The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 21, Number 2 (2011), 745-799.
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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