Agner Krarup Erlang
Encyclopedia
Agner Krarup Erlang was a Danish
mathematician
, statistician
and engineer
, who invented the fields of traffic engineering
and queueing theory
.
By the time of his relatively early death at the age of 51, Erlang 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, which became a foundational element of present day telecommunication network
studies.
, in Jutland
. He was the son of a schoolmaster, and a descendant of Thomas Fincke
on his mother's side. 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.
A distant relative provided free board and lodging, and Erlang prepared for and took the University of Copenhagen
entrance examination in 1896, and passed with distinction. He won a scholarship to the University and majored in mathematics
, and also studied astronomy
, physics
and chemistry
. He graduated in 1901 with an MA and over the next 7 years taught at several schools including the Milton House School of Statistics and the St John's Centre for Resource Planning. 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 (TBMI) and through this met amateur mathematician Johan Jensen, the Chief Engineer of the Copenhagen Telephone Company (KTAS in Danish), an offshoot of the International Bell Telephone Company
. 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
.
s were needed to handle a given volume of calls. Most telephone exchange
s then used human operators and cord boards
to switch telephone call
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
s to do so. He was also an expert in the history and calculation of the numerical tables of mathematical functions, particularly logarithm
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:
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 researcher from Bell Telephone Laboratories is said to have learned Danish to study them.
The British Post Office accepted his formula as the basis for calculating circuit facilities.
A unit of measurement, statistical distribution and programming language listed below have been named in his honour.
Denmark
Denmark is a Scandinavian country in Northern Europe. The countries of Denmark and Greenland, as well as the Faroe Islands, constitute the Kingdom of Denmark . It is the southernmost of the Nordic countries, southwest of Sweden and south of Norway, and bordered to the south by Germany. Denmark...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, statistician
Statistician
A statistician is someone who works with theoretical or applied statistics. The profession exists in both the private and public sectors. The core of that work is to measure, interpret, and describe the world and human activity patterns within it...
and engineer
Engineer
An engineer is a professional practitioner of engineering, concerned with applying scientific knowledge, mathematics and ingenuity to develop solutions for technical problems. Engineers design materials, structures, machines and systems while considering the limitations imposed by practicality,...
, who invented the fields of traffic engineering
Teletraffic engineering
Telecommunications traffic engineering, teletraffic engineering, or traffic engineering is the application of traffic engineering theory to telecommunications...
and queueing theory
Queueing theory
Queueing theory is the mathematical study of waiting lines, or queues. The theory enables mathematical analysis of several related processes, including arriving at the queue, waiting in the queue , and being served at the front of the queue...
.
By the time of his relatively early death at the age of 51, Erlang 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, which became a foundational element of present day telecommunication network
Telecommunication
Telecommunication is the transmission of information over significant distances to communicate. In earlier times, telecommunications involved the use of visual signals, such as beacons, smoke signals, semaphore telegraphs, signal flags, and optical heliographs, or audio messages via coded...
studies.
Life
Erlang was born at Lonborg (Lønborg), near TarmTarm
Tarm is a small railway town with a population of 4,131 in west Denmark, southwest of Herning....
, in Jutland
Jutland
Jutland , historically also called Cimbria, is the name of the peninsula that juts out in Northern Europe toward the rest of Scandinavia, forming the mainland part of Denmark. It has the North Sea to its west, Kattegat and Skagerrak to its north, the Baltic Sea to its east, and the Danish–German...
. He was the son of a schoolmaster, and a descendant of Thomas Fincke
Thomas Fincke
Thomas Fincke was a Danish mathematician and physicist, and a professor at the University of Copenhagen for more than 60 years.Fincke was born in Flensburg, Schleswig and died in Copenhagen...
on his mother's side. At age 14, he passed the Preliminary Examination of the University of Copenhagen
University of Copenhagen
The University of Copenhagen is the oldest and largest university and research institution in Denmark. Founded in 1479, it has more than 37,000 students, the majority of whom are female , and more than 7,000 employees. The university has several campuses located in and around Copenhagen, with the...
