一类服务中断和重试率为常数的M^([X])/M/1排队模型的主算子的点谱  

On the Point Spectrum of the Operator Corresponding to an M^([X])/M/1 Retrial Queueing Model with Sever Breakdowns and Constant Rate of Repeated Attempts

作　　者：汪云宏 艾尼·吾甫尔[1] WANG Yun-hong;GUPUR Geni(College of Mathematics and Systems Science,Xinjiang University,Urumqi 830046,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830046

出　　处：《数学的实践与认识》2021年第18期225-245,共21页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11961062)。

摘　　要：研究一类服务中断和重试率为常数的M^([X])/M/1排队模型的主算子的点谱,证明:当顾客的到达率λ,服务员的服务率v:顾客的重试率α,服务员的服务完成率b1,修复率b2满足一定的条件时,-α是该主算子的几何重数为1的特征值;-(λ+α)与-(λ+b2)不是该主算子的点谱.We study point spectrum of the operator corresponding to an M^([X])/M/1 retrial queueing model with sever breakdowns and constant rate of repeated attempts and prove that if the arrival rate of customers λ,the service rate of the server v,the repeated rate of customers α,the completion rate of the server b1 and the repair rate b2 satisfy a certain condition,then-α is an eigenvalues of the operator with geometric multiplicity one,-(λ+α)and-(λ+b2) are not eigenvalue of the operator.

关 键 词：M^([X])/M/1重试排队模型 特征值 几何重数 

分 类 号：O226[理学—运筹学与控制论]