Research On The M/G/1 Retrial G-queueing Model With N-policy, Feedback, Preemptive Resome And Unreliable Server

This thesis is divided into two chapters. Chapter 1 is divided into two sections. In Sec-tion 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 three sections. In Section 1, first we introduce the M/G/1 retrial G-queueing model with N-policy, feedback, preemptive resume and unreliable server, next we convert the model into an abstract Cauchy problem in a Banach space by introduc-ing a state space, operators and their domains. In Section 2, we study well-posedness of this queueing model and prove existence and uniqueness of a positive time-dependent solution of this queueing model by using the Hille-Yosida theorem and the Phillips theorem in func-tional analysis. In Section 3, we study asymptotic property of the time-dependent solution of the model when the failure rate functions are constants and obtain that its time-dependent solution is exponentially stable.