Study On The M/G/1 Queuing Model Of Preemptive Priority And Its Application

With the rapid development of science and technology, especially with the rapid development of computer and communication network, to fit the need of the application, more and more different queue disciplines, service mechanism and customer types have been applied to queuing models one after another. Priority queuing is the very common phenomenon in the actual problem, it has the very important application in postal service,transportation,medical establishment and so on. Therefore, carrying on the study to this kind of queuing system has certain theory value and the practical significance.This article introduces some elementary knowledge in the queuing theory: Markov process,Poisson process,Imbedded Markov Chain,Little formula and so on. Then introduce the general M/G/1 queuing model,the M/M/1 queuing model of preemptive priority and the M/G/1 queuing model of nonpreemptive priority systematically. In this foundation, the article gives the M/G/1 queuing model of preemptive priority and some important queuing quantities of the model (for example: the mean waiting time,the mean dwell time,the mean queue length and so on) are given by, then take some examples to show the application of the model in actual problems.Because the M/M/1 queuing model is the exceptional case of the M/G/1 queuing model, this article promotes some related results of the M /M /1 queuing model of preemptive priority which have been known to us.