# Erlang B: details & formula

The basic Erlang calculations enabled an good idea of traffic loading in a telecommunications circuit to be analysed.

The main drawback was that it did not take account of real life in terms of variations in loading. The Erlang B seeks address this issue by looking at peak loading.

Accordingly, the Erlang B is used to calculate how many lines are required from a knowledge of the traffic figure during the busiest hour.

The Erlang B figure assumes that any blocked calls are cleared immediately. This is the most commonly used figure to be used in any telecommunications capacity calculations.

## Erlang B

It is particularly important to understand the traffic volumes at peak times of the day. Telecommunications traffic, like many other commodities, varies over the course of the day, and also the week. It is therefore necessary to understand the telecommunications traffic at the peak times of the day and to be able to determine the acceptable level of service required. The Erlang B figure is designed to handle the peak or busy periods and to determine the level of service required in these periods.

Essentially, the Erlang B traffic model is used by telephone system designers to estimate the number of lines required for PSTN connections or private wire connections. The three variables involved are Busy Hour Traffic (BHT), Blocking and Lines.

Busy Hour Traffic (in Erlangs) is the number of hours of call traffic there are during the busiest hour of operation of a telephone system.

Blocking is the failure of calls due to an insufficient number of lines being available. E.g. 0.03 mean 3 calls blocked per 100 calls attempted.

Lines is the number of lines in a trunk group.

The Extended Erlang B is similar to Erlang B, but it can be used to factor in the number of calls that are blocked and immediately tried again.

## Erlang B formula

The formula for the Erlang B calculation can be seen below:

$B=\frac{\frac{{A}^{N}}{N!}}{\sum \left(\frac{{A}^{i}}{i!}\right)}$

Where:
B=Erlang B loss probability
N=Number of trunks in full availability group
A=Traffic offered to group in Erlangs

The summation is undertaken from i = 0 to N

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