Some comparability results for waiting times in single- and many-server queues
- 1 December 1984
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 21 (4) , 887-900
- https://doi.org/10.2307/3213704
Abstract
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.Keywords
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