Some comparability results for waiting times in single- and many-server queues
Keyword(s):
It is shown that the stationary waiting time random variables W′, W″ of two M/G/l queueing systems for which the corresponding service time random variables satisfy E(S′−x)+ ≦ E(S″−x)+ (all x >0), are stochastically ordered as W′≦dW″. The weaker conclusion, that E(W′−x)+ ≦ E(W″−x)+ (all x > 0), is shown to hold in GI/M/k systems when the interarrival time random variables satisfy E(x−T′)+ ≦ E(x−T″)+ (all x). A sufficient condition for wk≡EW in GI/D/k to be monotonic in k for a sequence of k-server queues with the same relative traffic intensity is given. Evidence indicating or refuting possible strengthenings of some of the results is indicated.
1984 ◽
Vol 21
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pp. 887-900
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1996 ◽
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1980 ◽
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pp. 1062-1071
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1980 ◽
Vol 17
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pp. 1062-1071
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1990 ◽
Vol 27
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Vol 34
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2014 ◽
Vol 2014
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