The telecommunications unit Erlang, and its application in teletraffic theory

Contents

• Erlang - a unit of traffic
• Erlang traffic models
• A.K. Erlang - a tribute

Erlang - a unit of traffic

An Erlang is a unit of telecommunications traffic measurement.  Strictly speaking, an Erlang represents the continuous use of one voice path.  In practice, it is used to describe the total traffic volume of one hour.

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

Erlang traffic measurements are made in order to help telecommunications network designers understand traffic patterns within their voice networks.  This is essential if they are to successfully design their network topology and establish the necessary trunk group sizes.

Erlang traffic measurements or estimates can be used to work out how many lines are required between a telephone system and a central office (PSTN exchange lines), or between multiple network locations.

Erlang traffic models

Several traffic models exist which share their name with the Erlang unit of traffic.  They are formulae which can be used to estimate the number of lines required in a network, or to a central office (PSTN exchange lines).  A formula also exists to model queuing situations, and lends itself well to estimating the agent staffing requirements of call centers.

The main Erlang traffic model are listed below, with links to the free online calculators on this Web site:

• Erlang B
  This is the most commonly used traffic model, and is used to work out how many lines are required if the traffic figure (in Erlangs) during the busiest hour is known.   The model assumes that all blocked calls are immediately cleared.
• Extended Erlang B
  This model is similar to Erlang B, but takes into account that a percentage of calls are immediately represented to the system if they encounter blocking (a busy signal).  The retry percentage can be specified.
• Erlang C
  This model assumes that all blocked calls stay in the system until they can be handled.  This model can be applied to the design of call center staffing arrangements where, if calls cannot be immediately answered, they enter a queue.

A.K. Erlang - a tribute

Agner Krarup Erlang 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.

Erlang never married.  He worked for the Copenhagen Telephone Company for twenty years, until his death in 1929.  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.

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