A resource-allocation queueing fairness measure

David Raz · Hanoch Levy C · Benjamin Avi-Itzhak

35 citations0/0 files storedACM SIGMETRICS Performance Evaluation Review

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Advanced Queuing Theory Analysis Network Traffic and Congestion Control Optimization and Search Problems

Abstract

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.

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References

1987OR Forum—Perspectives on Queues: Social Justice and the Psychology of Queueing 1967Time-shared Systems 1970Waiting Time Distributions for Processor-Sharing Systems 1969Queue Culture: The Waiting Line as a Social System 2003Classifying scheduling policies with respect to unfairness in an M/GI/1 2002The Effects of Queue Structure on Attitudes 1964Analysis of A time‐shared processor 1992How fair is fair queuing

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2007A resource allocation queueing fairness measure: properties and bounds 2020To Pool or Not to Pool: Queueing Design for Large-Scale Service Systems 2011Quantitative fairness for assessing perceived service quality in queues

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