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常微分方程形式的M/M/1排队算子的谱分析
  • 期刊名称：应用泛函分析学报
  • 时间：0
  • 页码：186-192
  • 语言：中文
  • 分类：O226[理学—运筹学与控制论;理学—数学]
  • 作者机构：[1]天津大学数学系,天津300072, [2]哈尔滨理工大学应用科学学院,哈尔滨150080
  • 相关基金：国家自然科学基金（NSFC-60874034）
  • 相关项目：偏微分网络系统的控制
作者： 赵志学|邵琛|许跟起|
关键词： M/M/1排队模型, 谱, 几何解, 概率母函数, M/M/1 queueing model, spectra, geometric solutions, probability generating function
中文摘要：

在l^1空间研究了常微分方程形式的M／M／1排队模型确定的算子А的谱问题．通过细致的谱分析，表明算子А的谱是一个椭圆型，椭圆内部点全是算子А的本征值．0位于椭圆的右边界点是边界上唯一的本征值，从而0不能与其它谱点相分离．这一结果表明常微分方程形式的M／M／1排队系统在有限时间不可能看到系统的稳定状态．

英文摘要：

In this paper, the spectral properties of operator А determinedby M/M/1 queueing model described by ordinary differential equations are studied in l^1. By complete spectral analysis, we show that the spectra of А have an elliptic shape, and all the interior points of the ellipse are the eigenvalues of .А. 0 is the only eigenvalue on the boundary, so it can not be separated from other spectra. The results show that it is impossible to see the steady-state of queueing system described by ordinary differential equations in the limited time.

同期刊论文项目
偏微分网络系统的控制
期刊论文 36 会议论文 16 著作 2
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