The Analysis Based On Discrete Time Queue With Working Vacation And Bulk Input

Along with the rapid development of Electronic Commerce and modern technology, the operation in management institutions and the networks is more and more complex, and the requirement for the quality of service and performance is increasing. Queuing theory, as an effective tool to solve the theoretical analysis and application problems of the systems, is required constantly to introduce new vacation policy and establish new queuing models. Under this background, the working vacation policy is introduced. However, in the real life and production, the bulk input queue system with the customer reaching at a certain point is very common. In this thesis the random characteristic and other influence factors of the system are fully considered. This thesis is devoted to study the bulk input queue system with single vacation and the bulk input queue system with multiple working vacations and vacation interruptions, enriched the study on the working vacation policy. These models are new and extend the existing models.The paper gives a basic assumption of the study model and sets the transition probability matrix of the models. The homogeneous linear sets of equations that the stationary queue length satisfied are listed. By recursive method, the distributions of stationary queue length and the waiting time are derived, the stochastic decompositions of them are presented, and the special examples of the models are listed to prove the results.Firstly, the thesis studies the bulk input Geo/Geo/1 queue with single working vacation. Using the Markov chain and Matrix geometric solution, the generating function and the stochastic decomposition of the steady state queue length and waiting time distributions are given.Secondly, the paper studies the bulk input Geo/Geo/1 queue with multiple vacation and vacation interruptions. A particular assumption of the studied model is given, with Markov chain and transition probability matrix the distributions of stationary queue length and waiting time and their stochastic decomposition results are induced.Finally, the numerical results with Matlab are presented to analyze the effect of the different models'parameters on the function quota of the system and the effect of the same function quota on the different models. At the same time, the rationality and the feasibility of the model are verified.