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Convex ordering of sojourn times in single-server queues: extremal properties of FIFO and LIFO service disciplines

Published online by Cambridge University Press:  14 July 2016

J. George Shanthikumar  and
Ushio Sumita
J. George Shanthikumar*
Affiliation:
University of California, Berkeley
Ushio Sumita*
Affiliation:
University of Rochester
*
∗Postal address: School of Business Administration, University of California, Berkeley, CA 94720, USA.
∗∗Postal address: William E. Simon Graduate School of Business Administration, University of Rochester, Rochester NY 14627, USA.
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Abstract

In this paper, the extremal properties of the ergodic sojourn times in G/G/1queues under various service disciplines are studied in terms of the convex ordering. It is shown that among work-conserving non-preemptive service disciplines that are service time independent, the FIFO and the LIFO service disciplines provide the minima and the maxima, respectively, of the ergodic sojourn times for any G/G/1 queue. For G/M/1 queues, this class of work-conserving service disciplines is extended to include preemptive/resume disciplines. In this case the FIFO and LIFO-P (preemptive/resume LIFO) service disciplines attain the minima and maxima, respectively. These extend results of Durr (1971), Kingman (1962) and a recent result of Ramaswami (1984). Further results are obtained for G/Em/1 and G/D/1 queues.

Keywords

INCREASING CONVEX ORDERINGSTOCHASTIC ORDERING
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 3 , September 1987 , pp. 737 - 748
Copyright
Copyright © Applied Probability Trust 1987 

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References

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