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

Boxma, Onno and Denisov, Denis 2011. Sojourn time tails in the single server queue with heavy-tailed service times. Queueing Systems 69 (2) , pp. 101-119. 10.1007/s11134-011-9229-y

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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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	GI/GI/1 queue; Regular variation; Sojourn time tail
Publisher:	Springer
ISSN:	1572-9443
Last Modified:	26 Jun 2019 01:56
URI:	https://orca.cardiff.ac.uk/id/eprint/17458

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