On Large Delays in Multi-Server Queues with Heavy Tails

2011/04/30 by Sergey Foss, Dmitry Korshunov
Mathematics · #math.PR #msc:60F10 #msc:60K25 #msc:90B22

paper · pdf · doi:10.1287/moor.1120.0539

published as Mathematics of Operations Research, 37 (2012) 201-218

arxiv created 2012/08/18 · arxiv updated 2013/03/20

Abstract

We present upper and lower bounds for the tail distribution of the stationary waiting time D in the stable GI/GI/s 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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