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 $\backslash mu$, individual arrival rate $\backslash lambda$ (i.e., the time until a user tries to request service is exponentially distributed with mean $1/\backslash lambda$), and offered load $A=\backslash lambda/\backslash mu$.

$$ P_b(A, m, n) = {{\displaystyle{A^m {n \choose m}}} \over {\displaystyle{\sum_{k=0}^m A^k {n \choose k}}}} $$

INPUTS

A

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

m

Number of identical servers (integer, $m\; \ge \; 1$). Default $m\; =\; 1$

n

Number of requests (integer, $n\; \ge \; 1$). 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