Well-Posedness Of The M/G/1 Queueing Model With Compulsory Server Vacations

This paper is divided into two chapters.Chapter 1 is divided into two sections.In Section 1,we introduce briefly the history of queueing theory. In Section 2,we first introduce supplementary variable technique,then we put forward the problems that we study in this thesis.Chapter 2 is split into two sections.In Section 1,first we introduce the M/G/1 queueing model with compulsory server vacations,next we convert the model into an abstract Cauchy problem in a Banach space by introducing state space, operators and their domains. In Section 2,we study well-posedness of this queueing model,that is,prove existence and uniqueness of a positive time-dependent solution of the queueing model by using the Hille-Yosida theorem,the Phillips theorem and the Fattorini theorem in functional analysis.