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Bounds on the delay distribution in GI/G/1 queues

Published online by Cambridge University Press:  14 July 2016

Sheldon M. Ross
Sheldon M. Ross*
Affiliation:
University of California, Berkeley
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Abstract

Bounds are obtained for the limiting distribution of the delay in queue for a GI/G/1 system via Martingale theory. These bounds are somewhat stronger than similar bounds recently obtained by Kingman. Simplifications of the bounds are obtained in the special cases where the service distribution is either IFR, DFR, NBU or NWU.

Keywords

DELAY DISTRIBUTIONGI/G/1 QUEUESMARTINGALESTOPPING TIMENBUNWUIFRDFR
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 2 , June 1974 , pp. 417 - 421
Copyright
Copyright © Applied Probability Trust 1974 

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References

[1] Kingman, J. F. C. (1964) A martingale inequality in the theory of queues. Proc. Camb. Phil. Soc. 59, 359–361.CrossRefGoogle Scholar
[2] Kingman, J. F. C. (1970) Inequalities in the theory of queues. J. R. Statist. Soc. B 32, 102–110.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] Marshall, K. T. (1968) Some inequalities in queueing. Operat. Res. 16, 651–665.CrossRefGoogle Scholar
[5] Wald, A. (1947) Sequential Analysis. John Wiley, New York.Google Scholar