Fluid and diffusion limits for transient sojourn times of processor sharing queues with time varying rates |
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Authors: | Robert C Hampshire Mor Harchol-Balter William A Massey |
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Institution: | (1) Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ;(2) School of Computer Science, Carnegie Mellon University, USA |
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Abstract: | 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. Our analysis is enabled by the introduction of a “virtual customer” which differs from the notion
of a “tagged customer” in that the former has no effect on the processing time of the other customers in the system. Our analysis
generalizes to non-exponential service and interarrival times, when the fluid and diffusion limits for the queueing process
are known. |
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Keywords: | Processor sharing Fluid limits Diffusion limits Transient behavior Time-varying queues Uniform acceleration Sojourn times Virtual customers |
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