Well-Posedness Of The M^[x]/G/1Retrial Queueing Model With Absorbent State Of Failure State And Constant Rate Of Repeated Attempts

This thesis is divided into two chapters. Chapter1is split into two sections. In Section1, we introduce briefly the history of queueing theory. In Section2, we first introduce thesupplementary variable technique, then we state the problem that we will study in this thesis.Chapter2consists of two sections. In Section1, firstly we introduce the M[X]/G/1retrialqueueing model with absorbent state of failure state and constant rate of repeated attempts,then we convert the model into an abstract Cauchy problem in a Banach space by introducinga state space, operators and their domains. In the section2, by using the Hille-Yosida theoremand the Phillips theorem we prove that the model has a unique positive time-dependentsolution.