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Queueing Systems

, Volume 52, Issue 4, pp 237–250 | Cite as

Large deviations of sojourn times in processor sharing queues

  • Michel Mandjes
  • Bert Zwart
Article

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.

Keywords

Processor sharing queues Sojourn time Large deviations Change of measure Importance sampling 

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Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.CWIAmsterdamThe Netherlands
  2. 2.Faculty of Mathematical SciencesUniversity of TwenteEnschedeThe Netherlands
  3. 3.Department of Mathematics & Computer ScienceEindhoven University of TechnologyEindhovenThe Netherlands

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