Function File: B = engset (A, m, n)

Evaluate the Engset loss formula.

The Engset formula computes the blocking probability P_b(A,m,n) for a system with a finite population of n users, m identical servers, no queue, individual service rate \mu, individual arrival rate \lambda (i.e., the time until a user tries to request service is exponentially distributed with mean 1/\lambda), and offered load A=\lambda/\mu.

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

n

Number of requests (integer, n ≥ 1). Default n = 1

OUTPUTS

B

The value P_b(A, m, n)

A, m or n 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, erlangc.

Package: queueing