View five larger pictures. Biography Agner Erlang 's mother, Magdalene Krarup, came from an ecclesiastical family but she was descended from the mathematician Thomas Fincke. Magdalene broke with the family tradition, which was that all sons became clergymen and all daughters married clergymen, when she married Hans Nielsen Erlang, a schoolmaster and parish clerk. Hans Nielsen had trained to be a schoolteacher at the college in Jelling, choosing this Danish style training in preference to the German style training offered at the college in Tonder. Agner was the second of his parents' four children, having an older brother Frederik and two younger sisters Marie and Ingeborg.

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Erlang's work provided the methodological framework of queueing theory for application to telephone traffic and was a precursor to much modern theory of stochastic processes. He was descended on his mother's side from the famous Krarup family which had strong academic and ecclesiastical traditions. His father was the village schoolmaster and parish clerk and Erlang was initially educated at his father's school.

Later he taught at his father's school for for two years before passing the entrance examination to the University of Copenhagen in with distinction, and the award of a scholarship. At the University of Copenhagen, Erlang's studies were in mathematics, with minors in astronomy, physics and chemistry. He attended the mathematics lectures of H. Zeuthen and S. Juel and these gave him a lifelong interest in geometrical problems.

After graduation with a MA degree in , Erlang taught in various schools for 7 years. He was an excellent teacher, but not a particularly social person. During this time he kept up his studies in mathematics and was a member of the Danish Mathematical Association. It was through meetings of the Mathematical Association that Erlang made contact with the mathematician J. Jensen remembered for Jensen's inequality , then chief engineer at the Copenhagen Telephone Company.

Jensen introduced Erlang to F. Johanssen, then managing director of the Company, who had recently introduced probabilistic methods into telephony, and Erlang was recruited in A new physico-technical laboratory was established with Erlang as its head. Erlang quickly established a conceptual and methodological framework of queueing theory for application to telephone traffic which can be regarded as a precursor of much modern theory of stochastic processes. In he published his first major work in which he showed that the number of calls during an arbitrary time interval, assuming calls originate at random, follows a Poisson law, and that the intervals between calls were then exponentially distribured.

This simple, but physically realistic formulation has provided the benchmark for the subject. In Erlang published his most important paper. These formulae are now basic in telephone practice. He introduced the concept of "statistical equilibrium", essentially the modern ergodic hypothesis, which allows the interchange of time and space averages.

Erlang's writing style was brief and elegant and sometimes proofs were omitted. Vaulot in France and T. Fry in the USA, both important contributors to the subject, studied Danish in order to be able to read Erlang's papers in the original language. A great deal of attention has subsequently been devoted to the extension and modification of the formulae of Erlang, and to the investigation of their validity.

Among the earliest major contributors to this were C. Palm and F. Pollaczek q. Erlang was concerned with practical procedures as well as with the theory. For example, he systematized the dealing with stray currents which damaged the lead sheaths of telephone cables. Initially he had no laboratory staff to assist him with the measurement of stray currents. An incidental interest of Erlang's was the extinction of family names, as the Krarup family name of his mother was shortly to become extinct.

In he raised the mathematical problem, essentially as it had been earlier and independently posed by F. Galton q. Erlang provided a partial solution which was completed by the Danish actuary J. Steffensen in Erlang never married and he devoted himself to his work and studies. He was known as a good and charitable man. He worked for the Copenhagen Telephone Company for nearly 20 years, never having time off for illness until he went to hospital just prior to his death.

Log in. Namespaces Page Discussion. Views View View source History. Jump to: navigation , search. References [1] Brockmeyer, E. Jensen The Life and Works of A. Encyclopedia of Mathematics. Categories : Statprob Biographical. This page was last edited on 22 September , at This article Agner Krarup Erlang was adapted from an original article by C. Brockmeyer, E. Syski, R.

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## Agner Erlang and the Mathematics of Telecommunication Traffic

The foundation of any good call center outsourcer is a proper understanding of Erlang and thus queueing theory. Agner Krarup AK Erlang was a Danish pioneer of the study of telecommunications traffic in the early s. He is credited with being one of the early creators of queuing theory and is often cited as the father of Erlang measurement. He was also a pretty handsome dude. While working for the Copenhagen Telephone Exchange, he sought to solve the problem of determining how many circuits were needed to provide an acceptable phone service to a local village. His also wanted to figure out how many telephone operators were needed to handle a given volume of calls. Back then, most telephone exchanges used human operators and cord boards to switch telephone calls using jack plugs.

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## Erlang, Agner Krarup

He developed mathematical theories applying the theory of probability, while working for the Copenhagen Telephone Company. He provided significant insights for planning the operation of automatic telephone exchanges that proved so useful that his formulas were used by telephone companies in other countries. Agner was a bright child, learning quickly and having an excellent memory. 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 , and passed with distinction.

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## Agner Krarup Erlang

Erlang was the first person to study the problem of telephone networks. By studying a village telephone exchange he worked out a formula, now known as Erlang's formula, to calculate the fraction of callers attempting to call someone outside the village that must wait because all of the lines are in use. Although Erlang's model is a simple one, the mathematics underlying today's complex telephone networks is still based on his work. His father, Hans Nielsen Erlang, was the village schoolmaster and parish clerk. His mother was Magdalene Krarup from an ecclesiastical family and had a well known Danish mathematician, Thomas Fincke, amongst her ancestors.

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## Agner Krarup Erlang (1878 - 1929)

Agner Erlang was descended on his mother's side from Thomas Fincke. His father was a schoolmaster and Erlang was educated at his father's school when he was young. He took his examinations in Copenhagen at the age of 14 and passed with special distinction after having to obtain special permission to take the examinations because he was below the minimum age. He returned to Lonberg and taught at his father's school for two years. In he passed the entrance examination to the University of Copenhagen with distinction and, since his parents were poor, he was given free board and lodgings in a College of the University of Copenhagen. His studies at Copenhagen were in mathematics and natural science. He attended the mathematics lectures of Zeuthen and Juel and these gave him an interest in geometrical problems which were to remain with him all his life.