On measuring fairness in queues

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.