Editing Queueing theory (section)

{{short description|Mathematical study of waiting lines, or queues}}
{{redirect|First come, first served|the Kool Keith album|First Come, First Served}}

[[File:ServidorParalelo.jpg|thumb|right|[[#Queueing networks|Queue networks]] are systems in which single queues are connected by a routing network. In this image, servers are represented by circles, queues by a series of rectangles and the routing network by arrows. In the study of queue networks one typically tries to obtain the [[equilibrium distribution]] of the network, although in many applications the study of the [[transient state]] is fundamental.]]

'''Queueing theory''' is the mathematical study of [[Queue area|waiting lines]], or [[wikt:queue|queues]].<ref name="sun">{{cite book | title = Probability, Statistics and Queueing Theory | first = V. | last = Sundarapandian | publisher = PHI Learning | year = 2009 | chapter = 7. Queueing Theory | isbn = 978-81-203-3844-9 }}</ref> A queueing model is constructed so that queue lengths and waiting time can be predicted.<ref name="sun" /> Queueing theory is generally considered a branch of [[operations research]] because the results are often used when making business decisions about the resources needed to provide a service.

Queueing theory has its origins in research by [[Agner Krarup Erlang]], who created models to describe the system of incoming calls at the Copenhagen Telephone Exchange Company.<ref name="sun" /> These ideas were seminal to the field of [[teletraffic engineering]] and have since seen applications in [[telecommunications]], [[traffic engineering (transportation)|traffic engineering]], [[computing]],<ref>{{cite web
  | last = Lawrence W. Dowdy, Virgilio A.F. Almeida
  | first = Daniel A. Menasce
  | title = Performance by Design: Computer Capacity Planning by Example
  | url = http://www.cs.gmu.edu/~menasce/perfbyd/
  | access-date = 2009-07-08
  | archive-date = 2016-05-06
  | archive-url = https://web.archive.org/web/20160506025515/http://cs.gmu.edu/~menasce/perfbyd/
  | url-status = live
  }}</ref> [[project management]], and particularly [[industrial engineering]], where they are applied in the design of factories, shops, offices, and hospitals.<ref>{{Cite news
  | first = Kira
  | last = Schlechter
  | title = Hershey Medical Center to open redesigned emergency room
  | newspaper = The Patriot-News
  | date = March 2, 2009
  | url = http://www.pennlive.com/midstate/index.ssf/2009/03/hershey_med_to_open_redesigned.html
  | access-date = March 12, 2009
  | archive-date = June 29, 2016
  | archive-url = https://web.archive.org/web/20160629151917/http://www.pennlive.com/midstate/index.ssf/2009/03/hershey_med_to_open_redesigned.html
  | url-status = live
  }}</ref><ref>{{cite book |url= https://openaccess.city.ac.uk/id/eprint/2309/ |archive-url= https://web.archive.org/web/20210907100556/https://openaccess.city.ac.uk/id/eprint/2309/ |archive-date= September 7, 2021 |access-date= 2008-05-20 |author= Mayhew, Les |author2= Smith, David |date= December 2006 |title= Using queuing theory to analyse completion times in accident and emergency departments in the light of the Government 4-hour target |publisher= [[Cass Business School]] |isbn= 978-1-905752-06-5 }}</ref>