Discrete-Time Queuing With Vacation And Batch Arrival

Vacation queue is the expansion of the classicsal queuing theory, which wan first studied by Levy and Yechiali. In 1980s; vacation queue had been developed into a study direction with distinguishing features, and formed a basic theoretical framework, whose core was stochastic decomposition. It has been applied to all kinds of up-to-date technical fields, such as, computer and communication network, manufacture system (FMS), asynchronously transfer mode (ATM) and electronic commerce (EC). Vacation queue reflect the fact that the service may be interrupted one side, and the other side, it provide flexibility for all kinds of vacation strategy's optimize designs and process control. So vacation queue has a broad attention, and become a focus in queue model studied.In this thesis, we add the vacation policy with set-up time and single vacation and multiple adaptive vacations to the classical Geom~X /G/1queuing system, and derive two very valuable vacation queue models. These are fully new vacation queue model. We provide the necessary and sufficient condition in which the queuing system is positive recurrent, and the generating function of the steady-state queue length and the steady-state waiting time distribution and their stochastic decomposition results, at the same time, show the generating function of the busy period, the busy period cycle, and analyze on-line period, At last, we show the probability which the server is in various stator in the steady-state situation.The whole thesis includes four chapters. In the chapter one, we show the development history of the queue theory and the vacation queue theory, and their applications in the up-to-date technical fields. In the chapter two, we introduce some basic knowledge. In the chapter three, we quote the indices analysis of the set-up time and single vacation Geom~X /G/1 discrete time queuing system, by using the imbedded Markov chain which made the model to be resolved easily, We gain the positive recurrent condition of the system. And discuss the generating function and their stochastic decomposition theorem of the steady-state queue length and waiting time distribution. Further, we give the analysis of the busy period, the busy period cycle and the on-line period. In the chapter four, we analyze of the set-up time and multiple adaptive vacations Geom~X /G/1 discrete time queuing system.