---
title: "Calls handled by 30 servers carrying 15 E"
subject: "Telecommunications"
chapter: 6
key: "semester_8/telecommunications:servers-15e-calls-per-hour"
source: https://www.bctengineer.com/q/semester_8/telecommunications/servers-15e-calls-per-hour
site: BCT Engineering
---

# Calls handled by 30 servers carrying 15 E

Telecommunications · Chapter 6: Telephone Traffic

- Asked in: 2071 Shrawan, 5 marks; 2070 Asar, 5 marks (asked 2 times)
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/telecommunications/servers-15e-calls-per-hour
- Whole chapter: https://www.bctengineer.com/md/semester_8/telecommunications/chapter-6

## Question

A group of 30 servers carry traffic of 15E. If the average duration of a call is 3 minutes, determine the number of calls put through by a single server and group as a whole in 1 hour.

## Short answer

Using C = A×T/h, group calls = 15×60/3 = 300 calls per hour. Each server carries 0.5 E, so single server calls = 0.5×60/3 = 10 calls per hour.

## Answer

**Traffic (Erlang) definition:** traffic intensity $A = C\,h / T$, where C = number of calls in period T and h = mean holding time. So the number of calls is $C = A\,T/h$.

**Given:** N = 30 servers, A = 15 E, h = 3 min, T = 1 h = 60 min.

#### Calls by the group as a whole
$$
\begin{aligned}
C_{group} &= \frac{A\,T}{h} \\
&= \frac{15 \times 60}{3} \\
&= 300\ \text{calls per hour}
\end{aligned}
$$

#### Calls by a single server
Assuming traffic is shared equally, each server carries
$$
\begin{aligned}
A_1 &= \frac{15}{30} = 0.5\ \text{E}
\end{aligned}
$$
i.e. each server is busy 50% of the time = 30 min in the hour.
$$
\begin{aligned}
C_1 &= \frac{A_1\,T}{h} = \frac{0.5 \times 60}{3} = 10\ \text{calls per hour}
\end{aligned}
$$

Check: $30 \times 10 = 300$ calls.

**Answer:** a single server handles **10 calls/hour**; the group handles **300 calls/hour**.

## Check yourself

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

1. Which formula gives the number of calls from traffic A?
   A. C = A h / T
   B. C = A T / h
   C. C = h T / A
   D. C = A / (h T)
   Answer: B. From A = C h / T, C = A T / h. (Key point: Calls formula)

2. How many calls does the group of 30 servers carry in 1 hour (A = 15 E, h = 3 min)?
   A. 150
   B. 300
   C. 450
   D. 900
   Answer: B. C = 15 × 60 / 3 = 300. (Key point: Group calls)

3. What is the number of calls per hour for one server?
   A. 5
   B. 10
   C. 15
   D. 20
   Answer: B. Each server carries 0.5 E, so 0.5 × 60 / 3 = 10 calls; check 30 × 10 = 300. (Key point: Single server)

## Close variants set in other exams

- [Calls handled by 25 servers carrying 5 E](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Aservers-25-5e-calls) — 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×