A discrimination frequency based queueing fairness measure with regard to job seniority and service requirement

Queueing theory has dealt comprehensively with waiting times, throughput, or related properties. Another important issue, which is fair queueing, has been neglected for a long time and has received reasonable attention only very recently. As of today there are no generally accepted definitions and measures although some have been proposed. It has been recognized that measuring fairness in queues suffers from the dilemma that, depending on the application, queue scheduling pursues contradictory aims. Sometimes preference is given to short jobs, sometimes to jobs that already wait for quite a long time. In both cases one may get the impression that some jobs do not receive a fair treatment. In this paper we propose a queueing fairness measure which considers both service requirement and seniority of a job or customer. Our measure counts two types of discriminations that may bother customers: to be overtaken by other customers, and to wait due to customers with large service requirements. We show that our fairness measure adheres to previously published different preference principles, and we discuss possible measure refinements and the fairness of some scheduling policies.