The Annals of Applied Probability

Diffusion limits of limited processor sharing queues

Jiheng Zhang, J. G. Dai, and Bert Zwart

Full-text: Open access

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.

Article information

Source
Ann. Appl. Probab., Volume 21, Number 2 (2011), 745-799.

Dates
First available in Project Euclid: 22 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1300800987

Digital Object Identifier
doi:10.1214/10-AAP709

Mathematical Reviews number (MathSciNet)
MR2807972

Zentralblatt MATH identifier
1220.60055

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22]
Secondary: 68M20: Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx] 90B22: Queues and service [See also 60K25, 68M20]

Keywords
Limited processor sharing heavy traffic diffusion approximation state-space collapse measure valued process

Citation

Zhang, Jiheng; Dai, J. G.; Zwart, Bert. Diffusion limits of limited processor sharing queues. Ann. Appl. Probab. 21 (2011), no. 2, 745--799. doi:10.1214/10-AAP709. https://projecteuclid.org/euclid.aoap/1300800987


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