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Engset Calculation




Businesses need to know the minimum number of voice circuits they need to have to and from the PSTN . An approximate approach is to use the Erlang-B Formula . However, if the business has a small number of extensions, then the more exact Engset calculation, which takes the user population size into account, should be used instead. (For a large user population, the Engset and the Erlang-B calculations give the same result.)

Engset's equation is similar to the Erlang-B formula; however it contains one major difference: Erlang's equation assumes an infinite source of calls and Engset specifies a finite number of callers {Link without Title} . Thus Engset's equation should be used when the source population is small (say less than 200 users, extensions or customers).

In practice, like Erlang's equations, Engset's formula requires recursion to solve for the blocking or congestion probability. To determine this probability, the calculation must first determine an initial estimate. This initial estimate is substituted into the equation and the equation then is solved. The answer to this initial calculation is then substituted back into the equation, resulting in a new answer which is again substituted. This Iterative process continues until the equation converges to the correct answer 2 .

Engset's equation follows {Link without Title} :

:P(b)= rac{\left[ rac{\left(S-1 ight)!}{N!\cdot\left(S-1-N ight)!} ight]\cdot M^N}{\sum_{X=1}^N\left[ rac{\left(S-1 ight)!}{X!\cdot\left(S-1-X ight)!} ight]\cdot M^X}

:M= rac{A}{S-A\cdot\left(1-P(b) ight)}

where

A

S

N

:Pr(''b'') = Probability of blocking or congestion


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