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Locality of reference and the use of sojourn time variance for measuring queue unfairness: extended abstract

Published: 01 September 2005 Publication History

Abstract

The variance of customer sojourn time (or waiting time) is used, either explicitly or implicitly, as an indication of fairness for as long as queueing theory exists. In this work we demonstrate that this quantity has a disadvantage as a fairness measure, since it is not local to the busy period in which it is measured. It therefore may account for customer discrepancies which are not relevant to fairness of scheduling. We show that RAQFM, a recently proposed job fairness measure, does possess such a locality property. We further show that within a large class of fairness measures RAQFM is unique in possessing this property.

References

[1]
B. Avi-Itzhak and H. Levy. On measuring fairness in queues. Advances in Applied Probability, 36(3):919--936, September 2004.
[2]
J. F. C. Kingman. The effect of queue discipline on waiting time variance. Proceedings of the Cambridge Philosophical Society, 58:163--164, 1962.
[3]
D. Raz, H. Levy, and B. Avi-Itzhak. A resource-allocation queueing fairness measure. In Proceedings of Sigmetrics 2004/Performance 2004 Joint Conference on Measurement and Modeling of Computer Systems, pages 130--141, New York, NY, June 2004. Also appears in Performance Evaluation Review, 32(1):130--141.
[4]
A. Wierman and M. Harchol-Balter. Classifying scheduling policies with respect to higher moments of conditional response time. In Proceedings of ACM Sigmetrics 2005 Conference on Measurement and Modeling of Computer Systems, pages 229--239, Banff, Alberta, Canada, June 2005.

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Published In

cover image ACM SIGMETRICS Performance Evaluation Review
ACM SIGMETRICS Performance Evaluation Review  Volume 33, Issue 2
Special issue on the workshop on MAthematical performance Modeling And Analysis (MAMA 2005)
September 2005
43 pages
ISSN:0163-5999
DOI:10.1145/1101892
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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 September 2005
Published in SIGMETRICS Volume 33, Issue 2

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