---
title: "Calls handled by 25 servers carrying 5 E"
subject: "Telecommunications"
chapter: 6
key: "semester_8/telecommunications:servers-25-5e-calls"
source: https://www.bctengineer.com/q/semester_8/telecommunications/servers-25-5e-calls
site: BCT Engineering
---

# Calls handled by 25 servers carrying 5 E

Telecommunications · Chapter 6: Telephone Traffic

- Asked in: 2071 Chaitra, 10 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/telecommunications/servers-25-5e-calls
- Whole chapter: https://www.bctengineer.com/md/semester_8/telecommunications/chapter-6

## Question

A group of 25 servers carry traffic of 5E. If the average duration of a call is 4 minutes, determine the number of calls put through by a single server and group as a whole in 1 hour.

## Short answer

Traffic A=5 E, holding time h=4 min, so group calls C = AT/h = 5×60/4 = 75 calls/hour. Each server carries 0.2 E, handling 0.2×60/4 = 3 calls/hour. Thus single server: 3 calls/hour; group: 75 calls/hour.

## Answer

**Given:** number of servers $n = 25$, total traffic carried $A = 5$ E, mean holding time $h = 4$ min, period $T = 1$ h $= 60$ min.

Traffic in erlang equals the call rate multiplied by the mean holding time:

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

#### Calls put through by the group

$$
\begin{aligned}
C_{group} &= \frac{5 \times 60}{4} \\
&= 75\ \text{calls per hour}
\end{aligned}
$$

#### Calls put through by a single server

Assuming the traffic is shared equally among the 25 servers, each server carries

$$
\begin{aligned}
A_1 &= \frac{5}{25} = 0.2\ \text{E}
\end{aligned}
$$

That is, each server is busy 20% of the time, i.e. $0.2 \times 60 = 12$ min in the hour. Number of calls handled by one server:

$$
\begin{aligned}
C_1 &= \frac{A_1\,T}{h} = \frac{0.2 \times 60}{4} \\
&= 3\ \text{calls per hour}
\end{aligned}
$$

Check: $25 \times 3 = 75$ calls, which matches the group total.

#### Interpretation

- Total busy time of all servers in the hour $= 75 \times 4 = 300$ call-minutes $= 5$ erlang-hours, which agrees with 5 E.
- The group occupancy is only $5/25 = 20\%$, so the group is lightly loaded; the blocking will be very small.

**Answer:** one server carries 0.2 E and puts through **3 calls per hour**; the group of 25 servers puts through **75 calls per hour**.

## Check yourself

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

1. Calls per hour of the group?
   A. 300
   B. 20
   C. 125
   D. 75
   Answer: D. C = A T/h = 5 x 60/4 = 75. (Key point: Group calls)

2. Traffic per server?
   A. 0.2 E
   B. 5 E
   C. 1.25 E
   D. 0.04 E
   Answer: A. 5/25 = 0.2 E, busy 12 min per hour. (Key point: Per-server traffic)

3. Calls per server per hour?
   A. 75
   B. 3
   C. 12
   D. 0.2
   Answer: B. 0.2 x 60/4 = 3, and 25 x 3 = 75. (Key point: Per-server calls)

4. What does 20% occupancy imply?
   A. Group is overloaded
   B. No calls are carried
   C. Lightly loaded group with very small blocking
   D. Blocking is high
   Answer: C. 5 E on 25 servers is light. (Key point: Occupancy)

## Close variants set in other exams

- [Calls handled by 30 servers carrying 15 E](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Aservers-15e-calls-per-hour) — Telecommunications, chapter 6, asked 3×

## Related in Telecommunications

- [Decision tree formulas; 20 servers, 10 E](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Adecision-tree-20-servers) — Telecommunications, chapter 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 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 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×
- [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×