Function File: B = erlangb (A, m)

Compute the steady-state blocking probability in the Erlang loss model.

The Erlang-B formula E_B(A, m) gives the probability that an open system with m identical servers, arrival rate \lambda, individual service rate \mu and offered load A = \lambda / \mu has all servers busy. This corresponds to the rejection probability of an M/M/m/0 system with m servers and no queue.

INPUTS

A

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

m

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

OUTPUTS

B

The value E_B(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: erlangc,engset,qsmmm.

Package: queueing