Editing Erlang (unit) (section)

{{Short description|Load measure in telecommunications}}
{{Infobox unit
| bgcolor      = 
| name         = erlang
| image        = 
| caption      = 
| standard     = [[ITU Telecommunication Standardization Sector]] standards
| quantity     = [[offered load]], carried load
| symbol       = E
| symbol2      = 
| namedafter   = [[Agner Krarup Erlang]]
| extralabel   = 
| extradata    = 
| units1 = 
| inunits1     = 
}}

<!--Unit-->The '''erlang''' (symbol '''E'''<ref>{{cite web| url = http://www.unc.edu/~rowlett/units/dictE.html| title = How Many? A Dictionary of Units of Measurement| access-date = 2008-04-20| archive-date = 2017-06-18| archive-url = https://web.archive.org/web/20170618144237/http://www.unc.edu/~rowlett/units/dictE.html| url-status = dead}}</ref>) 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 capacity to be used for 60 minutes in one hour. Full utilization of that capacity, 60 minutes of traffic, constitutes 1 erlang.<ref>{{cite book | title = Fundamentals of Telecommunications | page = 57 | first = Roger L. | last = Freeman | publisher = John Wiley | year = 2005 | isbn = 978-0471710455}}</ref>

<!--Traffic measurements of a telephone circuit-->Carried traffic in erlangs is the average number of concurrent calls measured over a given period (often one hour), while offered traffic is the traffic that would be carried if all call-attempts succeeded. How much offered traffic is carried in practice will depend on what happens to unanswered calls when all servers are busy.

<!--Erlang's analysis-->The [[CCITT]] named the international unit of telephone traffic the erlang in 1946 in honor of [[Agner Krarup Erlang]].<ref name=ccitt1946>{{Citation |contribution=Traffic handled on a circuit or group of circuits |title=CCIF - XIVth Plenary Assembly |publisher=International Telephone Consultative Committee |place=Montreux, 26–31 October |year=1946 |pages=60–62 |hdl=11.1004/020.1000/4.237.43.en.1001 |hdl-access=free}}</ref><ref name=brockmeyer1948>{{citation |last1=Brockmeyer |first1=E. |last2=Halstrøm |first2=H. L. |last3=Jensen |first3=Arne |title=The life and works of A.K. Erlang |date=1948 |series=Transactions of the Danish Academy of Technical Sciences |volume=2 |publisher=Akademiet for de Tekniske Videnskaber  |url=http://oldwww.com.dtu.dk/teletraffic/erlangbook/pp001-278.pdf |url-status=dead |archive-date= July 19, 2011 |archive-url=https://web.archive.org/web/20110719122546/http://oldwww.com.dtu.dk/teletraffic/erlangbook/pp001-278.pdf |language=en}}{{rp |pages=19–22}}</ref> In Erlang's analysis of efficient telephone line usage, he derived the formulae for two important cases, Erlang-B and Erlang-C, which became foundational results in [[teletraffic engineering]] and [[queueing theory]]. His results, which are still used today, relate quality of service to the number of available servers. <!--Calculating offered traffic-->Both formulae take offered load as one of their main inputs (in erlangs), which is often expressed as call arrival rate times average call length.

<!--Erlang B formula-->A distinguishing assumption behind the Erlang B formula is that there is no queue, so that if all service elements are already in use then a newly arriving call will be blocked and subsequently lost. The formula gives the probability of this occurring. <!--Erlang C formula-->In contrast, the Erlang C formula provides for the possibility of an unlimited queue and it gives the probability that a new call will need to wait in the queue due to all servers being in use. <!--Limitations of the Erlang formulae-->Erlang's formulae apply quite widely, but they may fail when congestion is especially high causing unsuccessful traffic to repeatedly retry. <!--Extended Erlang B-->One way of accounting for retries when no queue is available is the Extended Erlang B method.