| 附有选择性服务与无等待能力的M/G/1排队系统稳定性分析 |
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| 引用本文： | 郭卫华,叶留青,徐厚宝,朱广田. 附有选择性服务与无等待能力的M/G/1排队系统稳定性分析[J]. 工程数学学报, 2006, 23(5): 821-826 |
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| 作者姓名： | 郭卫华 叶留青 徐厚宝 朱广田 |
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| 作者单位： | 郑州轻工业学院信息与计算科学系,河南,郑州,450002;焦作高等师范专科学校数学系,河南,焦作,454100;北京理工大学理学院数学系,北京,100081;中科院系统科学研究所,北京,100080 |
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| 基金项目： | 河南省教育厅自然科学基金(2004601141) |
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| 摘 要： | 研究附有选择性服务与无等待能力的M/G/1排队系统。通过对描述其系统行为的偏微分方程组的规范化,将其转化为Banach空间中抽象的Cauchy问题。然后,利用强连续有界线性算子半群理论,证明了系统的非负稳定解恰是系统算子的0本征值对应的非负本征向量。同时通过研究系统算子的谱特征,证明了系统算子的谱点均位于复平面的左半平面且虚轴上除0外无谱,进而得到系统的渐近稳定性,特别在范数意义下系统的动态解收敛到稳态解。
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| 关 键 词： | M/G/1排队系统 谱 渐近稳定性 |
| 文章编号： | 1005-3085(2006)05-0821-06 |
| 收稿时间： | 2005-09-21 |
| 修稿时间： | 2005-09-21 |
Stability Analysis to an M/G/1 Queueing System with Additional Optional Services and no Waiting Capacity |
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| GUO Wei-hua,YE Liu-qing,XU Hou-bao,ZHU Guang-tian. Stability Analysis to an M/G/1 Queueing System with Additional Optional Services and no Waiting Capacity[J]. Chinese Journal of Engineering Mathematics, 2006, 23(5): 821-826 |
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| Authors: | GUO Wei-hua YE Liu-qing XU Hou-bao ZHU Guang-tian |
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| Abstract: | Asymptotic behavior of an M/G/1 queueing system with additional optional service and no waiting capacity is studied.By normalizing the system which is described by differential eqnations, we transform the system to an abstract Cauchy problem in a Banach space.Then,by the theory of bounded linear operator semigroup,we show that the unique and nonnegative stability solution of system is the eigenvector of system operator corresponding to eigenvalue 0,By spectral analysis of the system,we find that 0 is the uniquespectral point of system on the imaginary axis.As a result,the asymptotic stability of the system is obtained. |
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| Keywords: | M/G/1 queueing system sperctral asymptotic stability |
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