Two Types Of Discrete Time GI/Geo/1/N Models With Multiple Work-vacations

Vacation queuing model has become a hot research topic in recent years, many researchers have already obtained very valuable research results. As its wide application in the computer,communication and other fields, we need to constantly improve vacation model, further-more, multiple working vacation queuing model with balking and vacati-on interruption is important in real life. Therefore, this paper mainly study two types of models:Firstly, the model GI/Geo/1/N with balking and multiple work vacations is analyzed, we construct the Markov processes by embedding Markov chain and get the one-step transition probabilities, then,we calculate the system length distribution at pre-arrival epochs. Using the supplementary variable technique, we have derived the system length distributions at pre-arrival and arbitrary epochs and obtain the system length at arbitrary epochs. Various performance measures,such as the loss probability, waiting time,sojourn time,etc., are discussed.Secondly,we study the GI/Geo/1/N model with multiple working vacations and vacation interruption. Using the same method,which are embedded Markov chain and supplementary variable method, we obtain the system steady-state distribution at pre-arrival and arbitrary epochs,then, analyze the performance measures. Finally, for the model with vacation interruption,we present some special cases and provide the graph showing the effect of model parameters on some performance measures.