Erlang B

Erlang B is a formula that is derived from the Erlang distribution . They can be used to determine the capacity of a telephone line that is required on average for an assumed number of calls with a specified probability of loss.

This formula was developed by Agner Krarup Erlang . It determines line capacities within a certain period of time based on a known call volume. The Erlang-B formula assumes that callers who encounter a busy tone will not call again and thus tends to underestimate the real need for telephone lines. Another evaluation of the Erlang distribution leads to Erlang C .

Assuming that the occupation attempts represent a Poisson process , i.e. originate from many independently and randomly acting participants, and blockages (these are conversation attempts that have not been made due to overload) are "lost", i.e. the person in question does not call again The following relationship between (B) blocking probability, traffic (A) n requirement (= traffic to be switched, measured in Erlang ) and the A (N) number of available lines:

${\displaystyle {\mbox{Blockierungswahrscheinlichkeit}}~B(N,A)={\frac {\frac {A^{N}}{N!}}{\sum _{i=0}^{N}{\frac {A^{i}}{i!}}}}}$

programming

The Erlang-B formula quickly leads to the capacity of the computer in a program, since the numbers quickly become large and create an overflow. When transformed, the Erlang-B formula can be easily programmed via a loop. However, as the computing capacity increases, this limiting fact decreases. Processing in a loop enables premature termination as soon as the blocking probability falls below a defined threshold value.

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

Web links

• Online calculation of the blocking probabilities