An Eigenvalue Of M/M/1 Retrial Queuing Model With Special Retrial Times And Its Application

This thesis is divided into two chapters. Chapter 1 is split into two sections. In Section 1 we introduce briefly the history of queueing theory. In Section 2 we introduce supplementary variable technique, then we state the problem that we will study in this thesis. Chapter 2 consists of three sections. In Section 1, first we introduce the mathematical model of M/M/1 retrial queue with special retrial times, then 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 the well-posedness of the queueing model, that is, prove existence and uniqueness of positive time-dependent solution of the queueing model by using the Hille-Yosida theorem, the Phillips theorem and the Fattorini theorem in functional analysis. In Section 3 we will study spectral properties of the operator corresponding to the queueing model. We will obtain that 0 is an eigenvalue of the operator corresponding to the model with geometric and algebraic multiplicity one. Thus we deduce that the time-dependent solution of the model is not asymptotic stable.