Fairness is a major issue in the operation of queues, perhaps it is the reason why queues were formed in the first place. Recent studies show that the fairness of a queueing system is important to customers not less than the actual delay they experience. Despite this observation little research has been conducted to study fairness in queues, and no commonly agreed upon measure of queue fairness exists. Two recent research exceptions are Avi-Itzhak and Levy [1], where a fairness measure is proposed, and Wierman and HarcholBalter [18] (this conference, 2003), where a criterion is proposed for classifying service policies as fair or unfair; the criterion focuses on customer service requirement and deals with fairness with respect to service times.In this work we recognize that the inherent behavior of a queueing system is governed by two major factors: Job seniority (arrival times) and job service requirement (service time). Thus, it is desired that a queueing fairness measure would account for both. To this end we propose a Resource Allocation Queueing Fairness Measure, (RAQFM), that accounts for both relative job seniority and relative service time. The measure allows accounting for individual job discrimination as well as system unfairness. The system measure forms a full scale that can be used to evaluate the level of unfairness under various queueing disciplines. We present several basic properties of the measure. We derive the individual measure as well as the system measure for an M/M/1 queue under five fundamental service policies: Processor Sharing (PS), First Come First Served (FCFS), Non-Preemptive Last Come First Served (NP-LCFS), Preemptive Last Come First Served (P-LCFS), and Random Order of Service (ROS). The results of RAQFM are then compared to those of Wierman and Harchol-Balter [18], and the quite intriguing observed differences are discussed.

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.

Multi-server and multi-queue architectures are common mechanisms used in a large variety of applications (call centers, Web services, computer systems). One of the major motivations behind common queue operation strategies is to grant fair service to the jobs (customers). Such systems have been thoroughly studied by Queueing Theory from their performance (delay distribution) perspective. However, their fairness aspects have hardly been studied and have not been quantified to date. In this work we use the Resource Allocation Queueing Fairness Measure (RAQFM) to quantitatively analyze several multi-server systems and operational mechanisms. The results yield the relative fairness of the mechanisms as a function of the system configuration and parameters. Practitioners can use these results to quantitatively account for system fairness and to weigh efficiency aspects versus fairness aspects in designing and controlling their queueing systems. In particular, we quantitatively demonstrate that: 1) Joining the shortest queue increases fairness, 2) A single "combined" queue system is more fair than "separate" (multi) queue system and 3) Jockeying from the head of a queue is more fair than jockeying from its tail.

In this article we discuss fairness in queues, view it in the context of social justice at large, and survey the recently published research work and publications dealing with the issue of measuring fairness of queues. The emphasis is placed on the underlying principles of the different measurement approaches, on reviewing their methodology, and on examining their applicability and intuitive appeal. Some quantitative results are also presented.The article has three major parts (sections) and a short concluding discussion. In the first part we discuss fairness in queues and its importance in the broader context of the prevailing conception of social justice at large, and the distinction between fairness of the queue and fairness at large is illuminated. The second part is dedicated to explaining and discussing three main properties expected of a fairness measure: conformity to the general concept of social justice, granularity, and intuitive 495 496 B. Avi-Itzhak, H. Levy and D. Raz appeal and rationality. The third part reviews the fairness of the queue evaluating and measuring approaches proposed and studied in recent years. We describe the underlying principles of the different approaches, present some of their results, and review them in context of the three main properties expected from a measure. The short discussion that follows centers on future research issues.

Fairness is a major issue in the operation of queues, perhaps it is the reason why queues were formed in the first place. Recent studies show that the fairness of a queueing system is important to customers not less than the actual delay they experience. Despite this observation little research has been conducted to study fairness in queues, and no commonly agreed upon measure of queue fairness exists. Two recent research exceptions are Avi-Itzhak and Levy [1], where a fairness measure is proposed, and Wierman and Harchol-Balter [18] (this conference, 2003), where a criterion is proposed for classifying service policies as fair or unfair; the criterion focuses on customer service requirement and deals with fairness with respect to service times.In this work we recognize that the inherent behavior of a queueing system is governed by two major factors: Job seniority (arrival times) and job service requirement (service time). Thus, it is desired that a queueing fairness measure would account for both. To this end we propose a Resource Allocation Queueing Fairness Measure, (RAQFM), that accounts for both relative job seniority and relative service time. The measure allows accounting for individual job discrimination as well as system unfairness. The system measure forms a full scale that can be used to evaluate the level of unfairness under various queueing disciplines. We present several basic properties of the measure. We derive the individual measure as well as the system measure for an M/M/1 queue under five fundamental service policies: Processor Sharing (PS), First Come First Served (FCFS), Non-Preemptive Last Come First Served (NP-LCFS), Preemptive Last Come First Served (P-LCFS), and Random Order of Service (ROS). The results of RAQFM are then compared to those of Wierman and Harchol-Balter [18], and the quite intriguing observed differences are discussed.