Steady-state Solution Of The M/M/1Retrial Queueing Model With Server Breakdowns

This thesis is divided into two chapters. Chapter1is split into two sections. In Section1, we introduce briefly the history of queueing theory. In Section2, we first introduce thesupplementary variable technique, then we state the problem that we will study in this thesis.Chapter2consists of two sections. In Section1, firstly we introduce the M/M/1retrialqueueing model with server breakdowns, then we convert the model into an abstract Cauchyproblem in a Banach space by introducing a state space, operators and their domains. Lastly,we introduce the main results obtained by other researchers. In Section2, we study steady-state solution of the M/M/1retrial queueing model with server breakdowns and prove thatif α+μ> λ, then0is not an eigenvalue of the operator which correspondents to the model.This implies that the model does not have steady-state solution.