David Raz

A resource-allocation queueing fairness measure

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.

Quantifying fairness in queuing systems: Principles, approaches, and applicability

In this article we discuss fairness in queues, view it in the context 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 measurement approaches, on reviewing their methodology, and on examining their applicability and intuitive appeal. Some quantitative results are also presented. The article has three major parts (sections) and a short concluding discussion. In the first part we discuss fairness in queues and its importance in the broader context of the prevailing conception of social justice at large, and the distinction between fairness of the queue and fairness at large is illuminated. The second part is dedicated to explaining and discussing 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 evaluating 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.

Locality of reference and the use of sojourn time variance for measuring queue unfairness

Sojourn time variance is widely used as an indication of queue unfairness. We demonstrate that this quantity has a disadvantage, since it is not local to the busy period in which it is measured. We show that RAQFM, a recently proposed queue fairness metric, does possess such a locality property.

Class treatment in queueing systems: discrimination and fairness aspects

Customer classification and prioritization are commonly utilized in applications to provide queue preferential service. Their fairness aspects, which are inherent to any preferential system and highly important to customers, have not been fully studied and quantified to date. We use the recently proposed Resource Allocation Queueing Fairness Measure (RAQFM), and a newly introduced metric called class discrimination, which is based on RAQFM, to analyze such systems and derive their relative fairness values as well as the discrimination experienced by the various classes. Specifically, we study two practices, commonly used in public facilities as well as in computer systems: class prioritization and dedication of resources to classes.

Class prioritization and server dedication in queueing systems: Discrimination and fairness aspects

Customer classification and prioritization are commonly utilized in applications to provide queue preferential service. Their fairness aspects, which are inherent to any preferential system and highly important to customers, have not been fully studied and quantified to date. We use the recently proposed Resource Allocation Queueing Fairness Measure (RAQFM), and a newly introduced metric called Class Discrimination, which is based on RAQFM, to analyze such systems and derive their relative fairness values as well as the discrimination experienced by the various classes. Specifically, we study two practices, commonly used in public facilities as well as in computer systems: class prioritization and dedication of servers to classes.

A Study of the Connectivity Over Time Behavior of On-Demand Ad Hoc Path Selection Schemes

Abstract Selecting the most appropriate path between each pair of nodes in an ad hoc network is an issue with major impact on network performance. Many schemes were proposed and compared in the literature, using various criteria. However, the connectivity over time behavior of these schemes, which is important to some practical applications, was not well studied, especially with regards to the terrain type. In this work we use simulation to study this aspect of network performance. We demonstrate that a different connectivity requirement and a different time horizon may dictate a different scheme to use. We also demonstrate that path selection schemes are not equally sensitive to the terrain.

A pseudo-efficient frontier method for solving two-phase packing problems

Packing problems are very common and popular but typical solution procedures involve computation of numerous feasible solutions even for a small scale problem. These types of problems are commonly categorized as knapsack problem or bin packing problems and many of them are NP complete. An efficient mechanism for finding an exact solution for a two phase packing problem is proposed. The mechanism reduces the number of feasible solutions considered by conducting a naïve search for a pseudo efficient frontier of solutions for the first phase. Furthermore, by conduction the first phase in such a way, evaluating the second phase is made more efficient. An algorithm for the two dimensional case is presented along with proofs of correctness and complexity.

Locality of reference and the use of sojourn time variance for measuring queue unfairness: extended abstract

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.

How fair is queue prioritization

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