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{{Use American English|date = January 2019}}
{{Short description|Queue with Markov (Poisson) arrival process, general service time distribution and multiple (k) servers}}
In [[queueing theory]], a discipline within the mathematical [[probability theory|theory of probability]], an '''M/G/k queue''' is a queue model where arrivals are '''M'''arkovian (modulated by a [[Poisson process]]), service times have a '''G'''eneral [[probability distribution|distribution]] and there are ''k'' servers. The model name is written in [[Kendall's notation]], and is an extension of the [[M/M/c queue]], where service times must be [[exponential distribution|exponentially distributed]] and of the [[M/G/1 queue]] with a single server. Most performance metrics for this queueing system are not known and remain an [[open problem]].<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>
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However, it is known that no approximation using only the first two moments can be accurate in all cases.<ref name="gbdz">{{Cite journal | last1 = Gupta | first1 = V. | last2 = Harchol-Balter | first2 = M. |author2-link=Mor Harchol-Balter| last3 = Dai | first3 = J. G. | last4 = Zwart | first4 = B. | title = On the inapproximability of M/G/K: Why two moments of job size distribution are not enough | doi = 10.1007/s11134-009-9133-x | journal = [[Queueing Systems]]| volume = 64 | pages = 5 | year = 2009 | url = http://repository.cmu.edu/cgi/viewcontent.cgi?article=1867&context=compsci| pmid = | pmc = }}</ref>
A [[Markov–Krein]]
==Inter-departure times==
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