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On large delays in multi-server queues with heavy tails

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>05/2012
<mark>Journal</mark>Mathematics of Operations Research
Issue number2
Volume37
Number of pages18
Pages (from-to)201-218
Publication StatusPublished
Early online date20/03/12
<mark>Original language</mark>English

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.