一类服务失效状态为吸收状态及重试率为常数的M^([X])/M/1排队模型的主算子的负特征值  

On the Negative Eigenvalues of the Operator Which Corresponds to an M^([X])/M/1 Retrial Queueing Model with Constant Rate of Repeated Attempts and Absorbent States of the Failure States

作　　者：李卓笑 艾尼.吾甫尔[1] LI Zhuoxiao;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,乌鲁木齐830046

出　　处：《应用泛函分析学报》2018年第4期323-335,共13页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金(11371303)

摘　　要：研究一类失效状态为吸收状态及重试率为常数的M^([X])/M/1排队模型的主算子在左半实轴上的特征值,证明:当顾客的到达率λ,服务员的服务率v,服务员的服务完成率b,顾客的重试率α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.We study eigenvalues of the operator which corresponds to an M^[X]/M/1 retrial queueing model with constant rate of repeated attempts and absorbent states of the failure states in the left real line and prove that if the arrival rate of customers λ, the service rate of the server μ, the completion rate of the server b and the repeated rate of customers a satisfy a certain condition, then-α is an eigenvalue of the operator with geometric multiplicity one.

关 键 词：M^[X]/M/1重试排队模型 特征值 几何重数 

分 类 号：O177.7[理学—数学]