Scheduling control for Markov-modulated single-server multiclass queueing systems in heavy traffic

被引:0
作者
Amarjit Budhiraja
Arka Ghosh
Xin Liu
机构
[1] University of North Carolina,Department of Statistics & Operations Research
[2] Iowa State University,Department of Statistics
[3] University of Minnesota,Institute for Mathematics and its Applications
来源
Queueing Systems | 2014年 / 78卷
关键词
Markov-modulated queueing networks; Multiscale queueing systems; Heavy traffic; Diffusion approximations ; Scheduling control; Scaling limits; Asymptotic optimality; rule; Brownian control problem (BCP); Primary 60K25; 90B22; 90B35; 90B36; secondary 60J70; 60F05;
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摘要
This paper studies a scheduling control problem for a single-server multiclass queueing network in heavy traffic, operating in a changing environment. The changing environment is modeled as a finite-state Markov process that modulates the arrival and service rates in the system. Various cases are considered: fast changing environment, fixed environment, and slowly changing environment. In all cases, the arrival rates are environment dependent, whereas the service rates are environment dependent when the environment Markov process is changing fast, and are assumed to be constant in the other two cases. In each of the cases, using weak convergence analysis, in particular functional limit theorems for Poisson processes and ergodic Markov processes, it is shown that an appropriate “averaged” version of the classical cμ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c\mu $$\end{document}-policy (the priority policy that favors classes with higher values of the product of holding cost c\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c$$\end{document} and service rate μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document}) is asymptotically optimal for an infinite horizon discounted cost criterion.
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页码:57 / 97
页数:40
相关论文
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