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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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.

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Journal Article
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Mathematics of Operations Research
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25 Nov 2015 09:22
Last Modified:
22 Nov 2022 02:36