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负实谱

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

研究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b_(1),修复率b_(2)都是正数且c≠b_(2)时,左半复平面中的竖线-(λ+b_(2))+iu上的所有点都不是该主算子的特征值,其中i^(2)=-1,u∈R.

We study spectrum of the underlying operator corresponding to the M^([X])/M/1retrial 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 b_(1)and the repair rate b_(2)are positive and α≠b_(2),then all-(λ+b_(2))+ iu are not eigenvalue of the underlying operator,where i^(2)=-1,u∈R.