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Some comparability results for waiting times in single- and many-server queues

Published online by Cambridge University Press:  14 July 2016

D. J. Daley  and
T. Rolski
D. J. Daley*
Affiliation:
The Australian National University
T. Rolski*
Affiliation:
Wrocław University
*
∗Postal address: Statistics Department, IAS, The Australian National University, GPO Box 4, Canberra ACT 2601, Australia.
∗∗Postal address: Mathematics Institute, Wrocław University, pl. Grunwaldski 2/4, 50-384 Wrocław, Poland.
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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

CONVEX ORDERINGSTOCHASTIC ORDERINGDISCRETE-TIME QUEUESLIGHT TRAFFIC ASYMPTOTICS
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 4 , December 1984 , pp. 887 - 900
Copyright
Copyright © Applied Probability Trust 1984 

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Footnotes

Work done during the tenure of a Visiting Fellowship at The Australian National University.

References

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