Other Eigenvalues Of The M/M/1 Queueing Model With Exceptional Service Time For The First Customer In Each Busy Period

This thesis is divided into two chapters. Chapter 1 is split into two sections. In Section1, we introduce brie?y the history of queueing theory. In Section 2, we first introduce sup-plementary 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 mathematical modelof the M/M/1 queueing system with exceptional service time for the first customer in eachbusy period, then we convert the model into an abstract Cauchy problem in a Banach spaceby introducing state space, operators and their domains. Last we introduce the main re-sults about this model obtained by other researchers. In Section 2, we study eigenvalue ofthe operator corresponding to this model in the left half complex plane, and prove that forall are eigenvalues of this operator with geometric multiplicityone.