# What is an Erlang

### - details & tutorial describing what is an Erlang - the unit used as a measure of traffic density in a telecommunications system or network.

### Erlang Tutorial Includes

The Erlang unit is widely used in telecommunications technology.

The Erlang unit is a statistical measure of the voice traffic density in a telecommunications system and it is widely used because, for any element in a telecommunications system, whether it is a landline, or uses cellular technology, it is necessary to be able to understand the traffic volume.

As a result it is helps to have a definition of the telecommunications traffic so that the volume can be quantified in a standard way and calculations can be made. Telecommunications network designers make great use of the Erlang to understand traffic patterns within a voice network and they use the figures to determine the capacity that is required in any area of the network.

## Who was Erlang?

The Erlang is named after a Danish telephone engineer named A.K Erlang (Agner Krarup Erlang). He was born on 1st January 1878 and although he trained as a mathematician, he was the first person to investigate traffic and queuing theory in telephone circuits.

After receiving his MA, Erlang worked in a number of schools. However, Erlang was a member of the Danish Mathematician's Association (TBMI) and it was through this organization that Erlang met the Chief Engineer of the Copenhagen Telephone Company (CTC) and as a result, he went to work for them from 1908 for almost 20 years.

While he was at CTC, Erlang studied the loading on telephone circuits, looking at how many lines were required to provide an acceptable service without installing too much over-capacity that would cost the company money. There was a trade-off between cost and service level.

Erlang developed his theories over a number of years, and published several papers. He expressed his findings in mathematical forms so that they could be used to calculate the required level of capacity, and today the same basic equations are in widespread use..

In view of his ground-breaking work, the International Consultative Committee on Telephones and Telegraphs (CCITT) honoured him in 1946 by adopting the name "Erlang" for the basic unit of telephone traffic.

Erlang died on 3rd February 1929 after an unsuccessful abdominal operation.

## Erlang basics

The Erlang unit is the basic measure of telecommunications traffic intensity representing continuous use of one circuit and it is given the symbol "E". It is effectively call intensity in call minutes per sixty minutes. In general the period of an hour is used, but it actually a dimensionless unit because the dimensions cancel out (i.e. minutes per minute).

The number of Erlangs is easy to deduce in a simple case. If a resource carries one Erlang, then this is equivalent to one continuous call over the period of an hour. Alternatively if two calls were in progress for fifty percent of the time, then this would also equal one Erlang (1E). Alternatively if a radio channel is used for fifty percent of the time carries a traffic level of half an Erlang (0.5E)

From this it can be seen that an Erlang, E, may be thought of as a use multiplier where 100% use is 1E, 200% is 2E, 50% use is 0.5E and so forth.

Interestingly for many years, AT&T and Bell Canada measured traffic in another unit called CCS, 100 call seconds. If figures in CCS are encountered then it is a simple conversion to change CCS to Erlangs. Simply divide the figure in CCS by 36 to obtain the figure in Erlangs

## Erlang function or Erlang formula and symbol

It is possible to express the way in which the number of Erlangs are required in the format of a simple function or formula.

**A = λ x h**

Where:

λ = the mean arrival rate of new calls

h = the mean call length or holding time

A = the traffic in Erlangs.

Using this simple Erlang function or Erlang formula, the traffic can easily be calculated.

## Erlang development

The basic Erlang concept was widely adopted, but it did not cover all the aspects required. Elements including traffic density at peak periods and factors to include the number of calls that were blocked and needed to be tried again were also important and needed to be incorporated. Other adaptations to handle queuing also needed to be developed. These were included in the Erlang B and C adaptations.

* By Ian Poole*

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