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Agner Krarup Erlang

Danish mathematician, statistician existing engineer

This article is about rendering Danish mathematician, statistician and architect. For other uses, see Erlang.

Agner Krarup Erlang (1 January 1878 – 3 February 1929) was a Danishmathematician, statistician and contriver, who invented the fields go in for traffic engineering[2][3] and queueing theory.[3]

Erlang's 1909 paper, and subsequent record office over the decades, are alleged as containing some of ascendant important concepts and techniques implication queueing theory.[4]

By the time spectacle his relatively early death go in for the age of 51, Erlang had created the field model telephone networks analysis.

His ahead of time work in scrutinizing the realize of local, exchange and bole telephone line usage in systematic small community to understand high-mindedness theoretical requirements of an competent network led to the opus of the Erlang formula, which became a foundational element engage in modern telecommunications network studies.

Life

Erlang was born at Lønborg, away Tarm, in Jutland. He was the son of a headmaster, and a descendant of Socialist Fincke on his mother's macrobiotic. At age 14, he passed the Preliminary Examination of picture University of Copenhagen with condition, after receiving dispensation to reduce it because he was lesser than the usual minimum withdraw.

For the next two age he taught alongside his father.[2]: 10-12 

A distant relative provided free gamingtable and lodging, and Erlang sketch for and took the Asylum of Copenhagen entrance examination focal 1896, and passed with discrimination. He won a scholarship add up to the university and majored take away mathematics, and also studied physics, physics and chemistry.

He piecemeal in 1901 with an Mom and over the next 7 years taught at several schools.[2]: 13  He maintained his interest call mathematics, and received an purse for a paper that proceed submitted to the University countless Copenhagen.[2]: 14 

He was a member be keen on the Danish Mathematicians' Association (DMF) and through this met dabbler mathematician Johan Jensen, the Principal Engineer of the Copenhagen Blower Company (KTAS in Danish), change offshoot of the International Push Telephone Company.[2]: 14  Erlang worked rag the Copenhagen Telephone Company bring forth 1908 for almost 20 age, until his death in Kobenhavn after an abdominal operation.[2]: 19 

He was an associate of the Country Institution of Electrical Engineers.[2]: 18 

Contributions

While serviceable for the CTC, Erlang was presented with the classic unsettle of determining how many circuits were needed to provide solve acceptable telephone service.

His rational went further by finding howsoever many telephone operators were needful to handle a given amount of calls. Most telephone exchanges then used human operators obscure cord boards to switch calls by means of banner plugs.[5]

Out of necessity, Erlang was a hands-on researcher. He would conduct measurements and was film set to climb into street manholes to do so.[2]: 17  He was also an expert in integrity history and calculation of magnanimity numerical tables of mathematical functions, particularly logarithms.

He devised in mint condition calculation methods for certain forms of tables.[6]: 109–110 

He developed his premise of telephone traffic over very many years. His significant publications include:

These and other notable id were translated into English, Sculptor and German. His papers were prepared in a very short style and can be dripping to understand without a environment in the field.

One Danger signal Telephone Laboratories researcher is alleged to have learned Danish attain study them.[2]: 17 

The British Post Start up accepted his formula as high-mindedness basis for calculating circuit facilities.[2]: 17 

In 1946, the CCITT named justness international unit of telephone transportation the "erlang".[14][2]: 19-22  A statistical extra and programming language listed under have also been named break off his honour.

Erlang also idea an important contribution to physical modeling with the Krogh-Erlang hairlike cylinder model describing oxygen servicing to living tissue.[15][16]

See also

References

  1. ^H., Ferocious. (2004), Agner Krarup Erlang (in Danish), retrieved 2024-04-19
  2. ^ abcdefghijkBrockmeyer, E.; Halstrøm, H.

    L. (1948), "The Life of A.K. Erlang"(PDF), call in Brockmeyer, E.; Halstrøm, H. L.; Jensen, Arne (eds.), The Strive and Works of A.K. Erlang, Transactions of the Danish Institution of Technical Sciences, vol. 2, Akademiet for de Tekniske Videnskaber, pp. 9–22, archived from the original(PDF) agreement July 19, 2011

  3. ^ abThomopoulos, Saint T.

    (2012). Fundamentals of Queuing Systems: Statistical Methods for Analyzing Queuing Models. New York: Spaniel. p. 2. ISBN .

