Monotonicity in the Limited Processor-Sharing Queue

Nuyens, Misja; Weij, W. van der

doi:10.1080/15326340903088545

Cited by 12 publications

(13 citation statements)

References 16 publications

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“…A computational analysis based on matrix geometric methods is performed in Zhang and Lipsky [23,24]. Some stochastic ordering results are derived in Nuyens and van der Weij [19]. Recently, Zhang, Dai and Zwart [25,26] studied the stochastic processes underlying the LPS queue in the heavy traffic regime, an asymptotic regime where the traffic intensity converges to 1.…”

Section: Introductionmentioning

confidence: 99%

Steady state approximations of limited processor sharing queues in heavy traffic

Zhang

Zwart

2008

Queueing Syst

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We investigate steady state properties of limited processor sharing queues in heavy traffic. Our analysis builds on previously obtained process limit theorems, and requires the interchange of steady state and heavy traffic limits, which are established by a coupling argument. The limit theorems yield explicit approximations of the steady state queue length and response time distribution in heavy traffic, of which the quality is supported by simulation experiments.

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Section: Introductionmentioning

confidence: 99%

Steady state approximations of limited processor sharing queues in heavy traffic

Zhang

Zwart

2008

Queueing Syst

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“…A computational analysis based on matrix geometric methods is performed in Zhang and Lipsky [27,28]. Some stochastic ordering results are derived in Nuyens and van de Weij [21]. Recently, Zhang, Dai and Zwart [29] have developed a fluid approximation for the LPS queue using the framework of measure-valued processes.…”

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confidence: 99%

Diffusion limits of limited processor sharing queues

Zhang¹,

Dai²,

Zwart³

2011

Ann. Appl. Probab.

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We consider a processor sharing queue where the number of jobs served at any time is limited to $K$, with the excess jobs waiting in a buffer. We use random counting measures on the positive axis to model this system. The limit of this measure-valued process is obtained under diffusion scaling and heavy traffic conditions. As a consequence, the limit of the system size process is proved to be a piece-wise reflected Brownian motion.Comment: Published in at http://dx.doi.org/10.1214/10-AAP709 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

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“…This lemma is proved by invoking a stochastic ordering result for the LPS-c queue by Nuyens and van der Weij [12]. We prove Lemma 7 in the appendix.…”

Section: Tail-robust Design: Performance In Expected Sojourn Timementioning

confidence: 99%

Scheduling for the tail: Robustness versus optimality

Nair

Wierman

Zwart

2010

2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Abstract-When scheduling to minimize the sojourn time tail, the goals of optimality and robustness are seemingly at odds. Over the last decade, results have emerged which show that scheduling disciplines that are near-optimal under light (exponential) tailed workload distributions do not perform well under heavy (power) tailed workload distributions, and vice-versa. Very recently, it has been shown that this conflict between optimality and robustness is fundamental, i.e., no policy that does not learn information about the workload can be optimal across both light-tailed and heavytailed workloads. In this paper we show that one can exploit very limited workload information (the system load) in order to design a scheduler that provides robust performance across heavy-tailed and light-tailed workloads.

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Monotonicity in the Limited Processor-Sharing Queue

Cited by 12 publications

References 16 publications

Steady state approximations of limited processor sharing queues in heavy traffic

Steady state approximations of limited processor sharing queues in heavy traffic

Diffusion limits of limited processor sharing queues

Scheduling for the tail: Robustness versus optimality

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