The Research Of T-mix-preemptive Priority Queueing System

This thesis introduces T-mix-preemptive priority into the queueing system based on the M/M/1 and Geo/Geo/1 queueing system. We establish a serial of mathematical models separately, and analyze these two models and derive several performance measures. The thesis is mainly composed of two parts as follows:Firstly, To explain why we choose this field to research, we describe the history of the priority queueing system and mainly introduce the mix-preemptive priority queueing system. For solving problems conveniently, we introduce the knowledge of Little formula, quasi birth and death chain and matrix-geometric solution and so on. That explain how we write this thesis and what the methods we use to write this thesis.Lately, we discuss about T-mix-preemptive priority queue in an M/M/1 queueing system. Using the Little formula to supply the demand of optimizing spectrum access in cognitive radio network we make discussion, and then we get the average waiting time, and the average queue length while customers stay in the queuing system and so on. Finally, we do simulation to prove the research of this kind of queueing system’s using value in daily life.Finally, we discuss about T-mix-preemptive priority queue in an Geo/Geo/1 queueing system. Using the quasi birth and death chain and matrix-geometric solution method, we establish a three-dimensional Markov chain and then gain an one-step state transition probability partitioned matrix, Then we obtain the distribution of the steady-state queue length and the average waiting time of a customer in the system in steady state using the method of matrix-geometric solution. Some numerical examples and the optimization of expense are given to find the influence of the parameters on several performance indicators and performance this thesis’ s using value in daily life.