Erlang was the first person to study the problem of telephone networks. 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. He had a brother, Frederik, who was two years older and two younger sisters, Marie and Ingeborg. Evenings were often spent reading a book with Frederik, who would read it in the conventional way and Agner would sit on the opposite side and read it upside down.

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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.

However, Magdalene and Hans Nielsen made a happy if simple home for their family making sure that they had sufficient food prepared which they prepared in the most hygienic manner possible. Agner was a bright child, learning quickly and having an excellent memory [ 6 ], [ 7 ] In the evenings, he and his elder brother would often share the reading of a book between them, the usual procedure being that brother Frederik would read it in the approved manner, while Agner, sitting opposite to him at the table, would read the book upside-down.

Astronomy was his favourite subject, encouraged by his maternal grandfather who also loved it, but Agner combined that interest with another passion by writing poems about astronomical objects. He took his Praeliminaereksamen examination in Copenhagen at the age of fourteen and passed with special distinction after having to obtain special permission to take the examinations because he was below the minimum age. His brother, who was two years older, went with him to Copenhagen with him and took the Praeliminaereksamen at the same time.

He continued his education during these years, however, being tutored in French and Latin. In he passed the entrance examination, the Studentereksamen, 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 Hieronymous Zeuthen and Christian Juel and these gave him an interest in geometrical problems which were to remain with him all his life. After graduating from Copenhagen in January with mathematics as his major subject and physics, astronomy and chemistry as secondary subjects, he taught in schools for the next seven years.

He was not highly sociable, he preferred to be an observer, and had a concise style of speech. His friends nicknamed him "The Private Person".

He used his summer holidays to travel abroad to France, Sweden, Germany and Great Britain, visiting art galleries and libraries. A few years later Nybolle became professor of statistics at the University of Copenhagen and their friendship also became a scientific collaboration.

Jensen persuaded Erlang to apply his skills to the solution of problems which arose from a study of waiting times for telephone calls. In Erlang joined the Copenhagen Telephone Company as a scientific collaborator and the head of their newly established physico-technical laboratory, and he began applying probability to various problems arising in the context of telephone calls. He published his first paper on these problems The theory of probability and telephone conversations in In this paper he showed that if telephone calls were made at random they followed the Poisson distribution, and he gave a partial solution to the delay problem.

In he published Solution of some problems in the theory of probability of significance in automatic telephone exchanges in which he gave a formula for loss and waiting time which was soon used by telephone companies in many countries including the British Post Office. In the twenty years that Erlang worked for the Copenhagen Telephone Company he never had to take a day off through illness.

However, in January , at the age of 51 he began suffering from abdominal pains and went into hospital for an operation. He died a few days later. The investigation of these problems constituted an essential part of his activities throughout the 20 years he spent as a scientific collaborator of the Copenhagen Telephone Company. The mathematically exact methods of solving problems of loss and waiting times, which Erlang developed by his employment of the principle of statistic equilibrium, are of fundamental importance in the theory of telephone traffic.

In addition to his work on probability Erlang was also interested in mathematical tables. This interest is described in [ 4 ] and [ 5 ]:- A subject that interested Erlang very much was the calculation and arrangement of numerical tables of mathematical functions, and he had an uncommonly thorough knowledge of the history of mathematical tables from ancient times right up to the present.

Erlang set forth a new principle for the calculation of certain forms of mathematical tables, especially tables of logarithms Originally published in Danish in , an expanded version describing these new principles was published in English as How to reduce to a minimum the mean error of tables which he contributed to the Napier Tercentenary Memorial Volume published by the Royal Society of Edinburgh in Erlang never married, perhaps because he fell in love with a young girl who eventually married one of his colleagues.

He lived with his youngest sister Ingeborg for many years. Let us quote from [ 6 ] or the reprint [ 7 ] concerning his personality:- Erlang had a noteworthy and original personality. He was a sincere Christian in a sympathetic way, at the same time being full of humour and satirical wit; outwardly, his heavy red full beard and his manner of dressing lent a certain artistic touch to his characteristic appearance.

Extremely modest and unobtrusive of demeanour, he preferred the peaceful atmosphere of his study to social gatherings and festivities; he never touched alcoholic liquors nor smoked tobacco. Erlang was a beneficent man; living frugally, he could afford to help others, which he did to an even very great extent. We get further insight into his character from [ 3 ]:- He collected a large library of books mainly on mathematics, astronomy and physics, but he was also interested in history, philosophy and poetry.

Friends found him to be a good and generous source of information on many topics. He was known to be a charitable man, needy people often came to him at the laboratory for help, which he would usually give them in an unobtrusive way. David Kendall writes [ 14 ]:- Telephone traffic is now said to have an intensity of m erlangs if m calls are expected during an interval equal to the mean holding-time. The quantity thus measured is of course dimensionless, and the erlang is to be compared with the octave, the stellar magnitude and the decibel in describing the mode of calculation rather than the unit of measurement in the usual sense of physics.

Erlang has also been honoured by Ericsson Communications when it named the Erlang programming language after him. This programming language is mainly used for large industrial real-time systems. His name is also given to the statistical probability distribution that he used in his work.

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## Agner Krarup Erlang (1878 - 1929)

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. He won a scholarship to the University and majored in mathematics , and also studied astronomy , physics and chemistry. He graduated in with an MA and over the next 7 years taught at several schools. 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. He would conduct measurements and was prepared to climb into street manholes to do so.

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## Agner Krarup Erlang

Jump to: navigation , search Copyright notice This article Agner Krarup Erlang was adapted from an original article by C. 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.

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## Erlang, Agner Krarup

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