Large deviations of sojourn times in processor sharing queues |
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| Authors: | Michel Mandjes Bert Zwart |
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| Affiliation: | (1) CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands;(2) Faculty of Mathematical Sciences, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands;(3) Department of Mathematics & Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands |
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| Abstract: | This paper presents a large deviation analysis of the steady-state sojourn time distribution in the GI/G/1 PS queue. Logarithmic estimates are obtained under the assumption of the service time distribution having a light tail, thus supplementing recent results for the heavy-tailed setting. Our proof gives insight into the way a large sojourn time occurs, enabling the construction of an (asymptotically efficient) importance sampling algorithm. Finally our results for PS are compared to a number of other service disciplines, such as FCFS, LCFS, and SRPT. 2000 mathematics subject classification: 60K25. |
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| Keywords: | Processor sharing queues Sojourn time Large deviations Change of measure Importance sampling |
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