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 $\backslash lambda$, individual service rate $\backslash mu$ and offered load $A\; =\; \backslash lambda\; /\; \backslash mu$ has all the servers busy. This is the waiting probability in an $M/M/m/\backslash infty$ system with $m$ servers and an infinite queue.

$$ E_C(A, m) = \displaystyle{ {A^m \over m!} {1 \over 1-\rho} \left( \sum_{k=0}^{m-1} {A^k \over k!} + {A^m \over m!} {1 \over 1 - \rho} \right) ^{-1}} $$

INPUTS

A

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

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