Study Of M/M/2 Queueing System With Absorbing State

M/M/2 queueing system with absorbing state have been widely used in many fields such as transportation and service profession. So dynamic analysis of the system is important in view of theory and practice. In this thesis, we will do dynamic analysis for the system. First by using the probability theory we will establish the mathematical model of the system, second we will convert the model into an abstract Cauchy problem in a Banach space, third by using C₀-semigroup theory we will prove that the model has a unique positive time-dependent solution which satisfies probability condition, fourth through studying spectral properties of the operator corresponding to the model we will obtain asymptotic property of the solution of the model.