应用数学2018，Vol.31Issue(1)：60-78,19.
附有不可靠服务台和无等待能力的M/G/1/1排队模型时间依赖解的 渐近性分析
Asymptotic Analysis of the Time-Dependent Solution of the M/G/1/1 Queue with Unreliable Server and No Waiting Capacity
摘要
Abstract
In this paper, we study the asymptotic behavior of the time-dependent solution of the M/G/1/1 queue with unreliable server and no waiting capacity. First, by using the strong continuous semigroup theory, we prove the existence and uniqueness of the nonnegative time-dependent solution of the system model. Next, by studying spectral properties of the operator corresponding to the system model, we obtain that zero is an eigenvalue of the operator and its adjoint operator with geometric multiplicity one and all points on the imaginary axis except zero belong to the resolvent set of the operator. Thus, by combining the above results, we deduce that the time-dependent solution of the system model converges strongly to its steady state solution.关键词
C0-半群/dispersive算子/特征值/几何重数/豫解集Key words
C0-semigroup/Dispersive operator/Eigenvalue/Resolvent set/Geometric multiplicity分类
数理科学引用本文复制引用
阿力木·米吉提..附有不可靠服务台和无等待能力的M/G/1/1排队模型时间依赖解的 渐近性分析[J].应用数学,2018,31(1):60-78,19.基金项目
Supported by the Special Training Research Project for Science and Technology Talents of Minority Nationalities in Xinjiang (2016D0211) （2016D0211）
