Function File: C = erlangc (A, m)

Compute the steady-state probability of delay in the Erlang delay model.

The Erlang-C formula E_C(A, m) gives the probability that an open queueing system with m identical servers, infinite wating space, arrival rate \lambda, individual service rate \mu and offered load A = \lambda / \mu has all the servers busy. This is the waiting probability in an M/M/m/\infty system with m servers and an infinite queue.

INPUTS

A

Offered load. A = \lambda / \mu where \lambda is the mean arrival rate and \mu the mean service rate of each individual server (real, 0 < A < m).

m

Number of identical servers (integer, m ≥ 1). Default m = 1

OUTPUTS

B

The value E_C(A, m)

A or m can be vectors, and in this case, the results will be vectors as well.

REFERENCES

• G. Zeng, Two common properties of the Erlang-B function, Erlang-C function, and Engset blocking function, Mathematical and Computer Modelling, Volume 37, Issues 12-13, June 2003, Pages 1287-1296

See also: erlangb,engset,qsmmm.

Package: queueing