M/D/1 queue: Difference between revisions

Revision as of 20:18, 3 September 2015

Revision as of 02:51, 31 March 2016

Line 1:

In [[queueing theory]], a discipline within the mathematical [[probability theory|theory of probability]], an '''M/D/1 queue''' represents the queue length in a system having a single server, where arrivals are determined by a [[Poisson process]] and job service times are fixed (deterministic). The model name is written in [[Kendall's notation]].<ref>{{Cite journal | last1 = Kendall | first1 = D. G. | authorlink1 = David George Kendall| title = Stochastic Processes Occurring in the Theory of Queues and their Analysis by the Method of the Imbedded Markov Chain | doi = 10.1214/aoms/1177728975 | jstor = 2236285| journal = The Annals of Mathematical Statistics | volume = 24 | issue = 3 | pages = 338 | year = 1953| url = http://projecteuclid.org/euclid.aoms/1177728975 | pmid = | pmc = }}</ref> [[Agner Krarup Erlang]] first published on this model in 1909, starting the subject of [[queueing theory]].<ref>{{Cite journal | last1 = Kingman | first1 = J. F. C. | authorlink1 = John Kingman | title = The first Erlang century—and the next | journal = [[Queueing Systems]] | volume = 63 | pages = 3–4 | year = 2009 | doi = 10.1007/s11134-009-9147-4}}</ref><ref>{{cite journal | title = The theory of probabilities and telephone conversations | journal = Nyt Tidsskrift for Matematik B | volume = 20 | pages = 33–39 | first = A. K. | last = Erlang | url=http://oldwww.com.dtu.dk/teletraffic/erlangbook/pps131-137.pdf |year=1909 http|deadurl=yes |archiveurl=https://web.archive.org/web/20111001212934/http://oldwww.com.dtu.dk/teletraffic/erlangbook/pps131-137.pdf |archivedate=October year1, =2011 1909}}</ref> An extension of this model with more than one server is the [[M/D/c queue]].

==Model definition==