---
title: "Two methods of calculating traffic intensity"
subject: "Telecommunications"
chapter: 6
key: "semester_8/telecommunications:traffic-intensity-two-methods"
source: https://www.bctengineer.com/q/semester_8/telecommunications/traffic-intensity-two-methods
site: BCT Engineering
---

# Two methods of calculating traffic intensity

Telecommunications · Chapter 6: Telephone Traffic

- Asked in: 2069 Chaitra, 6 marks
- Video: [Trunking and Grade of Service (GOS) | Traffic Intensity](https://www.youtube.com/watch?v=OGGEmAjMx7I) — ECIT Engineering
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/telecommunications/traffic-intensity-two-methods
- Whole chapter: https://www.bctengineer.com/md/semester_8/telecommunications/chapter-6

## Question

Explain two methods of calculating traffic intensity.

## Short answer

Method 1: A = (number of calls × mean holding time) / observation period. Method 2: A equals the total occupancy time of all circuits divided by the period, or equivalently the average number of busy circuits obtained by periodic scanning, e.g., scanning 100 times per hour.

## Answer

Traffic intensity $A$ (in erlang) is the average number of calls simultaneously in progress during a period, usually the busy hour. It can be calculated in two ways.

#### Method 1: From number of calls and mean holding time

If $C$ calls occur during an observation period $T$ and the mean holding time is $h$:

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

where $\lambda = C/T$ is the mean call arrival rate. $h$ and $T$ must be in the same unit.

**Example:** 1800 calls in the busy hour, mean holding time 2 min:

$$
A = \frac{1800 \times 2}{60} = 60\ \text{E}
$$

#### Method 2: From occupancy of circuits (sum of holding times / scanning)

Traffic intensity also equals the total occupancy time of all circuits divided by the period, which is the same as the average number of busy circuits:

$$
A = \frac{\sum_i t_i}{T} = \frac{1}{T}\int_0^T n(t)\,dt
$$

where $t_i$ is the holding time of call $i$ and $n(t)$ is the number of circuits busy at time $t$.

In practice the exchange **scans** the circuits at regular intervals (e.g. every 36 s, 100 times an hour) and counts how many are busy. The average of these counts is the traffic in erlang:

$$
A \approx \frac{1}{m}\sum_{j=1}^{m} n_j
$$

**Example:** a group of 5 circuits is scanned 6 times in an hour and shows 2, 3, 4, 3, 2, 4 busy circuits.

$$
A = \frac{2+3+4+3+2+4}{6} = 3\ \text{E}
$$

#### Comparison

| Point | Method 1 (calls × holding time) | Method 2 (occupancy / scanning) |
|---|---|---|
| Data needed | call count and mean holding time | busy time or busy count |
| Measured by | call counters, CDRs | scanning traffic meters |
| Accuracy | needs good mean holding time | improves with more scans |
| Use | planning, forecasting | live traffic measurement |

## Check yourself

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

1. In the calls x holding time method, A equals:
   A. C h / T
   B. C T / h
   C. h / (C T)
   D. C + h / T
   Answer: A. A = C h / T = lambda h, with h and T in the same unit. (Key point: Method 1 formula)

2. 1800 calls in the busy hour with mean holding time 2 min give:
   A. 3600 E
   B. 30 E
   C. 60 E
   D. 90 E
   Answer: C. A = 1800 x 2 / 60 = 60 E. (Key point: Method 1 calculation)

3. In the scanning method, traffic in erlang is obtained by:
   A. adding the number of calls and dividing by 60
   B. taking the maximum number of busy circuits
   C. multiplying number of circuits by scan interval
   D. averaging the counts of busy circuits found at regular scans
   Answer: D. The average of the busy counts over the scans estimates the average number of occupied circuits. (Key point: Scanning method)

4. Scans show 2, 3, 4, 3, 2, 4 busy circuits. The traffic is:
   A. 3 E
   B. 4 E
   C. 18 E
   D. 2 E
   Answer: A. Sum is 18 and 18/6 = 3 E. (Key point: Scanning example)

## Related in Telecommunications

- [Traffic intensity, GOS and national numbering](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atraffic-intensity-gos-numbering) — Telecommunications, chapter 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 intensity in CCS, CM and CS](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atraffic-intensity-ccs-cm) — Telecommunications, chapter 6

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