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Agner Krarup Erlang
Born	January 1, 1878 Lonborg, Denmark
Died	February 3, 1929
Occupation	mathematician, statistician, and engineer

Agner Krarup Erlang (January 1, 1878–February 3, 1929) was a Danish mathematician, statistician and engineer, who invented the fields of traffic engineering and queueing theory.

Contents 1 Life 2 Contributions 3 See also 4 External links

Erlang was born at Lonborg (Lønborg), near Tarm, in Jutland. He was the son of a schoolmaster, and a descendant of Thomas Fincke on his mother's side. He demonstrated his potential at an early age by being able to read books upside down. At age 14, he passed the Preliminary Examination of the University of Copenhagen with distinction, after receiving dispensation to take it because he was younger than the usual minimum age. For the next two years he taught alongside his father.

A distant relative provided free board and lodging, and Erlang prepared for and took the University of Copenhagen entrance examination in 1896, and passed with distinction. He won a scholarship to the University and majored in mathematics, and also studied astronomy, physics and chemistry. He graduated in 1901 with an MA and later taught at several schools over the next 7 years. He maintained his interest in mathematics, and received an award for a paper that he submitted to the University of Copenhagen.

He was a member of the Danish Mathematicians' Association and through this met amateur mathematician Johan Jensen, the Chief Engineer of the Copenhagen Telephone Company (CTC), an offshoot of the International Bell Telephone Company. Erlang worked for the CTC from 1908 for almost 20 years, until his death in Copenhagen after an abdominal operation.

He was an associate of the British Institution of Electrical Engineers.

While working for the CTC, Erlang was presented with the classic problem of determining how many circuits were needed to provide an acceptable telephone service. His thinking went further by finding how many telephone operators were needed to handle a given volume of calls. Most telephone exchanges then used human operators and cord boards to switch telephone calls by means of jack plugs.

Out of necessity, Erlang was a hands-on researcher. He would conduct measurements and was prepared to climb into street manholes to do so. He was also an expert in the history and calculation of the numerical tables of mathematical functions, particularly logarithms. He devised new calculation methods for certain forms of tables.

He developed his theory of telephone traffic over several years. His significant publications include:

• In 1909 - "The Theory of Probabilities and Telephone Conversations" - which proves that the Poisson distribution applies to random telephone traffic.
• In 1917 - "Solution of some Problems in the Theory of Probabilities of Significance in Automatic Telephone Exchanges" - which contains his classic formulae for loss and waiting time.

These and other notable papers were translated into English, French and German. His papers were prepared in a very brief style and can be difficult to understand without a background in the field. One researcher from Bell Telephone Laboratories is said to have learned Danish to study them.

The British Post Office accepted his formula as the basis for calculating circuit facilities.

A unit of measurement, statistical distribution and programming language listed below have been named in his honour.

• Erlang - a unit of communication activity
• Erlang distribution - a statistical probability distribution
• Erlang programming language - developed by Ericsson for large industrial real-time systems
• Queueing theory
• Telecommunications traffic engineering

• O'Connor, John J., and Edmund F. Robertson. "Agner Krarup Erlang". MacTutor History of Mathematics archive.
• Biography - from Millennium Mathematics Project
• Erlang Distribution
• An Introduction to Erlang B and Erlang C by Ian Angus (PDF Document - Has terms and formulae plus biography)
• "Telefon-Ventetider. Et Stykke Sandsynlighedsregning", in Matematisk Tidsskrift, B, 1920 (a paper on telephone waiting times, in Danish, digitized by Project Runeberg)