Agner Krarup Erlang | Biography

Erlang is regarded as the founder of queuing theory and of operations research. His formulas, designed and published in 1917, enabled early telephone switching systems to become operational. These formulas give the probability that a user will encounter a busy signal instead of a dial tone, or the length of waiting time for a system that can hold calls. They are used to calculate the number of circuits needed to give a specified level of service. Erlang's formulas may be applied to any system with a limited number of servers and customers that arrive at random times.

Agner Krarup Erlang was born on January 1, 1878, at Lonborg, near Tarm in Jutland, the mainland of Denmark. His parents were Hans Nielson Erlang, the parish clerk and schoolmaster, and Magdalene Krarup Erlang. Many of his mother's family were clergymen. Erlang had an older brother, Frederik, and two younger sisters, Marie and Ingeborg. Erlang studied at his father's school, then was tutored at home by his father and the assistant school teacher, P.J. Pedersen, for his preliminary examination. Erlang passed with distinction, although at age 14 he needed special permission to take the examination. Erlang served as assistant teacher at his father's school for two years, then stayed for two years with M. Funch, in Hillerod, to prepare for his university examination at the Frederikborg Grammar-school. In 1896, Erlang passed this examination and attended the University of Copenhagen. He studied mathematics, astronomy, physics and chemistry, and completed an M.A. in 1901.

After graduation, Erlang taught at a number of schools. He joined a Christian students' association where he met his friend H.C. Nybolle, who later became a professor of statistics at Copenhagen University. Erlang also was a member of the Mathematics Association. In 1904, he won a distinction for his answer to the University mathematics prize question about Christiaan Huygen's methods of solving infinitesimal problems. At the Mathematics Association, Erlang met J.L.W.V. Jensen of the Copenhagen Telephone Company. Jensen introduced Erlang to Fr. Johannsen, his managing director, who hired Erlang in 1908 as scientific collaborator and leader of the laboratory.

Johannsen had already published two essays on the barred access and waiting time problems inherent in telephone systems. He suggested that Erlang study these problems further. Erlang demonstrated in a 1909 paper that the number of calls to arrive during a period of time follows a Poisson distribution, and treated the problem of waiting time when holding times are constant, for the simplest case of one circuit. In 1917, Erlang's most important paper was published, in which he gives his B-formula for the probability of barred access, or a busy signal, for a group of circuits, and formulas for waiting time. His proof of the B-formula is based on the idea of statistical equilibrium, that transitions between pairs of states are in balance. In 1922 and 1926 Erlang published lectures on the contents of his earlier papers; the 1922 paper containing a new interconnection formula. In 1924 he wrote about a principal of K. Moe for deciding whether to add circuits to large or small groups of circuits. Erlang often presented his results as tables as well as formulas. He wrote several papers about producing accurate tables and published tables produced by his methods.

Erlang also wrote about cables, the induction coil in a telephone, and about a device for measuring transmission in cables. Also interested in more theoretical matters, Erlang used the idea of statistical equilibrium to prove Maxwell's Law in the kinetic theory of gases, and wrote short papers on geometry and on proportional representation in voting.

Erlang, who never married, lived with his sister Ingeborg in Copenhagen. He had a large collection of books on science and mathematics. Erlang's sister founded a home for mentally ill women, which he supported generously. Erlang died after a brief abdominal illness on February 3, 1929, at 51 years of age.

In addition to his widely used formulas, Erlang's name is attached to the gamma probability distribution. In 1946, the C.C.I.F. (La comite consultatif des communications telephoniques a grande distance) adopted the Erlang as the unit of telephone traffic. The average traffic in Erlangs is the sum of the lengths of calls originating during an interval of time, divided by the length of the time interval. ERLANG is also the name of a programming language which was developed at Ericsson and Ellemtel Computer Science Laboratories for programming telecommunications switching systems.