Well-posedness Of M/G/1 Queueing Model With Second Optional Service

This paper is divided into two chapters. Chapter 1 is divided into twosections. In Section 1, we introduce briefly the history of queueing theory.In Section 2, we first introduce supplementary variable technique,then weput forward the problem that we study in this thesis. Chapter 2 is split intotwo sections. In Section 1, first we introduce M/G/1 queueing model withsecond optional service, next we convert the model into an abstract Cauchyproblem in a Banach space by introducing state space, operators and theirdomains. In Section 2, we study well-posedness of the queueing model, thatis, prove existence and uniqueness of positive time-dependent solution of thequeueing model by using the Hille-Yosida theorem, the Phillips theorem andthe Fattorini theorem in functional analysis.