Tail asymptotics for delay in a half-loaded GI/GI/2 queue with heavy-tailed job sizes

被引:3
|
作者
Blanchet, Jose [1 ]
Murthy, Karthyek R. A. [1 ]
机构
[1] Columbia Univ, Dept IEOR, New York, NY 10027 USA
基金
美国国家科学基金会;
关键词
Regularly varying; FCFS multiserver queue; Large deviations; Stationary waiting time; INDEPENDENT RANDOM-VARIABLES; LARGE DEVIATIONS; RANDOM-WALKS; PROBABILITIES; SUMS;
D O I
10.1007/s11134-015-9451-0
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
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.
引用
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页码:301 / 340
页数:40
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