Asymptotic inversion of the Erlang B formula

J.S.H. Leeuwaarden, van; N.M. Temme

doi:10.1137/080722795

Asymptotic inversion of the Erlang B formula

J.S.H. Leeuwaarden, van, N.M. Temme

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

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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.

Original language	English
Pages (from-to)	1-23
Journal	SIAM Journal on Applied Mathematics
Volume	70
Issue number	1
DOIs	https://doi.org/10.1137/080722795
Publication status	Published - 2009

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title = "Asymptotic inversion of the Erlang B formula",

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.",

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Asymptotic inversion of the Erlang B formula

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