带有反馈与起动故障的M/G/1重新访问排队系统的适定性分析

文章研究一个带有贝努利反馈且系统服务台经常遭受启动故障的重新访问排队系统模型,利用线性算子半群理论,通过对描述其系统行为的偏微分方程组的研究,证明了该模型所描述的系统所确定的算子是闭稠定耗散算子,生成C0压缩半群,从而得到系统的适定性.在证明1是算子的预解点时,采用了共轭方法.

The Well-posed-ness of Retrial Queue System with Bernoulli Feed Back and Starting Failure

We study the well-posed-ness of a retrial queue with Bernoulli feedback, where the server is subjected to starting failure. We proved the operator determined by the system described by the model generates a strongly continuous semigroup in a Banach static space, and hence the well-posed-ness of the system follows from the semigroup theory of bounded linear operators. In the proof of semigroup generation of the system operator, we use the approach of adjoint operator. By showing 1 is not an eigenvalue of adjoint operator of the system operator, we prove that operator without Bernoulli feedback generates a C_0 semigroup of contraction, and then get desired result by the perturbation theory of semigroup.