Asymptotic Inversion of the Erlang B Formula

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2009 Netherlands English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Applied Mathematics, volume 70, pages 1-23 (issn: 0036-1399, eissn: 1095-712X,

Copyright policy )

Authors: J.S.H. van Leeuwaarden (Johan); N.M. Temme (Nico);

doi: 10.1137/080722795

Asymptotic Inversion of the Erlang B Formula

- Summary
- Subjects
- Metrics

Abstract

The Erlang B formula represents the steady-state blocking probability in the Erlang loss model or M/M/s/s queue. We derive asymptotic expansions for the offered load that matches, for a given number of servers, a certain blocking probability. In addressing this inversion problem we make use of various asymptotic expansions for the incomplete gamma function. A similar inversion problem is investigated for the Erlang C formula.

Country

Netherlands

Related Organizations

Dutch Research Council
Netherlands
Centrum Wiskunde & Informatica
Netherlands
Technical University Eindhoven
Netherlands
Eindhoven University of Technology
Netherlands

Keywords

Erlang loss model, incomplete gamma function, Erlang C formula, asymptotic analysis., queueing theory, Erlang B formula, asymptotic inversion

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	7
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Top 10%
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Top 10%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average