2009/12/31 by Jiheng Zhang, Jinghe Zhang, J. G. Dai +2
Business, Management and Accounting · Computer Science · Engineering · Mathematics · #Advanced Queuing Theory Analysis #Petri Nets in System Modeling #Scheduling and Optimization Algorithms #math.PR
paper · pdf · doi:10.1214/10-aap709
published as Annals of Applied Probability 2011, Vol. 21, No. 2, 745-799 · 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)
openalex publication_date 2011/03/22 · arxiv created 2011/04/08 · arxiv updated 2012/07/02 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/01
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.