Approximations and Optimal Control for State-Dependent Limited Processor Sharing Queues

Approximations and Optimal Control for State-dependent Limited Processor Sharing Queues

The paper studies approximations and control of a processor sharing (PS) server where the service rate depends on the number of jobs occupying the server. The control of such a system is implemented by imposing a limit on the number of jobs that can share the server concurrently, with the rest of the jobs waiting in a first-in-first-out (FIFO) buffer. A desirable control scheme should strike th...

Steady state approximations of limited processor sharing queues in heavy traffic

We investigate steady state properties of limited processor sharing queues in heavy traffic. Our analysis builds on previously obtained process limit theorems, and requires the interchange of steady state and heavy traffic limits, which are established by a coupling argument. The limit theorems yield explicit approximations of the steady state queue length and response time distribution in heav...

Limited Processor Sharing Queues and Multi-server Queues

Diffusion Limits of Limited Processor Sharing Queues

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 p...

Law of Large Number Limits of Limited Processor-Sharing Queues

Motivated by applications in computer and communication systems, we consider a processor sharing queue where the number of jobs served is not larger than K. We propose a measure-valued fluid model for this limited processor sharing queue and show that there exists a unique associated fluid model solution. In addition, we show that this fluid model arises as the limit of a sequence of appropriat...