Modeling And Analysis Of Delayed Product And Email Systems Based On Geo/geo/1 Queuing

As the queuing theory systematizing, its basic theories have been widely applied to computer and telecommunication networks, flexibility manufacture system, asynchronously transfer mode and electronic commerce. This thesis studies two different systems by Geo/Geo/1 queue model. One is a production system of delayed product differentiation (DPD), the other is an email contact center with disasters, which has a finite buffer.Firstly, we comprehensively summarize the queues, then, simply introduce the history and current situation of the classic queue, the vacation queue and the discrete time queue.Secondly, we comprehensively introduce the basic knowledge concerning the subject and give a concise summary on the theory of the discrete time Geo/Geo/1 queue, quasi-birth and death process, and matrix geometric solution, which provide theoretical preparations for the analysis of later models.Thirdly, in the research of the production system of delayed product differentiation, by using the method of quasi-birth and death process and matrix geometric solution, we obtain various performance measures of this system, and make examples to explain how the model is applied in production management, then we plot some figures obviously presenting the mutual effects between the system parameters and stationary distribution. It is found that higher system efficiency achieves by exiguously adjusting the system parameters in a given area. This model has provided theories basis for scientific management of the stock and controlling cost.Finally, in the research of the email contact center, the paper gives a basic assumption of the study model, and joins in some strategies, such as finite buffer, disasters, working vacation, which has better applicable and compatible. By using the method of quasi-birth and death process, we set up equilibrium equation, and gain stationary distribution of queue length, the amount of waiting time, also average waiting time. In the last, we put out examples for assistant explain.