Other Eigenvalues Of The Exhaustive-Service M/M/1 Queueing Model With Single Vacations

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 two sections. In Section 1. firstly we introduce the mathematical model of M/M/1 queueing model with single vacations, then we convert the model into an abstract Cauchy problem in a Banach space by introducing state space, operators and their domains, lastly we introduce the main results about the model obtained by other researchers. In Section 2, we study eigenvalue of the operator corresponding to this model in left half complex plane, and obtain thatθ((?) -λ-η) are eigenvalues of this operator with geometric multiplicity one for 0 <θ< 1.