Diffusion Limits of Limited Processor Sharing Queues.

J. Zhang; J.G. Dai; A.P. Zwart

doi:10.1214/10-AAP709

Diffusion Limits of Limited Processor Sharing Queues.

J. Zhang, J.G. Dai, A.P. Zwart

Mathematics

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

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. © Institute of Mathematical Statistics, 2011.

Original language	English
Pages (from-to)	745-799
Journal	Annals of Applied Probability
Volume	21
DOIs	https://doi.org/10.1214/10-AAP709
Publication status	Published - 2011

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title = "Diffusion Limits of Limited Processor Sharing Queues.",

abstract = "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. {\textcopyright} Institute of Mathematical Statistics, 2011.",

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AB - 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. © Institute of Mathematical Statistics, 2011.

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JO - Annals of Applied Probability

JF - Annals of Applied Probability

ER -

Diffusion Limits of Limited Processor Sharing Queues.

Abstract

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