Many-server Gaussian limits for overloaded non-Markovian queues with customer abandonment

被引：25

作者：

Aras, A. Korhan ^{[1
]}

Chen, Xinyun ^{[2
]}

Liu, Yunan ^{[3
]}

机构：

[1] SAS Inst, Cary, NC USA

[2] Wuhan Univ, Sch Econ & Management, Wuhan, Hubei, Peoples R China

[3] North Carolina State Univ, Ind & Syst Engn Dept, Raleigh, NC 27695 USA

来源：

QUEUEING SYSTEMS | 2018年 / 89卷 / 1-2期

基金：

美国国家科学基金会;

关键词：

Many-server queues; Many-server heavy-traffic limits; Nonexponential service times; Efficiency-driven regime; Customer abandonment; Gaussian approximation; Functional central limit theorem; FLUID MODELS; APPROXIMATIONS; SYSTEM;

D O I：

10.1007/s11134-018-9575-0

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

Extending Ward Whitt's pioneering work "Fluid Models for Multiserver Queues with Abandonments, Operations Research, 54(1) 37-54, 2006," this paper establishes a many-server heavy-traffic functional central limit theorem for the overloaded queue with stationary arrivals, nonexponential service times, n identical servers, and nonexponential patience times. Process-level convergence to non-Markovian Gaussian limits is established as the number of servers goes to infinity for key performance processes such as the waiting times, queue length, abandonment and departure processes. Analytic formulas are developed to characterize the distributions of these Gaussian limits.

引用

页码：81 / 125

页数：45

共 39 条

[31] Two-parameter heavy-traffic limits for infinite-server queues [J].