M/G/1排队论系统的渐近稳定性  

Asymptotic Stability of the M/G/1 Queueing System

作　　者：郑福[1,2] 高超[1] 朱广田[3] 

机构地区：[1]北京信息控制研究所,北京100048 [2]渤海大学数学系,锦州121002 [3]中国科学院数学与系统科学研究院,北京100190

出　　处：《应用泛函分析学报》2011年第2期218-224,共7页Acta Analysis Functionalis Applicata

摘　　要：通过M/G/1算子的谱分析得到了M/G/1排队论系统的渐近稳定性.首先,将系统方程转化为某一合适Banach空间上的抽象Cauchy问题,从而引入M/G/1算子.其次,分析了M/G/1算子的谱分布,得到了0是M/G/1算子的简单本征值且M/G/1算子的谱分布在左半平面的结果.最后,利用谱分析结果和算子半群理论得到了M/G/1排队论系统的渐近稳定性.In this paper,the asymptotic stability of the M/G/1 queueing system was obtained under reasonable assumptions on the service rate functions by analyzing the spectral distribution of the M/G/1 operator.Firstly,the governing integro-differential equations of M/G/1 queueing system were translated into an abstract Cauchy problem on some suitable Banach space and the M/G/1 operator was introduced.Secondly,the spectral distribution of the M/G/1 operator was analyzed and the spectral set of the M/G/1 operator belongs to negative half plane was obtained.Furthermore, zero is the unique point spectrum on the imaginary axis and it is the algebraically simple eigenvalue of the M/G/1 operator.At last,the main result of this note that the M/G/1 queueing system is asymptotically stable was shown.

关 键 词：C_0-半群 M/G/1排队论系统 渐近稳定性 

分 类 号：O177.29[理学—数学]