摘要
讨论了具有选择性服务的理发店M/G/1排队系统.此系统通过选取空间及定义算子,将模型方程转化成Banach空间中抽象的Cauchy问题,运用C0半群的理论,证明系统算子是耗散算子,得出系统算子的共轭算子及其定义域,并证明了0是系统算子的简单本征值且是虚轴上唯一的谱点,最后由算子的谱分析得到系统趋于稳定的时间依赖解.
We discussed the barber＇s selective service M/G/1 queueing system. By choosing state space and defining operators of systems,we transfer model into an abstract Cauchy problem. Studying the nature of the system operator,that is using C0-semigroup theory,we first prove the system operator is a dissipative operator operator. Then we obtain the adjoint operator of the system operator and its domain. Furthermore,we prove that the unique and nonnegative stability solution of system is the eigenvector of system operator corresponding to eigenvalue 0. Finally by the Spectral analysis of operator,the time dependent solution of the system tends to be stable is obtained.
作者
霍慧霞
原文志
HUO Hui-xia YUAN Wen-zhi(Department of Mathematics, Tai Yuan Normal University, Shanxi Yuci 030619, China)
出处
《淮阴师范学院学报（自然科学版）》
CAS
2017年第3期195-199,共5页
Journal of Huaiyin Teachers College;Natural Science Edition
关键词
M/G/1排队系统
耗散算子
虚轴
系统稳定性
M/G/1 queueing system
dissipative operator
imaginary axis
system stability