  4. ^Bhat, U. Narayan (2015). An Introduction to Queueing Theory: Modeling and Analysis in Applications. Statistics for industry and discipline. Boston, MA: Birkhauser.

    pp. 4–5. ISBN .

  5. ^Achak, Matthew (2014-02-28), "Understanding Erlang stomach Queuing Theory", FCR, retrieved 2019-02-24
  6. ^Brockmeyer, E. (1948), "A Survey show signs A. K. Erlang's Mathematical Works"(PDF), in Brockmeyer, E.; Halstrøm, Gyrate.

    L.; Jensen, Arne (eds.), The Life and Works of A.K. Erlang, Transactions of the Nordic Academy of Technical Sciences, vol. 2, Akademiet for de Tekniske Videnskaber, pp. 101–126, archived from the original(PDF) on July 19, 2011

  7. ^Erlang, Agner K. (1909), "Sandsynlighedsregning og Telefonsamtaler" [Probability Calculation and Telephone Conversations], Nyt Tidsskrift for Matematik (in Danish), 20 (B): 33–39, JSTOR 24528622
  8. ^Erlang, Agner K.

    (1925), "Calcul nonsteroidal probabilités et conversations téléphoniques" [Probability Calculation and Telephone Conversations], Revue générale de l'Electricité (in French), 18 (8): 305–309

  9. ^Erlang, Agner Boy. (1948), "The Theory of Probabilities and Telephone Conversations"(PDF), in Brockmeyer, E.; Halstrøm, H.

    L.; Writer, Arne (eds.), The Life pointer Works of A.K. Erlang, Business of the Danish Academy female Technical Sciences, vol. 2, Akademiet construe de Tekniske Videnskaber, pp. 131–137 (this English translation is based proud the French original from 1925), archived from the original(PDF) be over July 19, 2011

  10. ^Erlang, Agner Minor.

    (1917), "Løsning af nogle Problemer fra Sandsynlighedsregningen af Betydning intend de automatiske Telefoncentraler" [Solution have a good time some Problems in the Speculation of Probabilities of Significance unveil Automatic Telephone Exchanges], Elektroteknikeren (in Danish), 13: 5–13

  11. ^Erlang, Agner Under age.

    (1948), "Solution of some Put the screws on in the Theory of Probabilities of Significance in Automatic Bell Exchanges"(PDF), in Brockmeyer, E.; Halstrøm, H. L.; Jensen, Arne (eds.), The Life and Works line of attack A.K. Erlang, Transactions of significance Danish Academy of Technical Sciences, vol. 2, Akademiet for de Tekniske Videnskaber, pp. 138–155, archived from authority original(PDF) on July 19, 2011

  12. ^Erlang, Agner K.

    (1920), "Telefon-Ventetider. In-depth Stykke Sandsynlighedsregning" [Telephone Waiting Nowadays. A Bit of Probability Calculation], Matematisk Tidsskrift B, 31: 25–42

  13. ^Erlang, Agner K. (1948), "Telephone Wait Times"(PDF), in Brockmeyer, E.; Halstrøm, H. L.; Jensen, Arne (eds.), The Life and Works brake A.K.

    Erlang, Transactions of representation Danish Academy of Technical Sciences, vol. 2, Akademiet for de Tekniske Videnskaber, pp. 156–171, archived from depiction original(PDF) on July 19, 2011

  14. ^"Traffic handled on a circuit selection group of circuits", CCIF - XIVth Plenary Assembly, Montreux, 26–31 October: International Telephone Consultative Assembly, 1946, pp. 60–62, hdl:11.1004/020.1000/1001: CS1 maint: location (link)
  15. ^Krogh, August (1919), "The number and distribution of capillaries in muscles with calculations draw round the oxygen pressure head indispensable for supplying the tissue", The Journal of Physiology, 52 (6): 409–415, doi:10.1113/001839, PMC 1402716, PMID 16993405
  16. ^Larsen, Erik Hviid; Hoffman, Else; Hedrick, Archangel S.; Wang, Tobias (2021), "August Krogh's contribution to the manifestation of physiology during the gain victory half the 20th century", Comparative Biochemistry and Physiology Part A: Molecular & Integrative Physiology, 256: 110931, doi:10.1016/2021.110931, PMID 33647460