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  

Stability Analysis to an M/G/1 Queueing System with Additional Optional Services and no Waiting Capacity

作　　者：郭卫华[1] 叶留青 徐厚宝[3] 朱广田[4] 

机构地区：[1]郑州轻工业学院信息与计算科学系,河南郑州450002 [2]焦作高等师范专科学校数学系,河南焦作454100 [3]北京理工大学理学院数学系,北京100081 [4]中科院系统科学研究所,北京100080

出　　处：《工程数学学报》2006年第5期821-826,共6页Chinese Journal of Engineering Mathematics

基　　金：河南省教育厅自然科学基金(2004601141)

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。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 equations, 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.

关 键 词：M/G/1排队系统 谱 渐近稳定性 

分 类 号：O226[理学—运筹学与控制论]