Agner Krarup Erlang (1 January 1878 – 3 February 1929) was a

Danish Danish may refer to: * Something of, from, or related to the country of Denmark People * A national or citizen of Denmark, also called a "Dane," see Demographics of Denmark * Culture of Denmark * Danish people or Danes, people with a Danish a ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

statistician A statistician is a person who works with theoretical or applied statistics. The profession exists in both the private and public sectors. It is common to combine statistical knowledge with expertise in other subjects, and statisticians may wor ...

and

engineer Engineers, as practitioners of engineering, are professionals who invent, design, analyze, build and test machines, complex systems, structures, gadgets and materials to fulfill functional objectives and requirements while considering the l ...

, who invented the fields of traffic engineering and

queueing theory Queueing theory is the mathematical study of waiting lines, or queues. A queueing model is constructed so that queue lengths and waiting time can be predicted. Queueing theory is generally considered a branch of operations research because the ...

. By the time of his relatively early death at the age of 51, Erlang had created the field of telephone networks analysis. His early work in scrutinizing the use of local, exchange and trunk telephone line usage in a small community to understand the theoretical requirements of an efficient network led to the creation of the

Erlang formula The erlang (symbol E) is a dimensionless unit that is used in telephony as a measure of offered load or carried load on service-providing elements such as telephone circuits or telephone switching equipment. A single cord circuit has the capaci ...

, which became a foundational element of modern

telecommunication Telecommunication is the transmission of information by various types of technologies over wire, radio, optical, or other electromagnetic systems. It has its origin in the desire of humans for communication over a distance greater than that fe ...

network studies.

Life

Erlang was born at Lønborg, near

Tarm Tarm is a small railway town with a population of 4,010 (1 January 2022)Jutland Jutland ( da, Jylland ; german: Jütland ; ang, Ēota land ), known anciently as the Cimbric or Cimbrian Peninsula ( la, Cimbricus Chersonesus; da, den Kimbriske Halvø, links=no or ; german: Kimbrische Halbinsel, links=no), is a peninsula of ...

. He was the son of a schoolmaster, and a descendant of

Thomas Fincke Thomas Fincke (6 January 1561 – 24 April 1656) was a Danish mathematician and physicist, and a professor at the University of Copenhagen for more than 60 years. Biography Thomas Jacobsen Fincke was born in Flensburg in Schleswig. Fincke was ...

on his mother's side. At age 14, he passed the Preliminary Examination of the

University of Copenhagen The University of Copenhagen ( da, Københavns Universitet, KU) is a prestigious public university, public research university in Copenhagen, Copenhagen, Denmark. Founded in 1479, the University of Copenhagen is the second-oldest university in ...

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

entrance examination in 1896, and passed with distinction. He won a scholarship to the University and majored in

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, and also studied

astronomy Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

and

chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...

. He graduated in 1901 with an MA and over the next 7 years taught at several schools. He maintained his interest in mathematics, and received an award for a paper that he submitted to the University of Copenhagen. He was a member of the Danish Mathematicians' Association (DMF) and through this met amateur mathematician Johan Jensen, the Chief Engineer of the

Copenhagen Telephone Company Copenhagen ( or .; da, København ) is the capital and most populous city of Denmark, with a proper population of around 815.000 in the last quarter of 2022; and some 1.370,000 in the urban area; and the wider Copenhagen metropolitan ar ...

(

KTAS KTAS (channel 33) is a Spanish=language independent television station licensed to San Luis Obispo, California, United States, serving the Central Coast of California. Owned by Raul and Consuelo Palazuelos, the station maintains studios on Carm ...

in Danish), an offshoot of the

International Bell Telephone Company The International Bell Telephone Company (IBTC) of Brussels, Belgium, was created in 1879 by the Bell Telephone Company of Boston, Massachusetts, a precursor entity to the American Telephone and Telegraph Company (AT&T), initially to sell imported ...

. Erlang worked for the CTC (KTAS) from 1908 for almost 20 years, until his death in Copenhagen after an abdominal operation. He was an associate of the British

Institution of Electrical Engineers The Institution of Electrical Engineers (IEE) was a British professional organisation of electronics, electrical, manufacturing, and Information Technology professionals, especially electrical engineers. It began in 1871 as the Society of Te ...

Contributions

While working for the CTC, Erlang was presented with the classic problem of determining how many circuits were needed to provide an acceptable telephone service. His thinking went further by finding how many telephone operators were needed to handle a given volume of calls. Most

telephone exchange A telephone exchange, telephone switch, or central office is a telecommunications system used in the public switched telephone network (PSTN) or in large enterprises. It interconnects telephone subscriber lines or virtual circuits of digital syst ...

s then used human operators and cord boards to switch

telephone call A telephone call is a connection over a telephone network A telephone network is a telecommunications network that connects telephones, which allows telephone calls between two or more parties, as well as newer features such as fax and interne ...

s by means of jack plugs. Out of necessity, Erlang was a hands-on researcher. He would conduct measurements and was prepared to climb into street

manhole A manhole (utility hole, maintenance hole, or sewer hole) is an opening to a confined space such as a shaft, utility vault, or large vessel. Manholes are often used as an access point for an underground public utility, allowing inspection, m ...

s to do so. He was also an expert in the history and calculation of the numerical tables of mathematical functions, particularly

logarithm In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number to the base is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 o ...

s. He devised new calculation methods for certain forms of tables. He developed his theory of telephone traffic over several years. His significant publications include: * 1909 – "The Theory of Probabilities and Telephone Conversations", which proves that the

Poisson distribution In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known co ...

applies to random telephone traffic. * 1917 – "Solution of some Problems in the Theory of Probabilities of Significance in Automatic Telephone Exchanges", which contains his classic formulae for call loss and waiting time. * 1920 - "Telephone waiting times", which is Erlang's principal work on waiting times, assuming constant holding times. 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. One

Bell Telephone Laboratories Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984), then AT&T Bell Laboratories (1984–1996) and Bell Labs Innovations (1996–2007), is an American industrial research and scientific development company owned by mul ...

researcher is said to have learned Danish to study them. The British Post Office accepted his formula as the basis for calculating circuit facilities. In 1946, the

CCITT The ITU Telecommunication Standardization Sector (ITU-T) is one of the three sectors (divisions or units) of the International Telecommunication Union (ITU). It is responsible for coordinating standards for telecommunications and Information Commu ...

named the international unit of telephone traffic the " erlang". A statistical distribution and programming language listed below have also been named in his honour.

References

{{DEFAULTSORT:Erlang, Agner Krarup 20th-century Danish mathematicians Danish engineers Electrical engineers Queueing theorists Danish statisticians Danish business theorists 1878 births 1929 deaths People from Ringkøbing-Skjern Municipality

Life

Contributions

See also

References