Asymptotic Property Of The Time-Dependent Solution Of M/M/1 Queueing Model With Second Optional Service

This paper is divided into two chapters. Chapter 1 is divided into twosections. InSection 1 we introduce the history of queueing theory. In Section2, we first introduce supplementary variable technique, then we put forwardthe problem that we study in this thesis. Chapter 2 is split into two sections.In Section 1, first we introduce M/M/1 queueing model with second optionalservice, next we convert the model into an abstract Canchy problem in aBanach space by introducing state space, operators and their domains, lastintroduce other's results about the model. In Section 2, through studying theresolvent set of the adjoint operator of the operator corresponding to M/M/1queueing model with second optional service, we obtain the resolvent set ofthe operator: all points on the imaginary axis except for zero belong to theresolvent set of the operator. Last under a certain condition, we will obtainasymptotic property of the solution of the model.