Diffusion Limits of Limited Processor Sharing Queues
نویسندگان
چکیده
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.
منابع مشابه
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...
متن کاملSteady 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...
متن کاملFluid and diffusion limits for transient sojourn times of processor sharing queues with time varying rates
We provide an approximate analysis of the transient sojourn time for a processor sharing queue with time varying arrival and service rates, where the load can vary over time, including periods of overload. Using the same asymptotic technique as uniform acceleration as demonstrated in [12] and [13], we obtain fluid and diffusion limits for the sojourn time of the Mt/Mt/1 processor-sharing queue....
متن کاملAsymptotic behavior of generalized processor sharing queues under subexponential assumptions
We analyze the behavior of Generalized Processor Sharing (GPS) queues with heavy-tailed service times. We compute the exact tail asymptotics of the stationary workload of an individual class and give new conditions for reduced-load equivalence and induced burstiness to hold. We also show that both phenomena can occur simultaneously. Our proofs rely on the single big event theorem and new fluid ...
متن کاملDiffusion Limits of Limited Processor Sharing
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...
متن کامل