On the Inverse of Erlang's Function
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...
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| Veröffentlicht in: | Journal of applied probability 1998-03, Vol.35 (1), p.246-252 |
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| Sprache: | eng |
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| container_title | Journal of applied probability |
| container_volume | 35 |
| creator | Berezner, S. A. Krzesinski, A. E. Taylor, P. G. |
| description | 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 |
| doi_str_mv | 10.1017/S0021900200014856 |
| format | Article |
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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
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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
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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</abstract><doi>10.1017/S0021900200014856</doi><tpages>7</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0021-9002 |
| ispartof | Journal of applied probability, 1998-03, Vol.35 (1), p.246-252 |
| issn | 0021-9002 1475-6072 |
| language | eng |
| recordid | cdi_crossref_primary_10_1017_S0021900200014856 |
| source | Jstor Complete Legacy; JSTOR Mathematics & Statistics |
| title | On the Inverse of Erlang's Function |
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