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

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

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Article ID: iaor20119985
Volume: 69
Issue: 2
Start Page Number: 101
End Page Number: 119
Publication Date: Oct 2011
Journal: Queueing Systems
Authors: ,
Keywords: stochastic processes
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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