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.
Citation
Jiheng Zhang. J. G. Dai. Bert Zwart. "Diffusion limits of limited processor sharing queues." Ann. Appl. Probab. 21 (2) 745 - 799, April 2011. https://doi.org/10.1214/10-AAP709
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