Asymptotic Property Of The Time-Dependent Solution Of A Repairable Queueing System With Three Kinds Of States

This paper is divided into two chapters.Chapter 1 is divided into two sections.In Section 1 we introduce the history of queueing theory.In Section 2,we first introduce supplementary variable technique,then we put forward the problem that we study in this thesis.Chapter 2 is split into two sections.In Section 1,first we introduce a repairable queueing model with three kinds of states,next we convert the model into an abstract Cauchy problem in a Banach space by introducing state space,operators and their domains, last introduce other researcher's results about the model.In Section 2,through studying the resolvent set of the adjoint operator of the operator corresponding to the repairable queueing system with three kinds of states,we obtain the resolvent set of the operator whenμ₁(x)＝μ₁,μ₂(x)=μ₂,β(x)=β:all points on the imaginary axis except for zero belong to the resolvent set of the operator.Last under a certain condition,we will obtain asymptotic property of the solution of the model.