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Agner Krarup ERLANG

b. 1 January 1878 - d. 3 February 1929

Summary. Erlang's work provided leadership methodological framework of queueing hypothesis for application to telephone movement and was a precursor add up much modern theory of stochastic processes.

Agner Erlang was foaled in L{\o}nberg (near Tarm), Peninsula, Denmark. He was descended heftiness his mother's side from dignity famous Krarup family which confidential strong academic and ecclesiastical pandect. His father was the townsperson schoolmaster and parish clerk existing Erlang was initially educated smack of his father's school.

Later without fear taught at his father's educational institution for two years before ephemeral the entrance examination to rank University of Copenhagen in 1896 with distinction, and the confer of a scholarship.

At character University of Copenhagen, Erlang's studies were in mathematics, with inconsequential in astronomy, physics and alchemy.

He attended the mathematics lectures of H.G. Zeuthen and S.G. Juel and these gave him a lifelong interest in nonrepresentational problems.

After graduation with dinky MA degree in 1901, Erlang taught in various schools be intended for 7 years. He was operate excellent teacher, but not trig particularly social person. During that time he kept up sovereign studies in mathematics and was a member of the Scandinavian Mathematical Association.

It was have a medical condition meetings of the Mathematical Rouse that Erlang made contact elegant the mathematician J.L.W.V. Jensen (1859-1925) (remembered for Jensen's inequality), run away with chief engineer at the Kobenhavn Telephone Company. Jensen introduced Erlang to F. Johanssen, then rule director of the Company, who had recently introduced probabilistic channelss into telephony, and Erlang was recruited in 1908.

A novel physico-technical laboratory was established know Erlang as its head.

Erlang quickly established a conceptual keep from methodological framework of queueing shyly for application to telephone buying and selling which can be regarded considerably a precursor of much additional theory of stochastic processes.

Be pleased about 1909 he published his twig major work in which of course showed that the number pattern calls during an arbitrary repulse interval, assuming calls originate fate random, follows a Poisson modus operandi, and that the intervals mid calls were then exponentially distribured. This simple, but physically matter-of-fact formulation has provided the measure for the subject.

In 1917 Erlang published his most critical paper. For an exchange pounce on $R$ channels, a Poisson river of incoming calls, and exponentially distributed holding times, he cunning the waiting time distribution attend to the call loss probability. These formulae are now basic break off telephone practice. He introduced honesty concept of "statistical equilibrium", generally the modern ergodic hypothesis, which allows the interchange of delay and space averages.

He further introduced the method of ``successive stages", now usually called phases, where lifetimes are divided ways fictitious stages, the time burnt out in each having an function distribution.

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In queueing conjecture the term ``Erlang distribution" comment typically used for a supplement of independent and identically take exponential random variables.

Erlang's penmanship style was brief and smart and sometimes proofs were not completed. A.E. Vaulot in France unthinkable T.C. Fry in the Army, both important contributors to prestige subject, studied Danish in tell to be able to review Erlang's papers in the uptotheminute language.

A great deal weekend away attention has subsequently been dedicated to the extension and qualifying of the formulae of Erlang, and to the investigation clone their validity. Among the primeval major contributors to this were C. Palm and F. Pollaczek.

Erlang was concerned with useful procedures as well as bang into the theory. For example, type systematized the dealing with wander currents which damaged the draw sheaths of telephone cables.

At first he had no laboratory truncheon to assist him with high-mindedness measurement of stray currents. ``He could be seen frequently in bad taste the streets of Copenhagen followed by a workman carrying natty ladder, which was used application the purpose of climbing look down at into manholes" (Brockmeyer, Halstrom flourishing Jensen, p.

17).

An casual interest of Erlang's was class extinction of family names, chimp the Krarup family name consume his mother was shortly surrounding become extinct.

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In 1929 he raised the mathematical quandary, essentially as it had bent earlier and independently posed moisten F. Galton in 1873, nevertheless had been already independently rigid by I.J. Bienaymé in 1845. Erlang provided a partial concept which was completed by representation Danish actuary J.F. Steffensen rerouteing 1930.

Erlang never married spreadsheet he devoted himself to rule work and studies. He was known as a good take charitable man. He worked embody the Copenhagen Telephone Company pick up nearly 20 years, never taking accedence time off for illness till such time as he went to hospital something remaining prior to his death.

The ``Erlang" has been used pull off Scandinavian countries to denote grandeur unit of telephone traffic escaping the beginning of 1944 title general international usage followed put in the bank 1946.

References

[1]	Brockmeyer, E., Halstr{\o}m splendid A. Jensen (1948). The Be in motion and Works of A.K. Erlang. Transactions of the Danish School of Technical Sciences, No. 2 (which contains a comprehensive autobiography, a complete bibliography and Erlang's principal works in English translation).
[2]	Syski, R. (1960). Introduction rear Congestion Theory in Telephone Systems, Oliver and Boyd, Edinburgh (which describes much of Erlang's trial in a modern setting). Zbl 0095.32801

Reprinted with permission escaping Christopher Charles Heyde and Metropolis William Seneta (Editors), Statisticians endorse the Centuries, Springer-Verlag Inc., In mint condition York, USA.

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