MANY-SERVER HEAVY-TRAFFIC LIMIT FOR QUEUES WITH TIME-VARYING PARAMETERS

被引：35
|
作者：
Liu, Yunan [1 ]
Whitt, Ward [2 ]
机构：
[1] N Carolina State Univ, Dept Ind & Syst Engn, Raleigh, NC 27695 USA
[2] Columbia Univ, Dept Ind Engn & Operat Res, New York, NY 10027 USA
来源：
ANNALS OF APPLIED PROBABILITY | 2014年 / 24卷 / 01期
基金：
美国国家科学基金会;
关键词：
Many-server queues; queues with time-varying arrivals; nonstationary queues; customer abandonment; nonexponential patience distribution; heavy traffic; functional central limit theorem; Gaussian approximation; deterministic fluid approximation; MULTISERVER QUEUES; APPROXIMATIONS;
D O I：
10.1214/13-AAP927
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
A many-server heavy-traffic FCLT is proved for the Gt/M/st + GI queueing model, having time-varying arrival rate and staffing, a general arrival process satisfying a FCLT, exponential service times and customer abandonment according to a general probability distribution. The FCLT provides theoretical support for the approximating deterministic fluid model the authors analyzed in a previous paper and a refined Gaussian process approximation, using variance formulas given here. The model is assumed to alternate between underloaded and overloaded intervals, with critical loading only at the isolated switching points. The proof is based on a recursive analysis of the system over these successive intervals, drawing heavily on previous results for infinite-server models. The FCLT requires careful treatment of the initial conditions for each interval.
引用
收藏
页码：378 / 421
页数：44
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