On large delays in multi-server queues with heavy tails

Foss, Sergey and Korshunov, Dmitry (2012) On large delays in multi-server queues with heavy tails. Mathematics of Operations Research, 37 (2). pp. 201-218. ISSN 0364-765X

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Abstract

We present upper and lower bounds for the tail distribution of the stationary waiting time D in the stable GI/GI/s first-come first-served (FCFS) queue. These bounds depend on the value of the traffic load ρ which is the ratio of mean service and mean interarrival times. For service times with intermediate regularly varying tail distribution the bounds are exact up to a constant, and we are able to establish a “principle of s − k big jumps” in this case (here k is the integer part of ρ), which gives the most probable way for the stationary waiting time to be large. Another corollary of the bounds obtained is to provide a new proof of necessity and sufficiency of conditions for the existence of moments of the stationary waiting time.

Item Type:
Journal Article
Journal or Publication Title:
Mathematics of Operations Research
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/aacsb/disciplinebasedresearch
Subjects:
ID Code:
76867
Deposited By:
Deposited On:
25 Nov 2015 09:22
Refereed?:
Yes
Published?:
Published
Last Modified:
28 Oct 2020 04:17