Year: 2011
Type: article
Abstract: 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.
DOI: 10.1214/10-aap709
Authors: Jiheng Zhang, J. G. Dai, Bert Zwart
Language: English
Subfield: Management Information Systems
Domain: Social Sciences
Open Access status: bronze
Awards: COLLABORATIVE RESEARCH: CSR---SMA: New Breakthrough in Analyzing Limited Resource Sharing Systems, Stochastic Control In Semiconductor Supply Chain, Scalable Analysis for Customer Contact Centers, AMC-SS Collaborative research - Stochastic Processes and Time Series Models: Algorithms, Asymptotics and Phase Transitions
OpenAlex ID: W1545426346