---
title: "Short note: Finite and infinite source models"
subject: "Telecommunications"
chapter: 6
key: "semester_8/telecommunications:short-note-finite-infinite-models"
source: https://www.bctengineer.com/q/semester_8/telecommunications/short-note-finite-infinite-models
site: BCT Engineering
---

# Short note: Finite and infinite source models

Telecommunications · Chapter 6: Telephone Traffic

- Asked in: 2075 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-finite-infinite-models
- Whole chapter: https://www.bctengineer.com/md/semester_8/telecommunications/chapter-6

## Question

Write a short note on tele-traffic models with finite and infinite sources.

## Short answer

Infinite-source models assume many sources, constant Poisson arrival rate, and use Erlang B/Poisson/Erlang C formulas. Finite-source models have limited sources S, arrival rate per idle source falls as more servers are busy, yielding lower blocking; they use Engset (cleared) or Bernoulli (held) formulas.

## Answer

Tele-traffic models are classified by the number of **traffic sources** compared with the number of servers N.

#### Infinite-source models
- Number of sources is very large (S ≫ N), so the call arrival rate $\lambda$ is constant and independent of busy sources; arrivals are **Poisson**.
- Offered traffic $A = \lambda h$ is fixed.
- Formulas: **Erlang B** (lost calls cleared), **Poisson** (lost calls held), **Erlang C** (lost calls delayed).
- Erlang B: $B = \dfrac{A^N/N!}{\sum_{k=0}^{N}A^k/k!}$
- Used for junction routes between large exchanges.

#### Finite-source models
- Small number of sources S (comparable to N). A busy source cannot make a new call, so the arrival rate $(S-n)\gamma$ falls as more servers are busy.
- Formulas: **Engset** (S > N, lost calls cleared), **Bernoulli/binomial** (S ≤ N, no loss).
- Engset call congestion: $B = \dfrac{\binom{S-1}{N}\alpha^N}{\sum_{k=0}^{N}\binom{S-1}{k}\alpha^k}$, $\alpha$ = traffic per idle source.
- Used for PBXs, concentrators, small rural exchanges.

| Point | Infinite source | Finite source |
|---|---|---|
| Arrival rate | Constant | Falls as load rises |
| Distribution | Poisson | Binomial / Engset |
| Loss formula | Erlang B | Engset |
| Blocking | Higher (conservative) | Lower |

## Check yourself

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

1. What is true of infinite-source models?
   A. Arrival rate falls as more sources are busy
   B. Arrivals are binomial
   C. They apply only to small PBXs
   D. Arrival rate is constant and arrivals are Poisson
   Answer: D. With S much larger than N, busy sources barely change the arrival rate. (Key point: Infinite sources)

2. Why does arrival rate fall in finite-source models?
   A. Busy sources cannot place new calls, giving rate (S-n) gamma
   B. Calls are blocked by Erlang B
   C. Holding times shorten
   D. Sources are all idle
   Answer: A. Only idle sources can call. (Key point: Finite sources)

3. Which formula suits lost calls cleared with a small number of sources?
   A. Erlang B
   B. Engset
   C. Erlang C
   D. Poisson
   Answer: B. Engset is the finite-source LCC formula. (Key point: Loss formula)

4. How does blocking compare?
   A. Finite-source blocking is higher
   B. They are always identical
   C. Infinite-source (Erlang B) gives higher, conservative blocking
   D. Infinite source has no blocking
   Answer: C. Finite sources reduce load when busy, so blocking is lower. (Key point: Comparison)

## Related in Telecommunications

- [Decision tree; finite source blocking formulas](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Adecision-tree-finite-sources) — Telecommunications, chapter 6, asked 2×
- [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×
- [Infinite-source blocking; 40 subscribers](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Ainfinite-source-blocking-40-subscribers) — 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
- [Traffic engineering objectives; Engset formula](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atraffic-objectives-engset) — Telecommunications, chapter 6

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