Performance Analysis Of Machine Interference Problem With Balking, Reneging And Vacation

With the rapid development of communication system and computer technology, various queuing systems spring up increasingly to promote the development of Machine Interference Problem, especially for the model with balking, reneging and vacation policy. This model has great significance in that it has been widely used in manufacturing system, computer network and other fields.It has broad practical application background for the Machine Interference Model with balking and reneging. In this dissertation the researcher presents the research status quo of Machine Interference Problem with balking, reneging and vocation policy and generalizes analytical method and main application in dealing with the Machine Interference Problem. Then by combining the balking and reneging with vacation policy of repairman, the author proposes two new Machine Interference Problem Models, which is extended from the models mentioned in the literature review. These two models could depict some practical problem existed in the application even better.The thesis focuses on two new Machine Interference Problem Models about synchronous and asynchronous vacation of multi-repairmen. As for the synchronous vacation Model, the author derives the steady-state probability by the inverse of two matrices with adoption of the blocked matrix method. In addition the author derives the formula of performance index and sets up a cost model of the system. With regard to the asynchronous vacation model, the author obtains the steady-state probability in a simple vector form and each performance index of the system by the blocked matrices method and sets up a cost model of the system. And then the variety of the optimal number of servers and the lowest cost of the system in different parameters was presented by numerical analysis.