Editing Erlang (unit) (section)

== Extended Erlang B ==

''Extended Erlang B'' differs from the classic Erlang-B assumptions by allowing for a proportion of blocked callers to try again, causing an increase in offered traffic from the initial baseline level. It is an [[iteration|iterative calculation]] rather than a formula and adds an extra parameter, the recall factor <math>R_\text{f}</math>, which defines the recall attempts.<ref>'Designing optimal voice networks for businesses, government, and telephone companies' by J. Jewett, J. Shrago, B. Yomtov, TelCo Research, Chicago, 1980.</ref>

The steps in the process are as follows.<ref>Inayatullah, M., Ullah, F.K., Khan., A.N., 'An Automated Grade Of Service Measuring System', IEEE—ICET 2006, 2nd International Conference on Emerging Technologies, Peshawar, Pakistan 13–14 November 2006, pp. 230–237</ref> It starts at iteration <math>k=0</math> with a known initial baseline level of traffic <math>E_{0}</math>, which is successively adjusted to calculate a sequence of new offered traffic values <math>E_{k+1}</math>, each of which accounts for the recalls arising from the previously calculated offered traffic <math>E_{k}</math>.

# Calculate the probability of a caller being blocked on their first attempt <math display="block">P_\text{b} = B(E_k,m)</math> as above for Erlang B.
# Calculate the probable number of blocked calls <math display="block">B_\text{e} = E_k P_\text{b}</math>
# Calculate the number of recalls, <math>R</math>, assuming a fixed recall factor, <math>R_\text{f}</math>, <math display="block">R = B_\text{e} R_\text{f}</math>
# Calculate the new offered traffic <math display="block">E_{k+1}=E_{0}+R</math> where <math>E_{0}</math> is the initial (baseline) level of traffic.
# Return to step 1, substituting <math>E_{k+1}</math> for <math>E_{k}</math>, and iterate until a stable value of <math>E</math> is obtained.

Once a satisfactory value of <math>E</math> has been found, the blocking probability <math>P_\text{b}</math> and the recall factor can be used to calculate the probability that all of a caller's attempts are lost, not just their first call but also any subsequent retries.