每个忙期中第一个顾客被特殊服务的M/M/1排队模型的主算子的点谱

On the Point Spectrum of the Operator Which Corresponds to the M/M/1 Queueing Model with Exceptional Service Time for the First Customer in Each Busy Period

研究每个忙期中第一个顾客被特殊服务的M/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μ及特殊服务率η满足λ<μ<λ+η时,λ-μ是该主算子的几何重数为1的特征值.

We consider the point spectrum of the operator, which corresponds to the M/M/1 queueing model with exceptional service time for the first customer in each busy period, on the left real line and prove that if the arrival rate of customers λ, the service rate of the server μ and the exceptional service rate of the server η satisfy λ〈μ〈λ＋η, then λ-μ is an eigenvalue of the operator with geometric multiplicity one.