M/G/k queue: Difference between revisions

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where ''C'' is the [[coefficient of variation]] of the service time distribution. [[Ward Whitt]] described this approximation as “usually an excellent approximation, even given extra information about the service-time distribution."<ref>{{Cite journal | last1 = Whitt | first1 = W. | author-link1 = Ward Whitt| title = Approximations for the GI/G/m Queue| doi = 10.1111/j.1937-5956.1993.tb00094.x | journal = [[Production and Operations Management]]| volume = 2 | issue = 2 | pages = 114–161 | year = 2009 | url = http://www.columbia.edu/~ww2040/ApproxGIGm1993.pdf}}</ref>
 
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 = 5–48 | year = 2009 | s2cid = 16755599 | url = http://repository.cmu.edu/cgi/viewcontent.cgi?article=1867&context=compsci| citeseerx = 10.1.1.151.5844 }}</ref>
 
A [[Markov–Krein]] characterization has been shown to produce tight bounds on the mean waiting time.<ref>{{Cite journal | last1 = Gupta | first1 = V. | last2 = Osogami | first2 = T. | doi = 10.1007/s11134-011-9248-8 | title = On Markov–Krein characterization of the mean waiting time in M/G/K and other queueing systems | journal = Queueing Systems | volume = 68 | issue = 3–4 | pages = 339 | year = 2011 | s2cid = 35061112 }}</ref>