Asymptotic Property Of The Time-Dependent Solution Of M/M/1 Retrial Queuing Model With Special Retrial Times

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 predecessors's research results, last we put forward the problem that we study in this thesis. Chapter 2 is split into two sections. In Section 1, first we introduce M/M/1 retrial queueing model with special retrial times, 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's results about the model. In Section 2, through studying the resolvent set of the adjoint operator of the operator corresponding to M/M/1 retrial queueing model with special retrial times, we obtain the resolvent set of the operator: all points on the imaginary axis except for zero belong to the resolvent set of the operator. Thus we obtain asymptotic property of the solution of the model based on both our results and predecessors's.