2081 Chaitra · 4 marks

Short note: Extended Erlang B

Short answer

Extended Erlang B models blocked callers who redial by adding a recall factor R. It iteratively recalculates offered traffic as A = A0 + R·B·A until convergence, giving a higher blocking probability and more trunks than standard Erlang B.

Write a short note on Extended Erlang B.

The Extended Erlang B (EEB) model is a version of Erlang B that allows for blocked callers who try again. Plain Erlang B assumes blocked calls are cleared and never return; in practice many callers redial, which raises the actual offered load. EEB therefore gives a more realistic, slightly larger number of trunks.

Parameters

$A_0$ – fresh (first-attempt) traffic in Erlangs
N – number of trunks
R – recall factor: fraction of blocked calls that are re-attempted (0 to 1)

Iterative method

Start with offered traffic $A = A_0$ .
Find blocking $B = E_{1,N}(A)$ from Erlang B:

B = \frac{A^N/N!}{\sum_{k=0}^{N} A^k/k!}

Blocked traffic $= B\,A$ ; retried traffic $= R\,B\,A$ .
New offered traffic $A = A_0 + R\,B\,A$ .
Repeat steps 2–4 until A stops changing. Final B is the blocking; lost traffic $= (1-R)\,B\,A$ .

 A0 -->(+)--> A --> N trunks --> carried
        ^           |
        |    blocked B*A
        +--R*B*A----+--(1-R)B*A--> lost

Notes

With R = 0 it reduces to ordinary Erlang B.
With R = 1 every blocked call keeps retrying until it is served, so no traffic is finally lost; the offered load grows until all fresh traffic is carried.
It is used in call-centre and trunk dimensioning where customers retry.

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