The Matrix-geometric Solution Of The Two-queue Polling Model With Multiple Vacations And State-dependent Service

Abstract:In this thesis, we consider the two-queue polling model with multiple vacations and state-dependent service. According to the model, we construct the QBD and get its generator. By using the matrix geome-tric solution, we obtain the equilibrium condition and the stationary probability of the system. In addition, we get some system performance measures. The thesis consists of five chapters.In chapter1, we introduce some basic knowledge of polling queuing system, the main work and the frame of the thesis.In chapter2, we consider the E/E polling model with multiple vacations and state-dependent service. We get the generator by analyzing the state transition, prove the equilibrium condition of the system and also derive the stationary probability of the system, present an algorithm of the matrix R and give the expressions of the system performance measures. Some numerical examples are given.In chapter3, we consider the E/1-L polling model with multiple vacations and state-dependent service. We derive the generator by analyzing the state transition. We obtain the equilibrium condition of the system and derive the stationary probability of the system.In chapter4, we consider the E/B polling model with multiple vacations and state-dependent service. In this chapter we extend the exhaustive service and1-limited service in the last two models to the general Bernoulli services. We get the same equilibrium condition in the last two models, and in chapter4the E/B polling model is proved to have the same condition. Finally, the variation of the system performance measures under different Bernoulli parameters p is given through some numerical examples.In chapter5, we make a summary for this thesis.