---
title: "GOS numerical: 1400 calls, 14 lost"
subject: "Telecommunications"
chapter: 6
key: "semester_8/telecommunications:gos-busy-hour-1400-calls"
source: https://www.bctengineer.com/q/semester_8/telecommunications/gos-busy-hour-1400-calls
site: BCT Engineering
---

# GOS numerical: 1400 calls, 14 lost

Telecommunications · Chapter 6: Telephone Traffic

- Asked in: 2081 Baisakh, 2+2+2+2 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/telecommunications/gos-busy-hour-1400-calls
- Whole chapter: https://www.bctengineer.com/md/semester_8/telecommunications/chapter-6

## Question

Define Grade of Service (GOS) and Busy hour. During a busy hour, 1400 calls were offered to a group of trunks and 14 calls were lost. The average call duration has 3 minutes. Find (i) Traffic offered (ii) GOS (iii) Traffic carried.

## Short answer

GoS is the fraction of calls lost in the busy hour. The busy hour is the peak 60‑minute period used for dimensioning. For 1400 offered calls, 14 lost, mean holding 3 min, traffic offered = (1400×3)/60 = 70 E, GoS = 14/1400 = 0.01, traffic carried = (1386×3)/60 = 69.3 E.

## Answer

#### Grade of Service (GoS)
GoS is the proportion of calls lost (or delayed) in the busy hour because all servers are busy: $GoS = \dfrac{\text{calls lost}}{\text{calls offered}}$. Smaller value = better service.

#### Busy hour
The **busy hour** is the continuous 60-minute period of the day during which the traffic is maximum. Exchanges and trunks are dimensioned for busy-hour traffic so that GoS is met even at peak.

#### Numerical
**Given:** calls offered = 1400, calls lost = 14, h = 3 min = 1/20 h, T = 1 h.

**(i) Traffic offered**
$$
\begin{aligned}
A_o &= \frac{C_o\,h}{T} = \frac{1400 \times 3}{60} = 70\ \text{E}
\end{aligned}
$$

**(ii) Grade of service**
$$
\begin{aligned}
GoS &= \frac{14}{1400} = 0.01
\end{aligned}
$$

**(iii) Traffic carried**
Calls carried = 1400 − 14 = 1386
$$
\begin{aligned}
A_c &= \frac{1386 \times 3}{60} = 69.3\ \text{E}
\end{aligned}
$$
(Check: $A_c = A_o(1 - GoS) = 70 \times 0.99 = 69.3$ E.)

**Answer:** traffic offered = **70 E**, GoS = **0.01** (1%), traffic carried = **69.3 E**.

## Check yourself

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

1. The busy hour is:
   A. Any hour with a call
   B. The continuous 60-min period of maximum traffic
   C. The first hour
   D. The average hour
   Answer: B. Dimensioning uses it so GoS holds at peak. (Key point: Busy hour)

2. 1400 calls, h = 3 min: offered traffic?
   A. 14 E
   B. 70 E
   C. 140 E
   D. 4200 E
   Answer: B. 1400 × 3/60 = 70 E. (Key point: Offered traffic)

3. 14 of 1400 calls lost; GoS?
   A. 0.001
   B. 0.01
   C. 0.1
   D. 0.014
   Answer: B. 14/1400 = 0.01. (Key point: GoS)

4. Carried traffic?
   A. 69.3 E
   B. 70 E
   C. 68 E
   D. 0.7 E
   Answer: A. Ao(1 - GoS) = 70 × 0.99 = 69.3 E. (Key point: Carried)

## Close variants set in other exams

- [Traffic numerical: 800 calls, 50 lost](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Agos-800-calls-50-lost) — Telecommunications, chapter 6, asked 6×
- [Traffic numerical: 1000 calls, 5 lost](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atraffic-1000-calls-5-lost) — Telecommunications, chapter 6, asked 6×
- [Traffic numerical: 1200 calls, 6 lost](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atraffic-1200-calls-6-lost) — Telecommunications, chapter 6, asked 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×

## Related in Telecommunications

- [Traffic numerical: 600 calls, 40 lost, 120 s](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Agos-600-calls-120s) — Telecommunications, chapter 6, asked 5×
- [Trunk group numerical: 40 E, 20 s, 4 lost](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atrunks-40e-20s-four-lost) — Telecommunications, chapter 6, asked 2×
- [Trunk group numerical: 30 E, 12 s, 2 lost](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atrunks-30e-12s-two-lost) — Telecommunications, chapter 6, asked 2×
- [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