A resource allocation queueing fairness measure: properties and bounds

Abstract

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.

On the Impact of Heterogeneity and Back-End Scheduling in Load Balancing Designs

“…For our purposes, we will need only results characterizing the mean response time under these policies. The interested reader may find surveys of distributional results for SRPT and PS in [6], [21] and studies of the fairness of SRPT in [3], [29].…”

Inequity averse optimization in operational research

“…Avi-Itzhak, Levy, and Raz (2007) and Avi-Itzhak et al (2008) discuss a resource-allocation based fairness measure, which assumes that every customer in a queuing system is entitled to an equal share of the resource (server). Hence the discrimination of a customer i (with a service requirement s i ) who arrives in apoch a i and departs at epoch d i is as follows:…”

Characteristics of Fairness Metrics and Their Effect on Perceived Scheduler Effectiveness

“…Users (jobs) should get the best possible performance and some of the jobs should not be discriminated at the expense of others. The general behavior of queuing systems is determined by seniority and service requirements [18] of jobs. Job seniority can be looked at as the time the jobs have spent in the queue and service requirements can be looked at the processor hours required to process a job.…”

“…RAQFM was proposed in [17] and analyzed in [18]. It uses the difference between the resources allotted to a job and that it is fairly entitled to.…”

“…This is because in some cases, good 'performance' is got by starving some jobs at the expense of others (unfairness). Measures of dispersion [6][4], Fair start-time analysis [5] and the Resource Allocation Queuing Measure (RAQFM) [17] [18] are common fairness metrics. These measures can, sometimes, give misleading deductions for parallel job schedulers.…”