In this paper we discuss fairness in queues, view it in the perspective 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 measuring approaches, on reviewing their methodology and on examining their applicability and intuitive appeal. Some quantitative results are also presented. The paper has three major parts (sections) and a short concluding discussion. In the first part, fairness in queues and its importance are discussed in the broader context of the prevailing conception of social justice at large. A special effort, including illustrative examples, is made to differentiate between fairness of the queue and fairness at large, which derives from favoring the more needy. The second part is dedicated to explaining and discussing the three main properties expected of a fairness measure: conformity to the general concept of social justice, granularity, and intuitive appeal and rationality. The third part reviews the fairness of the queue evaluation and

Fairness is an inherent and fundamental factor of queue service disciplines in a large variety of queueing applications, ranging from computer systems, communica-tions systems and call centers to airport and supermarket waiting lines. Service time variability across jobs is a major factor affecting both system performance and schedul-ing 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) de-pends 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 distribu-tion (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 1 this parameter.

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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.

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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.

Abstract — 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. I.

service time variability and job scheduling fairness Abstract. Fairness is an inherent and fundamental factor of queue service disciplines in a large variety of queueing applications. Service time variability across jobs is an important factor affecting both system performance and scheduling rules (for example, computer systems that 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 [25], and study it under a wider variety of service time distributions (rather than exponential only) with a large range of service time variability. This serves two objectives: 1) Extend the understanding of queue fairness, and 2) Examine the capabilities and properties of RAQFM as a fairness measure. For the LCFS-PR scheduling we use a new approach and provide an analysis of the M/G/1 system; this is the first analysis of RAQFM for a non-Markovian system. We show that for this system the fairness depends on the first two moments of the service time and only on them. We also show that under LCFS-PR the expected discrimination of a job, conditioned on the service time, equals zero for every service time. For other service disciplines (FCFS, LCFS-NPR, ROS-NPR, ROS-PR) we approximate service time distributions by Coxian distributions and demonstrate a Markovian-type approach for deriving the RAQFM fairness level of M/Cox/1 systems. 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 this parameter. The results demonstrate that the fairness values of RAQFM widely agree with common intuition, and thus provide further confidence in this metric. Page 2 RRR 24-2005 1

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