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The single-server queue with service depending on queue size and with the preemptive-resume last-come–first-served queue discipline

Published online by Cambridge University Press:  14 July 2016

D. Fakinos
D. Fakinos*
Affiliation:
University of Thessaloniki
*
∗Department of Mathematics, Faculty of Sciences, Aristotle University of Thessaloniki, Thessaloniki, Greece.
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Abstract

This paper studies the GI/G/1 queueing system assuming that customers have service times depending on the queue size and also that they are served in accordance with the preemptive-resume last-come–first-served queue discipline. Expressions are given for the limiting distribution of the queue size and the remaining durations of the corresponding services, when the system is considered at arrival epochs, at departure epochs and continuously in time. Also these results are applied to some particular cases of the above queueing system.

Keywords

GI/G/1 QUEUEING SYSTEMEQUILIBRIUM DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 3 , September 1987 , pp. 758 - 767
Copyright
Copyright © Applied Probability Trust 1987 

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References

Fakinos, D. (1981) The G/G/1 queueing system with a particular queue discipline. J.R. Statist. Soc. B 43, 190–196.Google Scholar
Fakinos, D. (1986) On the single server queue with the preemptive-resume last-come–first-served queue discipline. J. Appl. Prob. 23, 243–248.Google Scholar
Kelly, F. P. (1976) The departure process from a queueing system. Math. Proc. Camb. Phil. Soc. 80, 283–285.Google Scholar
Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, New York.Google Scholar
Shanthikumar, J. G. and Sumita, U. (1986) On G/G/1 queues with LIFO-P service discipline. J. Operat. Res. Soc. Japan 29,Google Scholar
Yamazaki, G. (1982) The GI/G/1 queue with last-come–first-served. Ann. Inst. Statist. Math. 34, 599–609.Google Scholar
Yamazaki, G. (1984) Invariance relations of GI/G/1 queueing systems with preemptive-resume last-come–first-served queue discipline. J. Operat. Res. Soc. Japan 27, 338–346.Google Scholar