Engset calculation

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The Engset calculation is named after its developer, T. O. Engset, who created it to determine the probability of congestion occurring within a circuit group. The level of congestion can be used to determine a network's performance as it measured by the grade of service. The formula requires that the user knows the expected peak traffic, the number of sources (callers) and the number of circuits in the network.

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 [1]. 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 [1, 2].

Engset's equation follows [1]:

P(b)=\frac{\left[\frac{\left(S-1\right)!}{N!\cdot\left(S-1-N\right)!}\right]\cdot M^N}{\sum_{X=1}^N\left[\frac{\left(S-1\right)!}{X!\cdot\left(S-1-X\right)!}\right]\cdot M^X}
M=\frac{A}{S-A\cdot\left(1-P(b)\right)}

where

A = offered traffic intensity in erlangs, from all sources
S = number of sources of traffic
N = number of circuits in group
P(b) = probability of blocking or congestion

[edit] References

  • [1] Parkinson R., Traffic Engineering Techniques in Telecommunications, Infotel Systems Inc (pdf). Last accessed 17 October 2005.
  • [2] ITU-T Study Group 2, Teletraffic Engineering Handbook(pdf). Last accessed 17 October 2005.
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