Page 2 RRR 12 - 2005 1 Introduction

Fairness is an inherent and fundamental factor of queue service disciplines in a large variety of queueing applications. Service time variability across jobs is an important factor affecting both system performance and scheduling rules (for example, computer systems that prioritize short jobs over long jobs). Service time variability and its effects on mean response times have been studied extensively. However, its effect on queue fairness has not been researched. This work studies the effect of service time variability on queue fairness. We use the RAQFM queue fairness measure, whose analysis for the case of the M/M/1 queue was provided in [25], and study it under a wider variety of service time distributions (rather than exponential only) with a large range of service time variability. This serves two objectives: 1) Extend the understanding of queue fairness, and 2) Examine the capabilities and properties of RAQFM as a fairness measure. For the LCFS-PR scheduling we use a new approach and provide an analysis of the M/G/1 system; this is the first analysis of RAQFM for a non-Markovian system. We show that for this system the fairness depends on the first two moments of the service time and only on them. We also show that under LCFS-PR the expected discrimination of a job, conditioned on the service time, equals zero for every service time. For other service disciplines (FCFS, LCFS-NPR, ROS-NPR, ROS-PR) we approximate service time distributions by Coxian distributions and demonstrate a Markovian-type approach for deriving the RAQFM fairness level of M/Cox/1 systems. The analysis reveals that queue fairness is sensitive to service time variability and that the fairness ranking of common scheduling policies (e.g. FCFS, LCFS, ROS) depends on this parameter. The results demonstrate that the fairness values of RAQFM widely agree with common intuition, and thus provide further confidence in this metric.