Another Eigenvalue Of M/M/1 Operator

This thesis is divided into two chapters. Chapter 1 is split into twosections. In Section 1, we introduce briefly the history of queueing theory.In Section 2, we first introduce supplementary variable technique, then westate the problem that we will study in this thesis. Chapter 2 consists oftwo sections. In Section 1. first we introduce the mathematical model ofM/M/1 queue, then we convert the model into an abstract Cauchy problemin a Banach space by introducing state space, operators and their domains.Last we introduce the main results obtained by predecessors. In Section 2,we study eigenvalue of the operator corresponding to the model in left halfcomplex plane, and obtain thatλμ^1/2-λ-μis an eigenvalue of the operatorwith geometric multiplicity one.