| 常微分方程形式的M/M/1排队算子的谱分析 |
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| 引用本文： | 赵志学,邵琛,许跟起.常微分方程形式的M/M/1排队算子的谱分析[J].应用泛函分析学报,2010,12(2):186-192. |
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| 作者姓名： | 赵志学 邵琛 许跟起 |
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| 作者单位： | 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 |
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| 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A的谱问题.通过细致的谱分析,表明算子A的谱是一个椭圆型,椭圆内部点全是算子A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.
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| 关 键 词： | M／M／1排队模型 谱 几何解 概率母函数 |
Spectral Analysis of Operator in M/M/1 Queueing Model Described by Ordinary Differential Equations |
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| ZHAO Zhixue,SHAO Chen,XU Genqi.Spectral Analysis of Operator in M/M/1 Queueing Model Described by Ordinary Differential Equations[J].Acta Analysis Functionalis Applicata,2010,12(2):186-192. |
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| Authors: | ZHAO Zhixue SHAO Chen XU Genqi |
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| Institution: | 1. Department of Mathematics, Tianjin University, Tianjin 300072, China 2. Applied Science College, Harbin University of Science and Technology, Harbin 150050, China) |
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| Abstract: | 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. |
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| Keywords: | M/M/1 queueing model spectra geometric solutions probability generating function |
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