On the inverse of Erlang's function
SA Berezner, AE Krzesinski, PG Taylor
JOURNAL OF APPLIED PROBABILITY | APPLIED PROBABILITY TRUST | Published : 1998
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. © 1998 Applied Probability Trust.