Validity of heavy-traffic steady-state approximations in many-server queues with abandonment
Validity of heavy-traffic steady-state approximations in many-server queues with abandonment
复制标题
放弃的多服务器队列中大流量稳态近似的有效性
DOI:
10.1007/s11134-014-9394-x
复制
发表时间:
2013
期刊:
影响因子:
1.2
通讯作者:
Xuefeng Gao
中科院分区:
文献类型:
--
作者:
J. Dai;A. Dieker;Xuefeng Gao
We consider GI/Ph/n+M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$GI/Ph/n+M$$\end{document} parallel-server systems with a renewal arrival process, a phase-type service time distribution, n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document} homogenous servers, and an exponential patience time distribution with positive rate. We show that in the Halfin–Whitt regime, the sequence of stationary distributions corresponding to the normalized state processes is tight. As a consequence, we establish an interchange of heavy-traffic and steady-state limits for GI/Ph/n+M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$GI/Ph/n+M$$\end{document} queues.