M/G/k queue: Difference between revisions

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==Two servers==

For an M/G/2 queue (the model with two servers) the problem of determining marginal probabilities can be reduced to solving a pair of [[integral equation]]s<ref>{{Cite journal | last1 = Knessl | first1 = C. | last2 = Matkowsky | first2 = B. J. | last3 = Schuss | first3 = Z. | last4 = Tier | first4 = C. | title = An Integral Equation Approach to the M/G/2 Queue | doi = 10.1287/opre.38.3.506 | journal = [[Operations Research (journal)|Operations Research]]| volume = 38 | issue = 3 | pages = 506 | year = 1990 | jstor = 171363| pmid = | pmc = }}</ref> or the Laplace transform of the distribution when the service time distribution is a mixture of exponential distributions.<ref>{{Cite journal | last1 = Cohen | first1 = J. W. | authorlink1 = Wim Cohen| title = On the M/G/2 queueing model | doi = 10.1016/0304-4149(82)90046-1 | journal = Stochastic Processes and their Applications | volume = 12 | issue = 3 | pages = 231–248 | year = 1982 | pmid = | pmc = }}</ref> The Laplace transform of queue length<ref>{{cite jstor|1426776}}</ref> and waiting time distributions<ref>{{citeCite journal doi| last1 = Boxma | first1 = O. J. | authorlink1 = Onno Boxma| last2 = Deng | first2 = Q. | last3 = Zwart | first3 = A. P. | journal = [[Queueing Systems]]| volume = 40 | pages = 5 | year = 2002 | doi = 10.1023/A:1017913826973 | title = Waiting-Time Asymptotics for the M/G/2 Queue with Heterogeneous Servers| pmid = | pmc = }}</ref> can be computed when the waiting time distribution has a rational Laplace transform.

==References==