---
title: "GOS vs blocking probability; E.164 plan"
subject: "Telecommunications"
chapter: 6
key: "semester_8/telecommunications:gos-vs-blocking-e164"
source: https://www.bctengineer.com/q/semester_8/telecommunications/gos-vs-blocking-e164
site: BCT Engineering
---

# GOS vs blocking probability; E.164 plan

Telecommunications · Chapter 6: Telephone Traffic

- Asked in: 2074 Chaitra, 3+5 marks
- Video: [Grade of Service and Blocking Probability](https://www.youtube.com/watch?v=t49ca-qV1e0) — Dipanjan De
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/telecommunications/gos-vs-blocking-e164
- Whole chapter: https://www.bctengineer.com/md/semester_8/telecommunications/chapter-6

## Question

Define and differentiate between GOS and Blocking probability in a loss system. Explain the national numbering planning according to E.164.

## Short answer

GoS is the proportion of lost calls (quality target), while blocking probability is the chance all servers are busy (formula-based). For a single group they are equal. E.164 numbering: maximum 15 digits, format CC (1-3 digits) + NDC + SN. Prefixes: 00 for international, 0 for trunk calls.

## Answer

#### GoS and blocking probability in a loss system
- **Grade of Service (GoS):** ratio of calls lost to calls offered in the busy hour, $GoS = \dfrac{\text{calls lost}}{\text{calls offered}}$. It is the quality target set for a route or for the end-to-end connection (e.g. 0.01).
- **Blocking probability ($P_B$):** probability, given by a traffic model, that all N servers are busy when a call arrives. For Poisson traffic, Erlang B: $P_B = \dfrac{A^N/N!}{\sum_{k=0}^{N}A^k/k!}$.

| Point | GoS | Blocking probability |
|---|---|---|
| Meaning | Service quality measure | Probability all servers busy |
| Obtained by | Counting lost calls / target | Formula (Erlang B, Engset) |
| Scope | End to end or per route | Per server group |
| Use | Specify required service | Dimension N to meet GoS |

For infinite Poisson sources, call congestion = time congestion, so GoS = $P_B$ for a single group; for links in tandem GoS ≈ $\sum P_{B,i}$.

#### National numbering plan (ITU-T E.164 format)
A **numbering plan** gives every subscriber a unique number so that calls can be routed and charged. ITU-T **E.164** sets the international format, with at most **15 digits** (excluding prefixes):

```text
 |<------------ max 15 digits ------------->|
 +------+----------+--------------------------+
 |  CC  |   NDC    |           SN             |
 +------+----------+--------------------------+
 1-3 dig  |<----- national (significant) no. ----->|
```

- **CC – Country Code:** 1 to 3 digits, given by ITU (Nepal 977, India 91, USA 1). First digit is the world zone.
- **NDC – National Destination Code:** area/trunk code or mobile network code (Kathmandu valley 1; Nepal Telecom mobile 984/985/986, Ncell 980/981/982).
- **SN – Subscriber Number:** identifies the line within the NDC area.
- **NSN (National Significant Number) = NDC + SN**; its length is fixed by the national plan (maximum 15 − length of CC).

**Prefixes (not part of the number):**
- **Trunk (national) prefix:** dialled before the NSN for calls inside the country, usually 0 (e.g. 01-4xxxxxx in Nepal).
- **International prefix:** dialled before CC for outgoing international calls, ITU recommends 00.
- Short codes for emergency and services (100 police, 101 fire, 102 ambulance in Nepal).

**Example:** a Kathmandu fixed line: international format +977 1 4xxxxxx; national format 01-4xxxxxx; local format 4xxxxxx. A Nepali mobile: +977 98X XXXXXXX.

**Requirements of a good national plan:** unique numbers, enough spare capacity for growth (planned for 30–50 years), easy routing and charging from the leading digits, uniform length where possible, compatibility with E.164 and with number portability.

## Check yourself

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

1. How do GoS and blocking probability differ?
   A. GoS is calculated by Erlang B; PB is counted
   B. GoS is always much greater than PB
   C. GoS applies only to queues
   D. GoS is a quality measure/target (maybe end to end); PB is a model-calculated probability per server group
   Answer: D. GoS is specified or measured; PB is computed and used to dimension N. (Key point: GoS vs PB)

2. For links in tandem the GoS is approximately?
   A. Sum of the PB of the links
   B. Product of the PB values
   C. The largest PB only
   D. Zero
   Answer: A. For small blocking, end-to-end GoS is about the sum. (Key point: Tandem links)

3. What is the maximum length of an E.164 number?
   A. 10 digits
   B. 15 digits
   C. 12 digits
   D. 20 digits
   Answer: B. E.164 limits the international number to 15 digits excluding prefixes. (Key point: E.164 structure)

4. What is the national significant number?
   A. CC + NDC
   B. CC + SN
   C. NDC + SN
   D. Trunk prefix + CC
   Answer: C. NSN = National Destination Code plus Subscriber Number. (Key point: NSN)

## Related in Telecommunications

- [GOS and blocking probability in a loss system](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Agos-blocking-loss-system) — Telecommunications, chapter 6
- [Traffic intensity, GOS and national numbering](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atraffic-intensity-gos-numbering) — Telecommunications, chapter 6
- [GOS vs blocking; 600 calls, 2.5 min](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Agos-blocking-600-calls-2-5min) — Telecommunications, chapter 6, asked 6×
- [National and international numbering plans](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Anumbering-plan-national-international) — Telecommunications, chapter 7, asked 3×
- [NTA's role and ITU numbering plan](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Anta-role-itu-numbering) — Telecommunications, chapter 7
- [Traffic intensity, GOS and call duration probability](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atraffic-intensity-call-duration-probability) — Telecommunications, chapter 6

## Related in other subjects

- [Plan, importance, systematic planning process](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Aplan-importance-planning-process) — Project Engineering, chapter 3