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.
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.
出处
《应用泛函分析学报》
CSCD
2010年第2期186-192,共7页
Acta Analysis Functionalis Applicata
基金
国家自然科学基金(NSFC-60874034)
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
