The multiclass GI/PH/N queue in the Halfin-Whitt regime
2000 ◽
Vol 32
(2)
◽
pp. 564-595
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Keyword(s):
We consider a multiserver queue in the heavy-traffic regime introduced and studied by Halfin and Whitt who investigated the case of a single customer class with exponentially distributed service times. Our purpose is to extend their analysis to a system with multiple customer classes, priorities, and phase-type service distributions. We prove a weak convergence limit theorem showing that a properly defined and normalized queue length process converges to a particular K-dimensional diffusion process, where K is the number of phases in the service time distribution. We also show that a properly normalized waiting time process converges to a simple functional of the limit diffusion for the queue length.
2000 ◽
Vol 32
(02)
◽
pp. 564-595
◽
2008 ◽
Vol 40
(2)
◽
pp. 548-577
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1983 ◽
Vol 15
(02)
◽
pp. 420-443
◽
1989 ◽
Vol 21
(02)
◽
pp. 485-487
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Keyword(s):
1972 ◽
Vol 9
(04)
◽
pp. 821-831
◽
1977 ◽
Vol 9
(01)
◽
pp. 169-186
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2007 ◽
Vol 24
(03)
◽
pp. 293-312
◽