Another Eigenvalue Of The M/M~2/1 Queueing Model

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,first we introduce the M/M²/1 queueing model,then we convert this model into an abstract Cauchy problem in a Banach space by introducing state space,operators and their domains,last we introduce the main results obtained by other researchers.In Section 2,we study eigenvalue of the operator corresponding to this model in the left half complex plane,and obtain that whenλ/μ＜1/4,3(λ/2)^2/3μ^1/3-λ-μis an eigenvalue of this operator with geometric multiplicity two.