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On measuring fairness in queues

Part of: Special processes Computer system organization

Published online by Cambridge University Press:  01 July 2016

Benjamin Avi-Itzhak  and
Hanoch Levy
Benjamin Avi-Itzhak*
Affiliation:
Rutgers University
Hanoch Levy*
Affiliation:
Tel Aviv University
*
∗ Postal address: RUTCOR, Rutgers University, 640 Bartholomew Street, Piscataway, NJ 08554, USA. Email address: aviitzha@rutcor.rutgers.edu
∗∗ Postal address: School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel. Email address: hanoch@cs.tau.ac.il
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Abstract

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The issue of ‘fairness’ is raised frequently in the context of evaluating queueing policies, notably in relation to telecommunications and computer systems where it may be of no lesser importance than the conventional measures of performance. Comparisons of the fairness of various systems and policies are often awkward due to lack of generally accepted definitions and measures for this important property. The purpose of this work is to propose possible fairness measures enabling us to quantitatively measure and compare the level of fairness associated with G/G/R queueing systems. We define and discuss order (of service) fairness and use an axiomatic approach for developing a measure for it in the G/D/1 case. The measure obtained for the G/D/1 system is then generalized and applied to the G/G/R class of systems. A practical implication of this work is that, for a wide class of service disciplines, the variance of the waiting time can be used as a yardstick for comparing fairness levels.

Keywords

Queueingfairnessservice orderqueue disciplinecustomer scheduling

MSC classification

Primary: 68M20: Performance evaluation; queueing; scheduling 60K25: Queueing theory

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 36 , Issue 3 , September 2004 , pp. 919 - 936
Copyright
Copyright © Applied Probability Trust 2004 

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