Abstract
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.
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Boxma, O., Denisov, D. Sojourn time tails in the single server queue with heavy-tailed service times. Queueing Syst 69, 101–119 (2011). https://doi.org/10.1007/s11134-011-9229-y
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DOI: https://doi.org/10.1007/s11134-011-9229-y