English

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 KK, 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.

Keywords

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)

R2 v1 2026-06-21T14:29:07.048Z