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

Customer classification and prioritization are commonly used in many applications to provide queue preferential service. Their influence on queuing systems has been thoroughly studied from the delay distribution perspective. However, the fairness aspects, which are inherent to any preferential system and highly important to customers, have hardly been studied and not been quantified to date. In this work we use the Resource Allocation Queueing Fairness Measure (RAQFM) to analyze such systems and derive their relative fairness values. Results from analyzing and comparing systems with class priority to systems with no prioritization, show that assigning higher priority to short jobs often increases the system fairness, but not always. We also analyze the effect multiple servers have on fairness, showing that multiple servers increase the fairness of the system. Practitioners can use the derived results to weigh efficiency aspects versus fairness aspects in controlling their queueing systems.

The growing trend in computer systems towards using scheduling policies that prioritize jobs with small service requirements has resulted in a new focus on the fairness of such policies. In particular, researchers have been interested in whether prioritizing small job sizes results in large jobs being treated “unfairly.” However, fairness is an amorphous concept and thus difficult to define and study. This article provides a short survey of recent work in this area.

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.

R u t c o r

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 su#ers 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.

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.

R u t c o r

The variance of customer sojourn time (or waiting time) is used, either explicitly or implicitly, as an indication of fairness for as long as queueing theory exists. In this work we demonstrate that this quantity has a disadvantage as a fairness measure, since it is not local to the busy period in which it is measured. It therefore may account for customer discrepancies which are not relevant to fairness of scheduling. We show that RAQFM, a recently proposed job fairness measure, does possess such a locality property. We further show that within a large class of fairness measures RAQFM is unique in possessing this property. 1.

Abstract. In this paper, we investigate the problem of optimal server selection in “content replication networks, ” such as peer-to-peer (P2P) and content delivery networks (CDNs). While a number of server selection policies have been proposed or implemented, understanding of the theoretical performance limits of server selection and the relative performance of existing policies remains limited. In this paper, we introduce a mathematical framework, based on the M/G/1 Processor Sharing queueing model, and derive closed-form expressions for the optimal server access probabilities and the optimal average delay. We also analyze the performance of two general server selection policies, referred to as EQ DELAY and EQ LOAD, that characterize a wide range of existing algorithms. We prove that the average delay achieved by these policies can theoretically be as much as N times larger than the optimal delay, where N is the total number of servers in the system. Furthermore, simulation results obtained using our M/G/1-PS workload model and the ProWGen Web workload generator show that the optimal policy can reduce the average delay of requests by as much as 30 % as compared to EQ LOAD and EQ DELAY, in realistic scenarios. They also show that the optimal policy compares favorably to the other policies in terms of fairness and sensitivity to traffic parameters. 1