Diffusion limits of limited processor sharing queues
Probability
2012-07-02 v2
Abstract
We consider a processor sharing queue where the number of jobs served at any time is limited to , 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.
Cite
@article{arxiv.0912.5306,
title = {Diffusion limits of limited processor sharing queues},
author = {Jiheng Zhang and J. G. Dai and Bert Zwart},
journal= {arXiv preprint arXiv:0912.5306},
year = {2012}
}
Comments
Published in at http://dx.doi.org/10.1214/10-AAP709 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)