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arXiv · 0912.5306

Diffusion limits of limited processor sharing queues

Jiheng Zhang·J. G. Dai·Bert Zwart
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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.

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Jiheng Zhang, J. G. Dai, Bert Zwart. 2009-12-29. Diffusion limits of limited processor sharing queues. https://doi.org/10.1214/10-aap709

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