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Loss Systems with Slow Retrials in the Halfin–Whitt Regime

Part of: Computer system organization Special processes Approximations and expansions

Published online by Cambridge University Press:  04 January 2016

F. Avram ,
A. J. E. M. Janssen  and
J. S. H. Van Leeuwaarden
F. Avram*
Affiliation:
Université de Pau et des Pays de l'Adour
A. J. E. M. Janssen*
Affiliation:
Eindhoven University of Technology and EURANDOM
J. S. H. Van Leeuwaarden*
Affiliation:
Eindhoven University of Technology
*
∗ Postal address: Département de Mathématiques, Université de Pau et des Pays de l'Adour, Avenue de l'Université - BP 1155, 64013 Pau Cedex, France. Email address: florin.avram@univ-pau.fr
∗∗ Postal address: Department of Mathematics and Computer Science and Department of Electrical Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands. Email address: a.j.e.m.janssen@tue.nl
∗∗∗ Postal address: Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands. Email address: j.s.h.v.leeuwaarden@tue.nl
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Abstract

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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.

Keywords

Retrial systemloss systemErlang B modelCohen's equationMills' ratioHalfin–Whitt regime, QED regime

MSC classification

Primary: 60K25: Queueing theory 68M10: Network design and communication 41A60: Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 45 , Issue 1 , March 2013 , pp. 274 - 294
Copyright
© Applied Probability Trust 

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