Discrete-time Customers Have To Expel Geo / Geo / 1 Queuing System

The paper studies three kinds of discrete-time Geo/Geo/1queueing model. Based on the expulsions, the first two models consider negative customers to cause two different types of RCE offset strategy. By using the method of markov chain, the chapters obtain ergodic condition of the model, the generating function of the queue-length and the number of customers waiting. Then the chapters calculate and analyse the model results on the condition of no expulsions. Finally, the chapters analyses the influence of some parameters on the system indexes by numerical calculation.On the basis of the expulsions system, the third model discusses the single vacation of discrete-time Geo/Geo/1queueing model. Using the quasi-birth-death process and matrix geometric solution, the chapter gets stochastic decomposition of the model indexes:the conditional stochastic decomposition structure of the queue-length, the stochastic decomposition structure of the queue-length and that of the sojourn time. Then the chapter analyses the busy cycle. Finally, this chapter analyses the influence of some parameters on the system indexes by numerical calculation.