偏微分方程形式的M/M/1排队模型的主算子的谱分析  

Spectral Analysis of the Operator Corresponding to the M/M/1 Queueing Model Which is Described by Infinitely Many Partial Differential Equations

作　　者：朱春霞 艾尼·吾甫尔[1] ZHU Chun-xia;GUPUR Geni(College of Mathematics and Systems Science,Xinjiang University,Urumqi 830017,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830017

出　　处：《数学的实践与认识》2022年第6期187-206,共20页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11961062)。

摘　　要：研究偏微分方程形式的M/M/1排队模型的主算子在左半复平面中的谱,证明当顾客的到达率λ,服务员的服务率μ和非零实数b满足一定的条件时,-μ+ib不是该主算子的特征值,其中i^(2)=-1.We study spectrum on the left half complex plane of the operator which corresponds to the M/M/1 queueing model that is described by infinitely many partial differential equations and prove that if the arrival rate of customers λ,the service rate of the server μ and the nonzero real number b satisfy the certain conditions,then -μ+ib is not its eigenvalue.

关 键 词：M/M/1排队模型 C_(0)-半群 特征值 

分 类 号：O226[理学—运筹学与控制论]