What is Erlang ?

Definition:

·         An Erlang is a unit of telecommunications traffic measurement. An Erlang represents the continuous use of one voice path.  In practice, it is used to describe the total traffic volume of one hour. If one person makes one call and occupies one channel for an hour than we say that the system has 1 Erlang of traffic on it. 

History:

• Unit of traffic Erlang is name after Agner Krarup Erlang. He was born in 1878 in Lønborg, Denmark. He was a pioneer in the study of telecommunications traffic and, through his studies, proposed a formula to calculate the fraction of callers served by a village exchange who would have to wait when attempting to place a call to someone outside the village. 
• In 1909, he published his first work: The Theory of Probabilities and Telephone Conversations. He gained worldwide recognition for his work, and his formula was accepted for use by the General Post Office in the UK. 
• During the 1940s, the Erlang became the accepted unit of telecommunication traffic measurement, and his formula is still used today in the design of modern telecommunications networks.

Example:

·         For example, if a group of user made 30 calls in one hour, and each call had an average call duration of 5 minutes, then the number of Erlangs this represents is worked out as follows:

Minutes of traffic in the hour	=	number of calls x duration
Minutes of traffic in the hour	=	30 x 5
Minutes of traffic in the hour	=	150
Hours of traffic in the hour	=	150 / 60
Hours of traffic in the hour	=	2.5
Traffic figure	=	2.5 Erlangs

It is obvious that you will need at least three lines to handle this traffic. But even then, due to the random nature of calls, you will still have a significant rate of callers who do not get through and hear a busy signal instead.

Erlang related to telecommunication:

Averaged over time, one erlang of telephone traffic occupies exactly one channel. However, the arrival and closing of telephone calls are random processes. As time elapses, one erlang of traffic may occupy zero, one or multiple channels. The definition of the unit erlang does not say anything about how the traffic behaves statistically about this average. Thus one erlang of traffic can be generated for instance by

• One call of infinite duration, or
• A random process of many calls arriving and closing, such that the average number of active calls is one.

 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-B and Erlang-C

Erlang calculations are further broken down as follows:

• Erlang B:   The Erlang B is used to work out 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.
• Extended Erlang B:   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 C:   The Erlang C model assumes that not all calls may be handled immediately and some calls are queued until they can be handled. This model is mainly deployed in a call center environment.

These different models are described in further detail below.

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.

Erlang C

The Erlang C model is used by call centres to determine how many staff or call stations are needed, based on the number of calls per hour, the average duration of call and the length of time calls are left in the queue. The Erlang C figure is somewhat more difficult to determine because there are more interdependent variables. The Erlang C figure, is nevertheless very important to determine if a call centre is to be set up, as callers do not like being kept waiting interminably, as so often happens.