Erlang Cheatsheet

These notes taken from http://www.erlang.com/whatis.html, http://en.wikipedia.org/wiki/Erlang_(unit), and other sources....

Table of Contents

Erlang

the continuous use of one voice path
total traffic volume of one our (e.g. # of erlangs)

simplified Erlang/busy hour traffic example

24 calls / hour (during busy hour)
avg call duration 5 minutes (during busy hour)

minutes of traffic = # of calls x duration
                   = 24 x 5
                   = 120 minutes
hours of traf / hr = 120 / 60
                   = 2
traffic figure     = 2 erlangs

Erlang B

calculating probability of blocking given erlang distribution (including poisson arrival process, and infinite source of calls)

           E B(E,j-1)
B(E,j) = --------------          (j=1,2,...,m)
         E B(E,j-1) + j


B(E,j)          - probability of blocking
m               - number of resources (e.g. trunks)
E = lamda x h   - amount of traffic offered in erlangs

Calc inverse for numerical stabilty.

  1          j      1
------ = 1 + - ----------        (j=1,2,...,m)
B(E,j)       E  B(E,j-1)

PUT IN JAVASCRIPT FOR THIS - lifted from wikipedia page

Function ErlangB (E as Double, m As Integer) As Double
    Dim InvB As Double
    Dim j As Integer

    InvB = 1.0
    For j = 1 To m
        InvB = 1.0 + j / E * InvB
    Next j
    ErlangB = 1.0 / InvB
End Function

extended Erlang B

iterative calculation that incorporates recall attempts

Erlang C

Adds a queuing system (e.g. calls never blocked)

Online Calculators

http://www.erlang.com/calculator/