The Effect of Service Time Variability on Job Scheduling Fairness

Fairness is an inherent and fundamental factor of queue service disciplines in a large variety of queueing applications, ranging from computer systems, communications systems and call centers to airport and supermarket waiting lines. Service time variability across jobs is a major factor affecting both system performance and scheduling rules (for example, computer systems 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 Raz et al. (2004b), and aim at studying it under a wide variety of service time distributions (rather than exponential only) with a large range of service time variability. For the LCFS-PR scheduling we provide a full analysis of the M/G/1 system. We find that for this system the fairness (when expressed as second moment of discrimination) depends on the first two moments of the service time and only on them. For other service disciplines (FCFS, LCFS-NPR, ROS-NPR, ROS-PR) we propose to use the common approach of mapping an arbitrary service time distribution into a Coxian distribution (via moment mapping) and to use a Markovian-type fairness analysis of RAQFM for deriving the fairness level of the single server system with Poisson arrivals. 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