Two methods of calculating traffic intensity

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