Erlang (unit)#Erlang B formula

Erlang B is a formula, which is derived from the Erlang distribution. With their help, you can determine the capacity of a phone line, which is needed for an assumed average number of conversations at a fixed loss probability.

The mathematical formula Agner Krarup Erlang was developed by. It determines the leadership capacity within a specified period on the basis of a known volume of calls. The Erlang B formula presupposes, however, that callers who encounter a busy tone not to call again and thus tends to underestimate the real need for phone lines.

Assuming that the seizure attempts constitute a Poisson process, that is, by many, independently and randomly active participants come, and blockages (which are due to congestion not that have been made attempts at conversation ) " for loss " go ( ie: the individual it not immediately tried again ), there is the following relationship between lockierungswahrscheinlichkeit (B ), transport (A) ngebot ( = to intermediary traffic, measured in Erlang ) and A (N) number of available lines:

Programming

If you want to program the Erlang B formula, you come very quickly to the limits of the machine, since the numbers are very large very quickly and produce an overflow. Transformed the Erlang B formula can be easily programmed via a loop.

This method also has the advantage that you can break the loop early if the blocking probability is below a defined threshold.

Function ErlangB (N As Integer, A As Double ) As Double Dim InvBlock As Double = 1 Dim i As Integer    For i = 0 To N      InvBlock = i / A * InvBlock 1    Next i    ErlangB = 1 / InvBlock end Function see also

  • Erlang C
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