---
title: "Traffic numerical: 1200 calls, 6 lost"
subject: "Telecommunications"
chapter: 6
key: "semester_8/telecommunications:traffic-1200-calls-6-lost"
source: https://www.bctengineer.com/q/semester_8/telecommunications/traffic-1200-calls-6-lost
site: BCT Engineering
---

# Traffic numerical: 1200 calls, 6 lost

Telecommunications · Chapter 6: Telephone Traffic

- Asked in: 2073 Chaitra, 2+2+2+1+1 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/telecommunications/traffic-1200-calls-6-lost
- Whole chapter: https://www.bctengineer.com/md/semester_8/telecommunications/chapter-6

## Question

During the busy hour, 1200 calls were offered to a group of trunks and 6 calls were lost. The average call duration was 3 minutes. Find: a) The traffic offered b) The traffic carried c) The traffic lost d) The GoS e) The total duration of % congestion

## Short answer

Traffic offered = 60 E, carried = 59.7 E, lost = 0.3 E. Grade of service is 0.005 (0.5%). Total congestion duration is 18 seconds in the busy hour.

## Answer

**Given:** calls offered $C_o = 1200$ in the busy hour, calls lost $C_l = 6$, mean holding time $h = 3$ min, observation period $T = 60$ min.

Traffic intensity (in erlang) is the number of calls in the period multiplied by the mean holding time, divided by the period:

$$
A = \frac{C\,h}{T}
$$

#### a) Traffic offered

$$
\begin{aligned}
A_o &= \frac{1200 \times 3}{60} \\
&= 60\ \text{E}
\end{aligned}
$$

#### b) Traffic carried

Calls carried $= 1200 - 6 = 1194$.

$$
\begin{aligned}
A_c &= \frac{1194 \times 3}{60} \\
&= 59.7\ \text{E}
\end{aligned}
$$

#### c) Traffic lost

$$
\begin{aligned}
A_l &= A_o - A_c = 60 - 59.7 \\
&= 0.3\ \text{E}
\end{aligned}
$$

(Check: $6 \times 3 / 60 = 0.3$ E.)

#### d) Grade of service

GoS is the fraction of offered calls (or offered traffic) that is lost:

$$
\begin{aligned}
B &= \frac{\text{calls lost}}{\text{calls offered}} = \frac{6}{1200} \\
&= 0.005\ (\text{i.e. } 0.5\%)
\end{aligned}
$$

#### e) Total duration of the periods of congestion

For random (Poisson) traffic, the call congestion equals the time congestion, so the trunk group is fully busy for a fraction $B$ of the hour:

$$
\begin{aligned}
t_{cong} &= B \times T = 0.005 \times 3600\ \text{s} \\
&= 18\ \text{s}
\end{aligned}
$$

**Answer:** traffic offered = 60 E, traffic carried = 59.7 E, traffic lost = 0.3 E, GoS = 0.005 (0.5%), total congestion time = 18 s in the busy hour.

## Check yourself

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

1. 1200 calls of 3 min in 60 min?
   A. 3600 E
   B. 20 E
   C. 400 E
   D. 60 E
   Answer: D. 1200 x 3 / 60 = 60 E. (Key point: Offered traffic)

2. Traffic lost with 6 lost calls?
   A. 0.3 E
   B. 6 E
   C. 0.005 E
   D. 59.7 E
   Answer: A. 6 x 3 / 60 = 0.3 E, which is offered minus carried. (Key point: Lost traffic)

3. GoS?
   A. 0.05
   B. 0.005
   C. 0.5
   D. 0.0005
   Answer: B. 6/1200 = 0.005. (Key point: GoS)

4. Why is congestion time B x T = 18 s?
   A. Each lost call lasts 3 s
   B. 18 E is lost
   C. Call congestion equals time congestion for random traffic
   D. T is 18 min
   Answer: C. 0.005 x 3600 = 18 s. (Key point: Congestion time)

## Close variants set in other exams

- [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×
- [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 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: 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×
- [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×

## Related in Telecommunications

- [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