Another Eigenvalue Of The M/M/1 Queueing Model With Exceptional Service Times For The First Customer In Each Busy Period

This thesis is divided into two chapters. Chapter 1 is split into two sections. InSection 1, we introduce briefly the history of queueing theory. In Section 2, we firstintroduce supplementary variable technique, then we state the problem that we will studyin this thesis. Chapter 2 consists of two sections. In Section 1, first we introduce themathematical model of the M/M/1 queueing system with exceptional service time for thefirst customer in each busy period, then we convert the model into an abstract Cauchyproblem in a Banach space by introducing state space, operators and their domains. Lastwe introduce the main results about this model obtained by other researchers. In Section2, we study eigenvalue of this operator corresponding to this model in the left half complexplane, and obtain that 2√λμ-λ-μis an eigenvalue of this operator with geometricmultiplicity one.