Analysis of a queueing fairness measure

Scheduling policies significantly influence the performance of queueing systems, and performance measures like response and waiting times, throughput, or related properties have been comprehensively investigated in queueing and scheduling theory. The important issue of quantifying user perceived fairness has received less attention. Measuring fairness suffers from the subjective nature of fairness, and it has received growing attention only the past few years. Recently, an intuitive discrimination frequency based queueing fairness measure, which possesses important axiomatic properties, has been introduced. In this paper, we derive analytical expressions for the expected discrimination frequency in M/M/1, M/D/1 and M/GI/1 queues operating under FCFS, nonpreemptive LCFS, and SJF scheduling. Variances are evaluated by simulation and special attention is drawn to Pareto distributed service times.