---
title: "Traffic engineering objectives; Engset formula"
subject: "Telecommunications"
chapter: 6
key: "semester_8/telecommunications:traffic-objectives-engset"
source: https://www.bctengineer.com/q/semester_8/telecommunications/traffic-objectives-engset
site: BCT Engineering
---

# Traffic engineering objectives; Engset formula

Telecommunications · Chapter 6: Telephone Traffic

- Asked in: 2080 Bhadra, 3+5 marks
- Video: [Lec-18_Traffic Engineering | Telecommunication Engineering | ICT Engineering](https://www.youtube.com/watch?v=9Rc_XrgN9kA) — Computer_IT_ICT Engineering Department : LJIET
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/telecommunications/traffic-objectives-engset
- Whole chapter: https://www.bctengineer.com/md/semester_8/telecommunications/chapter-6

## Question

What are the objectives of traffic engineering in telecommunication? Explain the Engset formula used in traffic source.

## Short answer

The objectives of traffic engineering: dimensioning minimum trunks for busy-hour traffic, meeting grade of service, minimizing cost, traffic measurement and forecasting, efficient routing, overload control. The Engset formula gives the call congestion (loss probability) for finite sources S sharing N servers: B = binom(S-1,N)α^N / Σ_{k=0}^N binom(S-1,k)α^k, where α is offered traffic per idle source.

## Answer

#### Objectives of traffic engineering
1. **Dimensioning:** find the minimum number of trunks, switch paths, registers or channels that carry the expected busy-hour traffic.
2. **Meet the grade of service:** keep blocking (loss systems) or delay (delay systems) within the target, e.g. GoS = 0.01.
3. **Minimise cost:** balance equipment cost against service quality; avoid both over- and under-provision.
4. **Traffic measurement and forecasting:** measure busy-hour traffic and predict growth for planning.
5. **Efficient routing:** design direct, tandem and alternate (overflow) routes for high utilisation.
6. **Overload control and reliability:** keep the network stable during peaks and failures.

#### Engset formula (finite traffic sources)
The **Engset formula** gives the loss probability when a **finite number of sources** S share N servers (S > N) and blocked calls are cleared, e.g. a PBX or small rural exchange. Since busy sources cannot make new calls, the call rate falls as more sources are busy, so Erlang B (which assumes infinite sources) over-estimates loss.

**Assumptions:** S identical sources; each **idle** source calls at rate $\gamma$; mean holding time $h = 1/\mu$; $\alpha = \gamma h$ = offered traffic per idle source; full availability; lost calls cleared; equilibrium.

**Birth–death model:** in state n (n servers busy) arrival rate $=(S-n)\gamma$, departure rate $= n\mu$. Balance:
$$
(S-n+1)\gamma P_{n-1} = n\mu P_n \;\Rightarrow\; P_n = \binom{S}{n}\alpha^n P_0
$$

Normalising over $n = 0..N$:
$$
P_n = \frac{\binom{S}{n}\alpha^n}{\sum_{k=0}^{N}\binom{S}{k}\alpha^k}
$$

**Time congestion** (all N busy):
$$
E = \frac{\binom{S}{N}\alpha^N}{\sum_{k=0}^{N}\binom{S}{k}\alpha^k}
$$

**Call congestion** (probability an arriving call is lost) – the Engset loss formula:
$$
B = \frac{\binom{S-1}{N}\alpha^N}{\sum_{k=0}^{N}\binom{S-1}{k}\alpha^k}
$$

**Notes**
- $B < E$ for finite S.
- As $S \to \infty$ with $S\alpha = A$, Engset → Erlang B.
- If $S \le N$, no calls are lost (Bernoulli/binomial distribution).

## Check yourself

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

1. Which is a main objective of traffic engineering?
   A. Dimensioning to meet the GoS at minimum cost
   B. Maximise lost calls
   C. Eliminate busy hours
   D. Remove all signaling
   Answer: A. It finds the minimum resources that meet the GoS target. (Key point: Objective)

2. Why does Erlang B over-estimate loss for a small number of sources?
   A. It ignores holding time
   B. It assumes infinite sources, but busy sources cannot call
   C. It uses queuing
   D. It assumes cleared calls
   Answer: B. Engset accounts for falling call rate as sources get busy. (Key point: Erlang B limit)

3. Birth-death balance in the Engset model is:
   A. (S - n + 1)γ P(n-1) = nμ P(n)
   B. λ P(n) = μ P(n)
   C. SγP(n) = μ P(n)
   D. (S - n)γ = nμ
   Answer: A. Cut equation between states n-1 and n. (Key point: Balance eq)

4. As S → ∞ with Sα = A, Engset tends to:
   A. Erlang C
   B. Erlang B
   C. Binomial
   D. Poisson delay
   Answer: B. Infinite-source limit gives Erlang B. (Key point: Limit)

## Related in Telecommunications

- [Traffic engineering goals; E.600 busy hours](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atraffic-engineering-busy-hour-e600) — Telecommunications, chapter 6
- [Importance and unit of traffic engineering](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atraffic-engineering-importance-unit) — Telecommunications, chapter 6
- [Short note: Telephone traffic engineering](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Ashort-note-traffic-engineering) — Telecommunications, chapter 6, asked 2×
- [Role of traffic engineering](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Arole-of-traffic-engineering) — Telecommunications, chapter 6
- [Infinite and pure loss systems; Engset model](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Ainfinite-pure-loss-engset) — Telecommunications, chapter 6
- [Decision tree; infinite source blocking formulas](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Adecision-tree-infinite-sources) — Telecommunications, chapter 6, asked 2×

## Related in other subjects

- [Source coders used in speech coding](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aspeech-source-coders) — Wireless Communication, chapter 6
- [Objectives of FTR; cleanroom software engineering](https://www.bctengineer.com/question.md?key=semester_5%2Fsoftware_engineering%3Aftr-cleanroom) — Software Engineering, chapter 9
- [Traffic engineering; road user characteristics and HVE](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Ate-definition-road-user-hve) — Transportation Engineering II, chapter 1
- [Traffic engineering; road users and vehicular characteristics](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Ate-definition-road-users-vehicular) — Transportation Engineering II, chapter 1