Tails in scheduling

Boxma, Onno; Zwart, Bert

doi:10.1145/1243401.1243406

Cited by 62 publications

(61 citation statements)

References 47 publications

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“…Boxma and Zwart (2007). In contrast to the optimality of F , the decay rate L is the smallest possible decay rate.…”

Section: Review Of Results For Specific Scheduling Disciplinesmentioning

confidence: 99%

“…A comprehensive survey of the sojourn time tail behavior of various scheduling disciplines can be found in Borst et al (2003) and Boxma and Zwart (2007). To keep the paper self-contained, we now present some of the results that are crucial to the goal of the paper.…”

Section: Review Of Results For Specific Scheduling Disciplinesmentioning

confidence: 99%

“…A related definition is proposed in Boxma and Zwart (2007). We would like to point out that the notion of optimality we propose strikes a balance between the average-case behavior and worst-case behavior of scheduling algorithms; these two notions are more prevalent in the scheduling literature.…”

Section: Tail Optimalitymentioning

confidence: 99%

“…The first bound is trivial, and the second bound simply follows from (1); see Boxma and Zwart (2007) for details. An approach for proving optimality of 0 is to analyze the tail behavior of V 0 and then to compare it with the tail behavior of C max or B.…”

Section: Tail Optimalitymentioning

confidence: 99%

“…For example, results exist for the GI/GI/1 queue under both heavy-and light-tailed job sizes for first come first served (FCFS) (Asmussen 2003, Borovkov 1976, Cohen 1973, Pakes 1975, preemptive last come first served (LCFS) (Meyer andTeugels 1980, Zwart 2001), processor sharing (PS) (Borst et al 2006), shortest remaining processing time (SRPT) Zwart 2006, Nuyens et al 2008), and other disciplines. Complete surveys can be found in Borst et al (2003) and Boxma and Zwart (2007).…”

Section: Introductionmentioning

confidence: 99%

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Is Tail-Optimal Scheduling Possible?

Wierman

Zwart

2012

Operations Research

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This paper focuses on the competitive analysis of scheduling disciplines in a large deviations setting. Although there are policies that are known to optimize the sojourn time tail under a large class of heavy-tailed job sizes (e.g., processor sharing and shortest remaining processing time) and there are policies known to optimize the sojourn time tail in the case of light-tailed job sizes (e.g., first come first served), no policies are known that can optimize the sojourn time tail across both light-and heavy-tailed job size distributions. We prove that no such work-conserving, nonanticipatory, nonlearning policy exists, and thus that a policy must learn (or know) the job size distribution in order to optimize the sojourn time tail.

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“…Boxma and Zwart (2007). In contrast to the optimality of F , the decay rate L is the smallest possible decay rate.…”

Section: Review Of Results For Specific Scheduling Disciplinesmentioning

confidence: 99%

Section: Review Of Results For Specific Scheduling Disciplinesmentioning

confidence: 99%

Section: Tail Optimalitymentioning

confidence: 99%

Section: Tail Optimalitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Is Tail-Optimal Scheduling Possible?

Wierman

Zwart

2012

Operations Research

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Queueing Disciplines

Harchol‐Balter

2011

Wiley Encyclopedia of Operations Research and Management Science

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Optimal File Splitting for Wireless Networks with Concurrent Access

Hoekstra

Mei

Nazarathy

et al. 2009

Lecture Notes in Computer Science

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Abstract. The fundamental limits on channel capacity form a barrier to the sustained growth on the use of wireless networks. To cope with this, multi-path communication solutions provide a promising means to improve reliability and boost Quality of Service (QoS) in areas that are covered by a multitude of wireless access networks. Today, little is known about how to effectively exploit this potential. Motivated by this, we consider N parallel communication networks, each of which is modeled as a processor sharing (PS) queue that handles two types of traffic: foreground and background. We consider a foreground traffic stream of files, each of which is split into N fragments according to a fixed splitting rule (α1, . . . , αN ), where P αi = 1 and αi ≥ 0 is the fraction of the file that is directed to network i. Upon completion of transmission of all fragments of a file, it is re-assembled at the receiving end. The background streams use dedicated networks without being split. We study the sojourn time tail behavior of the foreground traffic. For the case of light foreground traffic and regularly varying foreground filesize distributions, we obtain a reduced-load approximation (RLA) for the sojourn times, similar to that of a single PS-queue. An important implication of the RLA is that the tail-optimal splitting rule is simply to choose αi proportional to ci − ρi, where ci is the capacity of network i and ρi is the load offered to network i by the corresponding background stream. This result provides a theoretical foundation for the effectiveness of such a simple splitting rule. Extensive simulations demonstrate that this simple rule indeed performs well, not only with respect to the tail asymptotics, but also with respect to the mean sojourn times. The simulations further support our conjecture that the same splitting rule is also tail-optimal for non-light foreground traffic. Finally, we observe near-insensitivity of the mean sojourn times with respect to the file-size distribution.

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Tails in scheduling

Cited by 62 publications

References 47 publications

Is Tail-Optimal Scheduling Possible?

Is Tail-Optimal Scheduling Possible?

Queueing Disciplines

Optimal File Splitting for Wireless Networks with Concurrent Access

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