Queueing Systems

, Volume 55, Issue 2, pp 107–121 | Cite as

Tail behavior of conditional sojourn times in Processor-Sharing queues

  • Regina Egorova
  • Bert Zwart


We investigate the tail behavior of the sojourn-time distribution for a request of a given length in an M/G/1 Processor-Sharing (PS) queue. An exponential asymptote is proven for general service times in two special cases: when the traffic load is sufficiently high and when the request length is sufficiently small. Furthermore, using the branching process technique we derive exact asymptotics of exponential type for the sojourn time in the M/M/1 queue. We obtain an equation for the asymptotic decay rate and an exact expression for the asymptotic constant. The decay rate is studied in detail and is compared to other service disciplines. Finally, using numerical methods, we investigate the accuracy of the exponential asymptote.


M/G/1 queue Processor Sharing Sojourn time Exponential asymptotics Tail behavior Laplace-Stieltjes transforms Branching processes Random sums 


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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.CWIAmsterdamThe Netherlands
  2. 2.Department of Mathematics & Computer ScienceEindhoven University of TechnologyEindhovenThe Netherlands

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