Star With Refuse Queuing Model Of The Nature Of Research

Markov process is one of the most important branches of stochastic processes and has quite extensive application in biology, the information, physics, queueing theory and so on. Decay property of processes is an important studying aspectIn this thesis, We mainly consider the recurrence and decay properties of a star-typed queueing model with refusal, besides, we also study the regularity and uniqueness of Collision-Branching Process with immigration and resurrection. The whole thesis consists of the following several parts.In chapter one, firstly, we roughly introduce the background,existing work, meaning of our studying problem, secondly, we display the main workings as well as the framework of the paper.In chapter two, we give some basic knowledge which is related to our studying content, providing a theory foundation for the building, analysis and studying of the model.In chapter three, the sufficient and necessary condition of recurrent and ergodic properties are presented, and under the ergodicity, we get the generating function of stationary distribution.In chapter four, in the non-recurrent situation, we discuss the decay property of the model and present the exact value of the decay parameter. Investing such properties is crucial in analyzing our queueing system’s idle period, busy period, waiting time and so on.In chapter five, we discuss the invariant measure of the model, obtaining the generating function of invariant measure. At the same time, we illustrate with an example the main conclusions in the thesis.In chapter six, we consider a new model---Collision-Branching Process with immigration and resurrection, the criteria for regularity and uniqueness of the process is presented.At last, we make some summary and prospect for my thesis.