Open Access
August 2002 The fluid limit of a heavily loaded processor sharing queue
H. Christian Gromoll, Amber L. Puha, Ruth J. Williams
Ann. Appl. Probab. 12(3): 797-859 (August 2002). DOI: 10.1214/aoap/1031863171


Consider a single server queue with renewal arrivals and i.i.d. service times in which the server operates under a processor sharing service discipline. To describe the evolution of this system, we use a measure valued process that keeps track of the residual service times of all jobs in the system at any given time. From this measure valued process, one can recover the traditional performance processes, including queue length and workload. We propose and study a critical fluid model (or formal law of large numbers approximation) for a heavily loaded processor sharing queue. The fluid model state descriptor is a measure valued function whose dynamics are governed by a nonlinear integral equation. Under mild assumptions, we prove existence and uniqueness of fluid model solutions. Furthermore, we justify the critical fluid model as a first order approximation of a heavily loaded processor sharing queue by showing that, when appropriately rescaled, the measure valued processes corresponding to a sequence of heavily loaded processor sharing queues converge in distribution to a limit that is almost surely a fluid model solution.


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H. Christian Gromoll. Amber L. Puha. Ruth J. Williams. "The fluid limit of a heavily loaded processor sharing queue." Ann. Appl. Probab. 12 (3) 797 - 859, August 2002.


Published: August 2002
First available in Project Euclid: 12 September 2002

zbMATH: 1017.60092
MathSciNet: MR1925442
Digital Object Identifier: 10.1214/aoap/1031863171

Primary: 60K25
Secondary: 68M20 , 90B22

Keywords: fluid model , heavy traffic , measure valued process , Processor sharing queue , renewal equation

Rights: Copyright © 2002 Institute of Mathematical Statistics

Vol.12 • No. 3 • August 2002
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