Advances in Applied Probability

Loss systems with slow retrials in the Halfin–Whitt regime

F. Avram, A. J. E. M. Janssen, and J. S. H. Van Leeuwaarden

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Abstract

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.

Article information

Source
Adv. in Appl. Probab., Volume 45, Number 1 (2013), 274-294.

Dates
First available in Project Euclid: 15 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aap/1363354111

Digital Object Identifier
doi:10.1239/aap/1363354111

Mathematical Reviews number (MathSciNet)
MR3077549

Zentralblatt MATH identifier
1267.60102

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22] 68M10: Network design and communication [See also 68R10, 90B18] 41A60: Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15]

Keywords
Retrial system loss system Erlang B model Cohen's equation Mills' ratio Halfin--Whitt regime, QED regime

Citation

Avram, F.; Janssen, A. J. E. M.; Van Leeuwaarden, J. S. H. Loss systems with slow retrials in the Halfin–Whitt regime. Adv. in Appl. Probab. 45 (2013), no. 1, 274--294. doi:10.1239/aap/1363354111. https://projecteuclid.org/euclid.aap/1363354111


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