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June 2007 Heavy traffic limit for a processor sharing queue with soft deadlines
H. Christian Gromoll, Łukasz Kruk
Ann. Appl. Probab. 17(3): 1049-1101 (June 2007). DOI: 10.1214/105051607000000014


This paper considers a GI/GI/1 processor sharing queue in which jobs have soft deadlines. At each point in time, the collection of residual service times and deadlines is modeled using a random counting measure on the right half-plane. The limit of this measure valued process is obtained under diffusion scaling and heavy traffic conditions and is characterized as a deterministic function of the limiting queue length process. As special cases, one obtains diffusion approximations for the lead time profile and the profile of times in queue. One also obtains a snapshot principle for sojourn times.


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H. Christian Gromoll. Łukasz Kruk. "Heavy traffic limit for a processor sharing queue with soft deadlines." Ann. Appl. Probab. 17 (3) 1049 - 1101, June 2007.


Published: June 2007
First available in Project Euclid: 22 May 2007

zbMATH: 1130.60087
MathSciNet: MR2326240
Digital Object Identifier: 10.1214/105051607000000014

Primary: 60K25
Secondary: 60F17, 68M20, 90B22

Rights: Copyright © 2007 Institute of Mathematical Statistics


Vol.17 • No. 3 • June 2007
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