一类对负顾客进行服务的排队系统主算子的豫解集

Resolvent Set of Queueing Model with Service to Negative Customers

针对M/G1/1系统排队模型,将其转化成Banach空间中抽象Cauchy问题,研究了模型主算子的豫解集。求出了该模型主算子的共轭算子,运用线性算子及其共轭算子谱之间的关系,研究其主算子的共轭算子的豫解集,得到在虚轴上除0外所有点都属于该模型主算子的豫解集。

According to M/G1/1 queue model, we study the resolvent set of this model by convering the model into an abstract Cauchy problem in a Banach space. We get the adjoint operator of the main operator of the queueing model with service to negative customers. By using the relation between the spectrum of a linear operator and its adjoint operator, we study the resolvet set of the operator corresponding to this model, and the result all points on the imaginary axis except for zero belong to the resolvent set of the operator is obtained.