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.
Publié le : 2011-04-15
Classification:
Limited processor sharing,
heavy traffic,
diffusion approximation,
state-space collapse,
measure valued process,
60K25,
68M20,
90B22
@article{1300800987,
author = {Zhang, Jiheng and Dai, J. G. and Zwart, Bert},
title = {Diffusion limits of limited processor sharing queues},
journal = {Ann. Appl. Probab.},
volume = {21},
number = {1},
year = {2011},
pages = { 745-799},
language = {en},
url = {http://dml.mathdoc.fr/item/1300800987}
}
Zhang, Jiheng; Dai, J. G.; Zwart, Bert. Diffusion limits of limited processor sharing queues. Ann. Appl. Probab., Tome 21 (2011) no. 1, pp. 745-799. http://gdmltest.u-ga.fr/item/1300800987/