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 University of Copenhagen
Copenhagen
Copenhagen is the capital and largest city of Denmark, with an urban population of 1,199,224 and a metropolitan population of 1,930,260 . With the completion of the transnational Øresund Bridge in 2000, Copenhagen has become the centre of the increasingly integrating Øresund Region...
entrance examination in 1896, and passed with distinction. He won a scholarship to the University and majored in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, and also studied astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
, physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
and chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
. He graduated in 1901 with an MA and over the next 7 years taught at several schools including the Milton House School of Statistics and the St John's Centre for Resource Planning. 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 (TBMI) and through this met amateur mathematician Johan Jensen, the Chief Engineer of the Copenhagen Telephone Company (KTAS in Danish), an offshoot of the International Bell Telephone Company
Bell System
The Bell System was the American Bell Telephone Company and then, subsequently, AT&T led system which provided telephone services to much of the United States and Canada from 1877 to 1984, at various times as a monopoly. In 1984, the company was broken up into separate companies, by a U.S...
. 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
Institution of Electrical Engineers
The Institution of Electrical Engineers was a British professional organisation of electronics, electrical, manufacturing, and Information Technology professionals, especially electrical engineers. The I.E.E...
.
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 operatorTelephone operator
A telephone operator is either* a person who provides assistance to a telephone caller, usually in the placing of operator assisted telephone calls such as calls from a pay phone, collect calls , calls which are billed to a credit card, station-to-station and person-to-person calls, and certain...
s were needed to handle a given volume of calls. Most telephone exchange
Telephone exchange
In the field of telecommunications, a telephone exchange or telephone switch is a system of electronic components that connects telephone calls...
s then used human operators and cord boards
Telephone switchboard
A switchboard was a device used to connect a group of telephones manually to one another or to an outside connection, within and between telephone exchanges or private branch exchanges . The user was typically known as an operator...
to switch telephone call
Telephone call
A telephone call is a connection over a telephone network between the calling party and the called party.-Information transmission:A telephone call may carry ordinary voice transmission using a telephone, data transmission when the calling party and called party are using modems, or facsimile...
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
Manhole
A manhole is an opening used to gain access to sewers or other underground structures, usually for maintenance.Manhole may also refer to:* Manhole , a metal band from Los Angeles* The Manhole, a computer game...
s to do so. He was also an expert in the history and calculation of the numerical tables of mathematical functions, particularly logarithm
Logarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...
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:
- In 1909 - "The Theory of Probabilities and Telephone Conversations" - which proves that the Poisson distributionPoisson distributionIn 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 and/or space if these events occur with a known average rate and independently of the time since...
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. One researcher from Bell Telephone Laboratories is said to have learned Danish to study them.
The British Post Office accepted his formula as the basis for calculating circuit facilities.
A unit of measurement, statistical distribution and programming language listed below have been named in his honour.
See also
- ErlangErlang unitThe erlang is a dimensionless unit that is used in telephony as a statistical measure of offered load or carried load on service-providing elements such as telephone circuits or telephone switching equipment. It is named after the Danish telephone engineer A. K...
- a unit of communication activity - Erlang distribution - a statistical probabilityProbabilityProbability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
distribution - Erlang programming language - developed by EricssonEricssonEricsson , one of Sweden's largest companies, is a provider of telecommunication and data communication systems, and related services, covering a range of technologies, including especially mobile networks...
for large industrial real-time systems - Queueing theoryQueueing theoryQueueing theory is the mathematical study of waiting lines, or queues. The theory enables mathematical analysis of several related processes, including arriving at the queue, waiting in the queue , and being served at the front of the queue...
- Teletraffic engineeringTeletraffic engineeringTelecommunications traffic engineering, teletraffic engineering, or traffic engineering is the application of traffic engineering theory to telecommunications...
External links
- Erlang Distribution
- "Telefon-Ventetider. Et Stykke Sandsynlighedsregning", in Matematisk Tidsskrift, B, 1920 (a paper on telephone waiting times, in Danish, digitized by Project RunebergProject RunebergProject Runeberg is an initiative patterned after Project Gutenberg that publishes freely available electronic versions of books significant to the culture and history of the Nordic countries...
)