Fairness considerations of scheduling in multi-server and multi-queue systems

Abstract

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 and classifications

“…Thus, the fairness of a policy is determined by looking at the variation from this service rate that jobs experience. Avi-Itzhak, Levy, & Raz, have a number of papers illustrating the properties of this interesting measure [31,2], but unfortunately, the fairness of many practically relevant policies, e.g. SRPT and FB, has proven difficult to analyze using RAQFM.…”

Fairness and scheduling in single server queues

“…Our hope is that this limited focus allows the reader to see the complexities of defining and analyzing fairness in a simple setting, and that the ideas conveyed are useful in more complex environments. But, the reader should definitely be aware that there is also a large literature studying fairness outside of the single server queue in, for example, fairness across flows in multi-server systems and general queueing networks [24,12,27,32,7,39,44]. In each of these contexts there is, again, a large literature studying a variety of fairness metrics that have emerged in the last decade.…”

“…In each of these contexts there is, again, a large literature studying a variety of fairness metrics that have emerged in the last decade. Some of this work builds on the measures discussed in this survey, e.g., [39,44]; however these more complex settings provide a variety of issues not present in the single server queue that motivate the use of different fairness metrics as well. For example, in the multi-server environment it may be important to be fair both to the customers and the servers, e.g., in a call center environment the dispatching scheme should be fair to the people answering the calls [1].…”

“…Research studying the fairness of scheduling policies can largely be divided into two pieces. First, a large literature has focused on developing fairness measures and studying the fairness of policies with respect to jobs in the context of a single resource (a single server queue), e.g., [40,39,45,51,53,52]. Second, a large (and nearly distinct) literature has focused on developing fairness measures and studying the fairness of policies with respect to flows in the context of multiple resource environments, e.g., sharing network resources among flows, e.g., [24,12,27,32,7,28].…”

“…In fact, there are a number of interesting studies using extensions of RAQFM in multi-server and multi-queue systems, e.g., [39].…”