Analysis Of The Queue System With Preemptive Priority And Server Vacation

Priority and vacation disciplines are often talked about in queuing theory,and are also the hot spots which scholars researched.This paper studies two kinds of priority queues,the first is the preemptive priority queuing,the second is the mixed priority queuing.At the same time,on the basis of these two models,we join vacation and working vacation strategy on the models,make our models better simulate the actual problem.The thesis is mainly composed of three parts except introduction as follows:Firstly,we consider a discrete time Geom/Geom/c queue system with preemptive priority discipline and multiple synchronization vacations.To derive the steady-state queue length,we build a discrete time three-dimension Markov chain(MC)for this queue system and obtain the state transition probability matrix of the Markov chain.Using matrix-geometric solution method,we get several performance measures in terms of the average queue length of the two types,the probability that customer II has to disappear and the server utilization.To demonstrate the effect of the parameters on several performance measures,we take some numerical results according to the proposed model.Secondly,we consider an M/M/c mixed queue with preemptive priority discipline and synchronization multiple working vacations.A three-dimension Markov process in this queue system is given.By using the quasi birth and death chain and matrix-geometric solution method,the distribution of the steady-state queue length is obtained.Then the average queue length of the two types,the probability of customer II disappeared and the server utilization are researched.Some numerical results are provided to illustrate the effect of the parameters on several performance characteristic,and by the analysis of individual and social optimality,some optimization results for this system are shown.Finally,we consider a Geom/Geom/1 queue system with(N,n)-preemptive priority discipline and multiple working vacations.A discrete time three-dimension Markov Chain of this queue system is given,and the three-dimension MC consists of the average length of the two classes of customers and the state of the server.By using the quasi birth and death chain and matrix-geometric solution theory,the average queue length of the two classes and the probability of a customer I being preempted are given.In the end,some numerical results are provided to illustrate the effect of the parameters on several performance characteristics,and by the analysis of individual and social optimality,some optimization results for this system are shown.