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On the Inverse of Erlang's Function

Part of:Operations research and management scienceComputer system organizationSpecial processes

Published online by Cambridge University Press:  14 July 2016

S. A. Berezner,
A. E. Krzesinski and
P. G. Taylor
S. A. Berezner*
Affiliation:
University of Natal
A. E. Krzesinski*
Affiliation:
University of Stellenbosch
P. G. Taylor*
Affiliation:
University of Adelaide
*
∗ Postal address: Department of Statistics, University of Natal, 4001 Durban, South Africa.
∗∗ Postal address: Department of Computer Science, University of Stellenbosch, 7600 Stellenbosch, South Africa. e-mail address: aek1@cs.sun.ac.za
∗∗∗ Postal address: Department of Applied Mathematics, University of Adelaide, South Australia 5005, Australia. e-mail address: ptaylor@maths.adelaide.edu.au
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Abstract

Erlang's function B(λ, C) gives the blocking probability that occurs when Poisson traffic of intensity λ is offered to a link consisting of C circuits. However, when dimensioning a telecommunications network, it is more convenient to use the inverse C(λ, B) of Erlang's function, which gives the number of circuits needed to carry Poisson traffic λ with blocking probability at most B. This paper derives simple bounds for C(λ, B). These bounds are close to each other and the upper bound provides an accurate linear approximation to C(λ, B) which is asymptotically exact in the limit as λ approaches infinity with B fixed

Keywords

Erlang's functionqueueing theory

MSC classification

Primary:60K25: Queueing theory
Secondary:68M20: Performance evaluation; queueing; scheduling90B22: Queues and service

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 35 , Issue 1 , March 1998, pp. 246 - 252
Copyright
Copyright © Applied Probability Trust 1998 

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