---
title: "GOS and blocking probability in a loss system"
subject: "Telecommunications"
chapter: 6
key: "semester_8/telecommunications:gos-blocking-loss-system"
source: https://www.bctengineer.com/q/semester_8/telecommunications/gos-blocking-loss-system
site: BCT Engineering
---

# GOS and blocking probability in a loss system

Telecommunications · Chapter 6: Telephone Traffic

- Asked in: 2081 Bhadra, 4+4 marks
- Video: [Lec-20_Grade of Service, Blocking Probability | Telecommunication Engineering | ICT Engineering](https://www.youtube.com/watch?v=74bzOy1PaQU) — 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/gos-blocking-loss-system
- Whole chapter: https://www.bctengineer.com/md/semester_8/telecommunications/chapter-6

## Question

Explain the Grade of Service (GOS) and Blocking Probability in the context of a loss system. How are these metrics used to design and evaluate telecommunication networks?

## Short answer

GoS is the measured fraction of calls lost in the busy hour. Blocking probability is the calculated probability all servers are busy (e.g., Erlang B). They guide dimensioning to meet a target GoS, split end-to-end loss budgets, balance cost and quality, and evaluate network performance.

## Answer

#### Grade of Service (GoS)
In a **loss system** (blocked calls cleared, no queue), GoS is the proportion of calls offered in the busy hour that are lost:
$$
GoS = \frac{\text{calls lost}}{\text{calls offered}} = \frac{A_o - A_c}{A_o}
$$
It is a **measured value or design target** set by the operator, e.g. 0.01 for trunk routes, and it describes the service seen by users over the whole network or a route.

#### Blocking probability
**Blocking probability** $P_B$ is the probability, calculated from a traffic model, that all N servers are busy when a call arrives. For Poisson traffic A offered to N trunks (Erlang B):
$$
P_B = E_{1,N}(A) = \frac{A^N/N!}{\sum_{k=0}^{N}A^k/k!}
$$
It has two forms: **time congestion** (fraction of time all servers are busy) and **call congestion** (fraction of calls lost). With infinite Poisson sources they are equal, so $GoS = P_B$; with finite sources (Engset), call congestion is less than time congestion.

| Point | GoS | Blocking probability |
|---|---|---|
| Nature | Service quality measure / target | Probability from a model |
| Found by | Measurement of lost calls | Erlang B, Engset formula |
| Scope | Route, exchange or end to end | One server group |
| Use | Specify quality | Calculate trunks needed |

#### Use in design and evaluation
1. **Dimensioning:** forecast the busy-hour traffic A, choose the GoS (e.g. 0.01), then find N from Erlang B tables. Example: A = 5 E with GoS 0.01 gives N = 11 trunks.
2. **End-to-end budget:** a call through several links in tandem has a total GoS ≈ $B_1 + B_2 + \dots$, so the overall target is split among the links (e.g. 0.002 per switch, 0.005 per trunk).
3. **Cost trade-off:** a lower GoS needs more circuits; designers pick the GoS that balances cost and customer satisfaction.
4. **Routing design:** high-usage direct routes are dimensioned for a high blocking value (large GoS) and overflow to a final route dimensioned for a low GoS.
5. **Evaluation:** measured lost calls in the busy hour are compared with the target; if the target is exceeded, trunks are added or traffic is re-routed.
6. **Cellular planning:** the number of channels per cell is chosen for 2% blocking.

## Check yourself

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

1. What is the difference between GoS and blocking probability?
   A. GoS is a measured/target quality; blocking is a probability calculated from a model
   B. They are never equal
   C. GoS is only for delay systems
   D. Blocking is measured, GoS is calculated
   Answer: A. GoS specifies/measures quality; blocking probability is computed e.g. by Erlang B. (Key point: GoS vs blocking)

2. When does GoS equal blocking probability?
   A. Finite sources
   B. Infinite Poisson sources, where time and call congestion are equal
   C. Never
   D. Only with queues
   Answer: B. With infinite sources time and call congestion coincide. (Key point: Equality)

3. How is the number of trunks N found?
   A. Forecast busy-hour traffic A, choose GoS, read N from Erlang B tables
   B. Divide A by h
   C. Use the average-hour traffic
   D. Multiply GoS by A
   Answer: A. E.g. A = 5 E and GoS 0.01 gives N = 11. (Key point: Dimensioning)

## Related in Telecommunications

- [GOS vs blocking probability; E.164 plan](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Agos-vs-blocking-e164) — 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×
- [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
- [Short note: Grade of service](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Ashort-note-grade-of-service) — Telecommunications, chapter 6
- [GOS numerical: 1400 calls, 14 lost](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Agos-busy-hour-1400-calls) — Telecommunications, chapter 6, asked 5×
- [Traffic intensity, GOS and national numbering](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atraffic-intensity-gos-numbering) — Telecommunications, chapter 6

## Related in other subjects

- [Design metrics of embedded system](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Adesign-metrics-embedded) — Embedded System, chapter 1, asked 3×
- [Numerical: 12-cell system capacity at 2% GOS](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Acellular-capacity-12-cell-system) — Wireless Communication, chapter 2
- [Design goals and performance metrics](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_organization_and_architecture%3Adesign-goals-metrics) — Computer Organization and Architecture, chapter 1
- [GoS and optimal N for 15 dB S/I (n = 3)](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Agos-optimal-cluster-size-n3) — Wireless Communication, chapter 2