排队模型的研究进展

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／C／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．

Advances in Queueing Models' Research

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.