排队模型的研究进展(英文)  

Advances in Queueing Models' Research

作　　者：艾尼.吾甫尔[1] 

机构地区：[1]新疆大学数学与系统科学学院,乌鲁木齐830046

出　　处：《应用泛函分析学报》2011年第3期225-245,共21页Acta Analysis Functionalis Applicata

基　　金：Natural Science Foundation of China(10861011)

摘　　要：根据近10多年来的研究成果介绍以补充变量方法建立的排队模型的动态分析.首先介绍问题的来源,其次介绍研究排队模型的泛函分析工具,然后以D.R.Cox在1955年建立的M/G/1排队模型为例介绍排队模型的适定性,解的渐近行为及排队队长等数量指标的渐近性质的研究方法.最后提出需要进一步研究的一些问题.On the basis of our previous research work, we introduce the dynamics for queueing models formulated by techniques of supplementary variables. We split this paper into 7 parts. Firstly, we state our motivation, next we provide the main tools in functional analysis, and then by studying the M/G/1 queueing model which was established by D. R. Cox in 1955 we state the idea to obtain the well-posedness of queueing models. After that, we introduce some progress in the study of the asymptotic behavior of time-dependent solutions of queueing models by studying the M/G/1 queueing model. In addition, we discuss structure of the time-dependent solutions of queueing models through researching the M/G/1 queueing model. Moreover, we study the asymptotic behavior of the queueing systems＇ indices for the M/G/1 queueing system. We conclude this paper with some open problems.

关 键 词：排队模型 C_0-半群 适定性 预解集 谱 

分 类 号：O177[理学—数学] O226[理学—基础数学]