Engset Calculation

The Engset calculation was named after its developer, T. O. Engset, who developed it to determine the probability of congestion occurring within a telecommunications network. The level of congestion can be used to determine a network's performance as it directly relates to 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. 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 calls 1. Engset's formula requires recursion to solve. To determine the probability of congestion, the user 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 is as 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 erlangs from all sources
S = number of sources
N = number of circuits
P(b) = probability of blocking or congestion

References

1 Parkinson R., Traffic Engineering Techniques in Telecommunications, Infotel Systems Inc http://www.tarrani.net/mike/docs/TrafficEngineering.pdf. Last accessed 13 February 2005 2 ITU-T Study Group 2, Teletraffic Engineering Handbook http://www.com.dtu.dk/teletraffic/handbook/telenook.pdf. Last accessed 13 February 2005

 

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