---
title: "Traffic numerical: 800 calls, 50 lost"
subject: "Telecommunications"
chapter: 6
key: "semester_8/telecommunications:gos-800-calls-50-lost"
source: https://www.bctengineer.com/q/semester_8/telecommunications/gos-800-calls-50-lost
site: BCT Engineering
---

# Traffic numerical: 800 calls, 50 lost

Telecommunications · Chapter 6: Telephone Traffic

- Asked in: 2074 Asoj, 2+6 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/telecommunications/gos-800-calls-50-lost
- Whole chapter: https://www.bctengineer.com/md/semester_8/telecommunications/chapter-6

## Question

Define blockage, lost calls and grade of service in telephone traffic engineering. During a busy hour 800 calls were offered to a group of trunks and 50 calls were lost. If the average call duration was 3 minutes, find the traffic offered, carried traffic, lost traffic, GoS and duration of congestion.

## Short answer

Blockage: all servers busy; lost calls: blocked calls cleared; GoS: lost/offered call ratio. For 800 calls offered, 50 lost, h=3 min: traffic offered = 40 E, carried = 37.5 E, lost = 2.5 E, GoS = 0.0625, congestion duration = 225 s.

## Answer

#### Definitions
- **Blockage (blocking):** the condition in which a call attempt cannot be connected because all suitable servers (trunks, switch paths) are busy; its probability is the blocking probability.
- **Lost call:** a blocked call in a loss system that is cleared and not served.
- **Grade of Service (GoS):** proportion of offered calls lost in the busy hour, $GoS = \dfrac{\text{calls lost}}{\text{calls offered}}$; a smaller value means better service.

**Given:** calls offered $C_o = 800$, calls lost $C_l = 50$, mean holding time $h = 3\ \text{min} = \tfrac{1}{20}$ h, period T = 1 h.

Traffic in Erlangs $= \dfrac{\text{calls} \times h}{T}$.

#### (a) Traffic offered
$$
\begin{aligned}
A_o &= \frac{C_o\,h}{T} = 800 \times \tfrac{1}{20} \\
&= 40\ \text{E}
\end{aligned}
$$

#### (b) Traffic carried
Calls carried $= 800 - 50 = 750$
$$
\begin{aligned}
A_c &= 750 \times \tfrac{1}{20} = 37.5\ \text{E}
\end{aligned}
$$

#### (c) Traffic lost
$$
\begin{aligned}
A_l &= A_o - A_c = 50 \times \tfrac{1}{20} = 2.5\ \text{E}
\end{aligned}
$$

#### (d) Grade of service
$$
\begin{aligned}
GoS &= \frac{C_l}{C_o} = \frac{50}{800} = 0.0625
\end{aligned}
$$

#### (e) Duration of congestion
For pure-chance (Poisson) traffic the proportion of time all trunks are busy (time congestion) equals the proportion of calls lost (call congestion), so congestion time in the busy hour is
$$
\begin{aligned}
T_c &= GoS \times 3600\ \text{s} = \frac{50}{800} \times 3600 \\
&= 225\ \text{s}
\end{aligned}
$$

**Answer:** traffic offered = **40 E**, carried = **37.5 E**, lost = **2.5 E**, GoS = **0.0625**, congestion duration = **225 s (3.75 min)**.

## Check yourself

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

1. What is blockage?
   A. A call that ends normally
   B. A call delayed by a queue only
   C. Any call longer than average
   D. A call attempt cannot be connected because all suitable servers are busy
   Answer: D. Blockage is failure to connect because of busy servers. (Key point: Blockage)

2. What is a lost call?
   A. A blocked call in a loss system that is cleared and not served
   B. A call in a queue
   C. A completed call
   D. A call carried on an alternative route
   Answer: A. In a loss system blocked calls are cleared. (Key point: Lost call)

3. 800 calls, 3 min, 50 lost: offered and carried traffic?
   A. 40 E and 40 E
   B. 40 E and 37.5 E
   C. 13.3 E and 12.5 E
   D. 800 E and 750 E
   Answer: B. 800 x 3/60 = 40; 750 x 3/60 = 37.5. (Key point: Traffic figures)

4. GoS and congestion time?
   A. 0.0625 and 62.5 s
   B. 0.05 and 180 s
   C. 0.0625 and 225 s
   D. 0.0625 and 3.75 s
   Answer: C. 50/800 = 0.0625; x 3600 = 225 s = 3.75 min. (Key point: Congestion duration)

## Close variants set in other exams

- [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×
- [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×
- [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
- [Traffic engineering goals; E.600 busy hours](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atraffic-engineering-busy-hour-e600) — Telecommunications, chapter 6
- [Device holding time and calls per hour](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Adevice-holding-time-calls) — Telecommunications, chapter 6