The Research Of The Queue System With Non-preemptive Priority And Vacation

Based on the discrete time queue system,this paper introduces non-preemptive priority and multiple working vacations strategies.This paper considers two queue models with nonpreemptive priority.By building a four-dimensional discrete time Markov chain,we give the steady-state distribution of the queue length.By using the method of matrix-geometric solution and the method of Gauss-Sidel iteration,we obtain some performance measures.At the same time,this paper can provide theoretical guidance for the research of wireless mesh networks by modelling for the wireless mesh networks.This paper is composed of three parts as follows:Firstly,we consider a discrete time queue model with relevant non-preemptive priority and infinite buffer space.By building a discrete time four-dimension Markov chain(MC)which includes the numbers of customers with different priorities in the system,the state of the server and the service state,we obtain the state transition probability matrix.Using the quasi birth and death(QBD)chain and matrix-geometric solution,we deduce the average queue length.Then,we provide some numerical results to evaluate the effect of the parameters on the system performance measures.Besides,to analyze the relation of the personal benefit with the social benefit,we develop some benefit functions and obtain some optimization results within a certain range.Secondly,we consider a discrete time queue model with irrelevant non-preemptive priority and finite buffer space.We develop a four-dimension MC which includes the number of the customers with different priorities and the state of the system and the server.By using the QBD chain and the method of Gauss-Sidel iteration,we give the steady-state distribution and some main performance measures.We use the numerical examples to illustrate the effect of different parameters on the system performance measures.Finally,we analyze the equilibrium behavior of customers and seek for the optimal strategy from the personal benefit of two types of customers and the social benefit.Finally,we consider the application of the non-preemptive priority strategy in the wireless Mesh networks.We model the wireless Mesh networks with half-asleep and wakeup strategy and dynamic channel bonding strategy as a discrete time Geom/Geom/1 queue model with non-preemptive priority and multiple working vacations.By constructing a fourdimension MC,we obtain the state transition probability matrix and the distribution of the steady-state queue length.The formulas for performance measures of the networks are given to evaluate the system.The numerical experiments show how the performance measures change with system parameters.Finally,the Nash equilibrium and the social optimization are shown by numerical experiments,and we obtain the Nash equilibrium as the Pareto optimal solution of this game.