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 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