Queueing Systems

, 69:101 | Cite as

Sojourn time tails in the single server queue with heavy-tailed service times



We consider the GI/GI/1 queue with regularly varying service requirement distribution of index −α. It is well known that, in the M/G/1 FCFS queue, the sojourn time distribution is also regularly varying, of index 1−α, whereas in the case of LCFS or Processor Sharing, the sojourn time distribution is regularly varying of index −α. That raises the question whether there exist service disciplines that give rise to a regularly varying sojourn time distribution with any index −γ∈[−α,1−α]. In this paper that question is answered affirmatively.


GI/GI/1 queue Regular variation Sojourn time tail 

Mathematics Subject Classification (2000)

60K25 60F10 68M20 90B18 90B22 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.EURANDOM and Department of Mathematics and Computer ScienceEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.School of Mathematical and Computer SciencesHeriot-Watt UniversityEdinburghUK
  3. 3.University of CardiffCardiffUK

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