Blanchet, J., A. Murthy, K.R. Tail asymptotics for delay in a half-loaded GI/GI/2 queue with heavy-tailed job sizes. Queueing Syst 81, 301–340 (2015). https://doi.org/10.1007/s11134-015-9451-0
Abstract
We obtain asymptotic bounds for the tail distribution of steady-state waiting time in a two-server queue where each server processes incoming jobs at a rate equal to the rate of their arrivals (that is, the half-loaded regime). The job sizes are taken to be regularly varying. When the incoming jobs have finite variance, there are basically two types of effects that dominate the tail asymptotics. While the quantitative distinction between these two manifests itself only in the slowly varying components, the two effects arise from qualitatively very different phenomena (arrival of one extremely big job or two big jobs). Then there is a phase transition that occurs when the incoming jobs have infinite variance. In that case, only one of these effects dominates the tail asymptotics; the one involving arrival of one extremely big job.
Authors
Jose Blanchet, Karthyek R A. Murthy
Publication date
2015/12
Journal
Queueing Systems
Volume
81
Pages
301-340
Publisher
Springer US
