Agner Krarup Erlang (January 1, 1878–February 3, 1929) was a Danish mathematician, statistician, and engineer who invented the fields of queueing theory and traffic engineering. January 1 is the first day of the calendar year in both the Julian and Gregorian calendars. ... 1878 was a common year starting on Tuesday (see link for calendar). ... February 3 is the 34th day of the year in the Gregorian Calendar. ... 1929 was a common year starting on Tuesday (link will take you to calendar). ... A mathematician is a person whose area of study and research is mathematics. ... For Wikipedia statistics, see m:Statistics Statistics is the science and practice of developing human knowledge through the use of empirical data expressed in quantitative form. ... An engineer may be someone who practices the engineering profession, or the driver of a rail locomotive. ... Queueing theory (spelled queuing theory in the United States) is the mathematical study of waiting lines (or queues). ... The term traffic engineering is used in more than one sense. ...

Erlang was born at Lonborg (Lønborg), near Tarm, in Jutland. He was the son of a schoolmaster and with his maternal mathematical ancestor Thomas Fincke, he demonstrated his potential from an early age by being able to read books upside down. He passed the Preliminary Examination offered by the University of Copenhagen, with distinction, at age 14, after receiving dispensation to sit because he was younger than the usual minimum age. Jutland Peninsula Jutland (Danish: Jylland, German: Jütland) is a peninsula in northern Europe that forms the continental part of Denmark and a northern part of Germany, dividing the North Sea from the Baltic Sea. ... Thomas Fincke (January 6, 1561 - April 24, 1656) was a Danish mathematician and physicist, and a professor at the University of Copenhagen for more than sixty years. ... University of Copenhagen The University of Copenhagen (Danish: Københavns Universitet) is the oldest and largest university and research institution in Copenhagen, Denmark. ...

For the next two years he taught alongside his father.

With a distant relative providing free board and lodgings, he prepared for and sat the University of Copenhagen entrance examination in 1896, which he passed with distinction. He won a scholarship to the University of Copenhagen and majored in mathematics, but also studied astronomy, physics and chemistry. He graduated in 1901 with an MA and subsequently taught at several schools over the next 7 years. He maintained his interest in mathematics and received an award for one paper that he submitted to the University of Copenhagen. City nickname: none Location in Denmark Area  - Total  - Water 526 km² xxx km² xx% Population  - City (2004)  - Metropolitan  - Density 502,204 1,116,979 954/km&sup2 [including water] xxx/km&sup2 [land only] Time zone Eastern: UTC+1 Latitude Longitude 55°43 N 12°34 W Copenhagen (Danish: K... 1896 was a leap year starting on Wednesday (see link for calendar). ... History Main article: History of mathematics In addition to recognizing how to count concrete objects, prehistoric peoples also recognized how to count abstract quantities, like time -- days, seasons, years. ... Astronomy (Greek: αστρονομία = άστρον + νόμος, literally, law of the stars) is the science involving the observation and explanation of events occurring beyond the Earth and its atmosphere. ... Physics (from the Greek, φυσικός (phusikos), natural, and φύσις (phusis), nature) is the science of nature in the broadest sense. ... Chemistry (in Greek: χημεία) is the science of matter and its interactions with energy and itself (see physics, biology). ... 1901 was a common year starting on Tuesday (see link for calendar). ...

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, an offshoot of the International Bell Telephone Company. Erlang subsequently obtained employment with the company in 1908. He worked for the Copenhagen Telephone Company for almost 20 years, until his death in Copenhagen after an abdominal operation. Johan Ludwig William Valdemar Jensen, mostly known as Johan Jensen, (May 8, 1859—March 5, 1925) was a Danish mathematician and engineer. ... The Bell System is an informal name given to the US telecommunications company American Telephone & Telegraph Company (AT&T) before AT&T divested its local exchange telephone service operating companies on January 1, 1984. ... 1908 is a leap year starting on Wednesday (link will take you to calendar). ...

It was while working for the Copenhagen Telephone Company that Erlang was presented with the classic problem of determining how many circuits were needed to provide an acceptable telephone service. However, his thinking went further in that he also realised that mathematics could be applied to assess how many operators were needed to handle a given volume of telephone calls. At that time most telephone exchanges 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 his own measurements and was prepared to climb into street manholes to do so.

Erlang was also an expert in both the history and calculation of the numerical tables of mathematical functions, particularly logarithms. He devised new calculation methods for certain forms of mathematical tables. In mathematics, a logarithm of x with base b may be defined as the following: for the equation bn = x, the logarithm is a function which gives n. ...

He developed his theory concerning 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. So that his papers could be studied in the original Danish, one researcher from Bell Telephone Laboratories learnt the language. In statistics and probability theory, the Poisson distribution is a discrete probability distribution (discovered by Siméon-Denis Poisson (1781-1840) and published, together with his probability theory, in 1838 in his work Recherches sur la probabilité des jugements en matières criminelles et matière civile) belonging to certain random variables N... Bell Telephone Laboratories or Bell Labs was originally the research and development arm of the United States Bell System, and was the premier corporate facility of its type, developing a range of revolutionary technologies from telephone switches to specialized coverings for telephone cables, to the transistor. ...

The British Post Office accepted his formula as the basis for calculating circuit facilities. BT Group plc (which trades as just BT, and is commonly known as, British Telecom or British Telecommunications) is the privatised former British state telecommunications operator. ...

He was an associate of the British Institution of Electrical Engineers. Not to be confused with the Institute of Electrical and Electronics Engineers. ...

The unit, distribution and language listed below have all been named in his honour.

See also

• 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

The dimensionless unit named the erlang is a statistical measure of telecommunications traffic used in telephony. ... The Erlang distribution is a probability distribution developed by A. K. Erlang to predict waiting times in queueing systems, particularly in the case of telephone traffic engineering. ... The word probability derives from the Latin probare (to prove, or to test). ... Erlang is a general-purpose concurrent programming language and runtime system. ... Ericsson () is a Swedish telecommunications equipment manufacturer, founded in 1876 as a telegraph equipment repair shop by Lars Magnus Ericsson. ... Queueing theory (spelled queuing theory in the United States) is the mathematical study of waiting lines (or queues). ... For another meaning of the term traffic engineering, please see transport traffic engineering. ...

External links

• Biography - from St.Andrews University (http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Erlang.html)
• Biography - from Millennium Mathematics Project (http://pass.maths.org.uk/issue2/erlang/index.html)
• Erlang Distribution (http://www.xycoon.com/erlang.htm)
• An Introduction to Erlang B and Erlang C by Ian Angus (http://www.angustel.ca/reports/Erlang%20B%20&%20C.PDF) (PDF Document - Has terms and formulae plus biography)
• "Telefon-Ventetider. Et Stykke Sandsynlighedsregning" (http://runeberg.org/matetids/1920b/0029.html), in Matematisk Tidsskrift, B, 1920 (a paper on telephone waiting times, in Danish, digitized by Project Runeberg)