---
title: "Short note: Extended Erlang B"
subject: "Telecommunications"
chapter: 6
key: "semester_8/telecommunications:short-note-extended-erlang-b"
source: https://www.bctengineer.com/q/semester_8/telecommunications/short-note-extended-erlang-b
site: BCT Engineering
---

# Short note: Extended Erlang B

Telecommunications · Chapter 6: Telephone Traffic

- Asked in: 2081 Chaitra, 4 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/telecommunications/short-note-extended-erlang-b
- Whole chapter: https://www.bctengineer.com/md/semester_8/telecommunications/chapter-6

## Question

Write a short note on 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.

## Answer

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
1. Start with offered traffic $A = A_0$.
2. Find blocking $B = E_{1,N}(A)$ from Erlang B:
$$
B = \frac{A^N/N!}{\sum_{k=0}^{N} A^k/k!}
$$
3. Blocked traffic $= B\,A$; retried traffic $= R\,B\,A$.
4. New offered traffic $A = A_0 + R\,B\,A$.
5. Repeat steps 2–4 until A stops changing. Final B is the blocking; lost traffic $= (1-R)\,B\,A$.

```text
 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.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What does Extended Erlang B add to Erlang B?
   A. Finite sources
   B. Blocked callers who retry
   C. Queuing of calls
   D. Priority calls
   Answer: B. It models a recall factor R: the fraction of blocked calls that retry. (Key point: EEB idea)

2. What is the iterative update of offered traffic?
   A. A = A0 + R B A
   B. A = A0 - R B A
   C. A = A0 (1 - B)
   D. A = A0 / R
   Answer: A. Retried traffic R B A is added to fresh traffic A0, repeated until A converges. (Key point: Recall update)

3. What does EEB reduce to when R = 0?
   A. Engset
   B. Ordinary Erlang B
   C. Erlang C
   D. Lost-calls-held
   Answer: B. No retries means blocked calls are cleared: plain Erlang B. (Key point: R = 0)