult to solve. During the last decade, a powerful many-server asymptotic theory has been developed to solve such problems and optimal staffing rules are known to obey the square-root staffing principle. In this paper we develop many-server asymptotics in the so-called quality and efficiency driven regime, and present refinements to many-server asymptotics and square-root staffing for a Markovian queueing model with admission control and retrials.

Keywords

Many-server systemsQED regimeHalfin-Whitt regimeheavy trafficdiffusion limitsadmission controlsquare-root staffingoptimality gapasymptotic dimensioning

MSC classification

Primary: 60K25: Queueing theory 68M10: Network design and communication 41A60: Asymptotic approximations, asymptotic expansions (steepest descent, etc.)

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 47 , Issue 2 , June 2015 , pp. 450 - 475
Copyright
© Applied Probability Trust 

References

Artalejo, J. R. and Gómez-Corral, A. (2008). Retrial Queueing Systems. Springer, Berlin.Google Scholar
Avram, F., Janssen, A. J. E. M. and van Leeuwaarden, J. S. H. (2013). Loss systems with slow retrials in the Halfin–Whitt regime. Adv. Appl. Prob. 45, 274-294.Google Scholar
Borst, S., Mandelbaum, A. and Reiman, M. (2004). Dimensioning large call centers. Operat. Res. 52, 17-34.Google Scholar
Cohen, J. W. (1957). Basic problems of telephone traffic theory and the influence of repeated calls. Philips Telecommunication Rev. 18, 49-100.Google Scholar
Falin, G. I. and Artalejo, J. R. (1995). Approximations for multiserver queues with balking/retrial discipline. OR Spektrum 17, 239-244.Google Scholar
Falin, G. I. and Templeton, J. G. C. (1997). Retrial Queues. Chapman & Hall, London.CrossRefGoogle Scholar
Gibbens, R. J., Hunt, P. J. and Kelly, F. P. (1990). Bistability in communication networks. In Disorder in Physical Systems. Oxford University Press, pp. 113-127.Google Scholar
Halfin, S. and Whitt, W. (1981). Heavy-traffic limits for queues with many exponential servers. Operat. Res. 29, 567-588.Google Scholar
Jagerman, D. L. (1974). Some properties of the Erlang loss function. Bell System Tech. J. 53, 525-551.Google Scholar
Janssen, A. J. E. M. and van Leeuwaarden, J. S. H. (2013). Staffing many-server systems with admission control and retrials (report version). Available at http://arxiv.org/abs/1302.3006.Google Scholar
Janssen, A. J. E. M., van Leeuwaarden, J. S. H. and Zwart, B. (2008). Gaussian expansions and bounds for the Poisson distribution applied to the Erlang B formula. Adv. Appl. Prob. 40, 122-143.Google Scholar
Janssen, A. J. E. M., van Leeuwaarden, J. S. H. and Zwart, B. (2011). Refining square-root safety staffing by expanding Erlang C. Operat. Res. 59, 1512-1522.Google Scholar
Nesenbergs, M. (1979). A hybrid of Erlang B and C formulas and its applications. IEEE Trans. Commun. 27, 59-68.Google Scholar
Zhang, B., van Leeuwaarden, J. S. H. and Zwart, B. (2012). Staffing call centers with impatient customers: refinements to many-server asymptotics. Operat. Res. 60, 461-474.Google Scholar