M/G/k queue: Difference between revisions

Revision as of 11:28, 13 June 2013

Revision as of 11:35, 13 June 2013

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Tijms ''et al.'' believe it is "not likely that computationally tractable methods can be developed to compute the exact numerical values of the steady-state probability in the M/G/''k'' queue."<ref name="tijms">{{cite jstor|1426474}}</ref>

Various approximations for the average queue size,<ref>{{cite doi|10.1287/opre.43.1.158}}</ref> stationary distribution<ref>{{cite doi|10.1007/s11134-008-9073-x}}</ref><ref>{{cite jstor|169760}}</ref> and approximation by a [[reflected Brownian motion]]<ref>{{cite doi|10.1287/opre.31.2.304}}</ref><ref name="yao">{{cite doi|10.1287/opre.33.6.1266}}</ref> have been offered by different authors

==Delay/waiting time distribution==

There are numerous approximations for the average delay a job experiences.<ref>{{cite jstor|169760}}</ref><ref>{{cite jstor|1426432}}</ref><ref>{{cite jstor|3212698}}</ref><ref>{{cite jstor|3213437}}</ref><ref>{{cite jstor|172087}}</ref><ref>{{cite jstor|170637}}<name="yao" /ref> The first such was given in 1959 using a factor to adjust the mean waiting time in an [[M/M/c queue]]<ref name="gbdz" /><ref>{{cite doi|10.1057/jors.1959.5}}</ref>

:<math>E[W^{\text{M/G/}k}] = \frac{C^2+1}{2} \mathbb E [ W^{\text{M/M/}c}]</math>