Diffusion Limits of Limited Processor Sharing Queues.

J. Zhang, J.G. Dai, A.P. Zwart

Research output: Contribution to JournalArticleAcademicpeer-review


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. © Institute of Mathematical Statistics, 2011.
Original languageEnglish
Pages (from-to)745-799
JournalAnnals of Applied Probability
Publication statusPublished - 2011


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