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

[1]  F. Kelly.  Blocking probabilities in large circuit-switched networks , 1986, Advances in Applied Probability.

[2]  R. I. Wilkinson.  Theories for toll traffic engineering in the U. S. A. , 1956 .

[3]  W. H. Haemers,et al.  Simple approximation techniques for congestion functions for smooth and peaked traffic , 1983 .

[4]  H. Akimaru,et al.  Asymptotic Expansion for Erlang Loss Function and Its Derivative , 1981, IEEE Trans. Commun..

[5]  A. A. Fredericks.  Congestion in blocking systems — a simple approximation technique , 1980, The Bell System Technical Journal.

[6]  Arne Jensen,et al.  The life and works of A. K. Erlang , 1960 .

[7]  D. L. Jagerman.  Methods in traffic calculations , 1984, AT&T Bell Laboratories Technical Journal.

[8]  Chen-Yuan Chang,et al.  An Efficient Approach to Real-Time Traffic Routeing for Telephone Network Management , 1994 .

[9]  Indra Widjaja.  Performance analysis of burst admission-control protocols , 1995 .

[10]  Keith W. Ross,et al.  Multiservice Loss Models for Broadband Telecommunication Networks , 1997 .

[11]  A. Borovkov.  On limit laws for service processes in multi-channel systems , 1967 .

[12]  Peter G. Taylor,et al.  Maximal Profit Dimensioning and Tariffing of Loss Networks , 1995 .

[13]  Andre Girard,et al.  Routing and Dimensioning in Circuit-Switched Networks , 1990 .

[14]  D. Jagerman.  Some properties of the erlang loss function , 1974 .

[15]  A. Jagers,et al.  On the continued Erlang loss function , 1986 .

[16]  W. Whitt,et al.  Heavy-traffic approximations for service systems with blocking , 1984, AT&T Bell Laboratories Technical Journal.