A metric of fairness for parallel job schedulers

Sigmetrics Performance Evaluation Review, 2004

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.

2011

Queues serve as a major scheduling device in computer networks, both at the network level and at the application level. A fundamental and important property of a queue service discipline is its fairness. Recent empirical studies show fairness in queues to be highly important to queueing customers in practical scenarios. The objective of this tutorial is to discuss the issue of queue fairness and its dilemmas, and to review the research conducted on this subject. We discuss the fundamental principles related to queue fairness in the perspective of the relevant applications, with some emphasis on computer communications networks. This is conducted in the context of the recent research in this area and the queueing related fairness measures which have been proposed in recent years. We describe, discuss and compare their properties, and evaluate their relevance to the various practical applications.

Queueing Systems - Theory and Applications, 2007

Fairness is an inherent and fundamental factor of queue service disciplines in a large variety of queueing applications, ranging from airport waiting lines to computer queueing systems. We study a newly proposed measure, a Resource Allocation Queueing Fairness Measure (RAQFM), first introduced in Raz, Levy, and Avi-Itzhak (Perform. Eval. Rev. 32(1):130–141, 2004). We analyze the properties of RAQFM and tie them to intuition, provide bounds for its values, and discuss briefly how it yields to analysis.

RUTCOR, Rutgers University, 2004

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.

2004

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 practical scenarios. 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 propose RAQFM, a Resource Allocation Queueing Fairness Measure. The measure 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 present the methodology of RAQFM and the principles on which it is based. We discuss its properties, emphasizing the way they appeal to one's intuition. We provide a methodology by which a wide variety of queueing systems can be analyzed to derive their fairness value.

2004

Job scheduling has been a much studied topic over the years. While past research has studied the effect of various scheduling policies using metrics such as turnaround time, slowdown, utilization etc., there has been little research on how fair a non-preemptive scheduling policy is. In this paper, we propose an approach to assessing fairness in nonpreemptive job scheduling. Our basic model of fairness is that no later arriving job should delay an earlier arriving job. We quantitatively assess the fairness of several job scheduling strategies and propose a new strategy that seeks to improve fairness.

Performance Evaluation, 2007

Expected slowdown has been proposed as a criterion to evaluate queue fairness. In this work we examine how the constant slowdown principle can be used as a basis for a queueing fairness measure. We propose the Slowdown Queueing Fairness (SQF) measure based on the principle that customers' waiting time should be proportional to their service time. We analyze its properties and examine how they react to both seniority and service requirements. We also examine whether its behavior fits intuition. Its values for a variety of single-server scheduling policies as well as for multi-server architectures are derived.

Expected slowdown has been proposed as a criterion to evaluate queue fairness. In this work we examine how the constant slowdown principle can be used as a basis for a queueing fairness measure. We propose the Slowdown Queueing Fairness (SQF) measure based on the principle that customers' waiting time should be proportional to their service time. We analyze its properties and examine how they react to both seniority and service requirements. We also examine whether its behavior fits intuition. Its values for a variety of single-server scheduling policies as well as for multi-server architectures are derived. c 2007 Elsevier B.V. All rights reserved.

Sigmetrics Performance Evaluation Review, 2004

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. We also analyze the effect multiple servers have on fairness, showing that multiple servers increase the fairness of the system. 1

Sigmetrics Performance Evaluation Review, 2005

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.

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 afiecting both system performance and schedul- ing rules (for example, computer systems prioritize short jobs over long jobs). Service time variability and its efiects on mean response times have been studied extensively. However, its efiect on queue fairness has not been researched. This work studies the efiect 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 s...

Journal of the Association For Computing Machinery, 1992

Fair Queuing is a novel queuing discipline with important applications to data networks that support variable-size packets and to systems where the cost of preempting jobs from service is high. The disciphne controls a single server shared by N job arrival streams with each stream allotted a separate queue. After every job completion, the server is assigned to serve, without possibihty of interruption, the job at the head of one of the queues (as soon as at least one job appears in the system). Fair Queuing is designed to handle arbitrary job arrival sequences with essentially no a priori knowledge of their attributes. such that each stream receives its 'Lfam share" of serwce. In this paper, we consider two variants of the fair queuing discipline, and rigorously establish their fairness wa sample path comparisons with the head-of-line processor sharing disclphne, a mathematical idealization that prowdes a fairness paradigm. An efficient Implementation of one of the fair queuing disciplines is presented, In passing, a new, fast method for simulating processor sharing is derived. Simulation results are presented to further explore the comparison between fair queuing and processor sharing.

Proceedings ISCC 2000. Fifth IEEE Symposium on Computers and Communications, 2000

Fair Queuing implementation for Unix routers -the WFQ implementation of the ALTQ project. It shows the WFQ/ALTQ weaknesses and explains why we cannot expect an interesting behavior from a system using such a scheduler. The conclusions here presented are supported by a set of tests using UDP traffic only. With a tool developed in our laboratory, we were able to show that changing the classes' weights does not necessarily result on a different Quality of Service for each of the existing classes. To achieve this differentiation, the lengths of the queues which serve the scheduler (one for each class) must be increased beyond reasonable values. We found that the low-level dynamics of FreeBSD systems practically turns WFQ schedulers useless. The same is applicable to any other work-conserving discipline. Thus, an important conclusion of this paper, is that one must design very carefully the platforms that support work conserving disciplines in order to expect adequate behaviors from those systems, in terms of QoS provision.

Probability in The Engineering and Informational Sciences, 2008

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.

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 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.