A resource allocation queueing fairness measure: properties and bounds

Fairness is an inherent and fundamental factor of queue service disciplines in a large variety of queueing applications, ranging from airport and supermarket waiting lines to computer and communication queueing systems. Recent empirical studies show that fairness is highly important to queueing customers in actual situations. Despite this importance, queueing theory has devoted very little effort to this subject and an agreed upon measure for evaluating the fairness of queueing systems does not exist. In this work we study a newly proposed Resource Allocation Queueing Fairness Measure (RAQFM). The measure, first introduced in Raz et al. (2004d), is built under the understanding that a widely accepted measure must adhere to the common sense intuition of researchers as well as practitioners and customers, and must also be based on widely accepted principles of social justice. We analyze the properties of RAQFM and provide bounds for its values. Both of these serve to intuitively understand the measure and provide confidence in it. The analysis shows that the measure properly reacts to both customer seniority and customer service time, and thus appeals to one’s intuition. The bounds provide a scale of reference on the measure. An Additional property of the measure, namely “locality of reference”, and how it yields to analysis, are discussed. Subject classifications: Queues: quantification of job fairness in queueing systems Area of review: Stochastic Models