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Another martingale bound on the waiting-time distribution in GI/G/1 queues

Published online by Cambridge University Press:  14 July 2016

Harry H. Tan
Harry H. Tan*
Affiliation:
Princeton University
*
∗Postal address: Department of Electrical Engineering and Computer Science, Engineering Quadrangle, Princeton University, Princeton, N.J. 08540, U.S.A.
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Abstract

A new upper bound on the stationary waiting-time distribution of a GI/G/1 queue is derived following Kingman's martingale approach. This bound is generally stronger than Kingman's upper bound and is sometimes stronger than an upper bound derived by Ross.

Keywords

GI/G/1 QUEUESUPERMARTINGALEWAITING-TIME DISTRIBUTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 16 , Issue 2 , June 1979 , pp. 454 - 457
Copyright
Copyright © Applied Probability Trust 1979 

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Footnotes

Research supported by the U. S. National Science Foundation under grants GK-42080 and ENG 76–21827.

References

[1] Doob, J. L. (1953) Stochastic Processes. Wiley, New York, 314–317.Google Scholar
[2] Kingman, J. F. C. (1964) A martingale inequality in the theory of queues. Proc. Camb. Phil. Soc. 59, 359–361.Google Scholar
[3] Lindley, D. V. (1952) The theory of queues with a single server. Proc. Camb. Phil. Soc. 48, 277–289.CrossRefGoogle Scholar
[4] Ross, S. M. (1974) Bounds on the delay distribution in GI/G/1 queues. J. Appl. Prob. 11, 417–421.Google Scholar