Point Spectrum Of The Operator Which Corresponds To 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 Section 1,we introduce briefly the history of queueing theory.In Section 2,we first 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 M/M/1 queueing model with exceptional service time for the first customer in each busy period,then we convert the model into an abstract Cauchy problem in a Banach space by introducing a state space,operators and their domains,lastly we introduce the main results obtained by other researchers.In Section 2,we prove that if the arrival rate of customers ?,the service rate of the server ? and the exceptional service rate of the server? satisfy ?<?<? + ?,then ?-? is an eigenvalue of the operator with geometric multiplicity one.