Asymptotic inversion of the Erlang B formula

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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 languageEnglish
Pages (from-to)1-23
JournalSIAM Journal on Applied Mathematics
Volume70
Issue number1
DOIs
Publication statusPublished - 2009

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