A Discrete Time Geom/Geom/1Queue Model With Multiple Working Vacation And Set-up And Closed-down Period

Abstract:Discrete-time working vacation queuing theory is an important new branch of queuing theory. This new type of queuing theory is widely used in many areas,such as computer science,communication networks and so on.It has greatly promoted the investigation and application of discrete-time working vacation queuing model.Working vacation model, which was firstly introduced by Servi and Finn,is an extension of classical vacation theory.Depending on the different backgrounds, it can be divided into a wide variety of vacation policy.Among these,the single working vacation queuing model and multiple working vacations queuing model are two most famous working vacation models. The single working vacation theory with interruption was firstly considered inGeom/Geom/1system by Li and TianThis paper is organized as follows.Firstly, we depict some related research results and basic theory of this area.The discrete-time vacation queuing theory with set-up and closed-down period is defined well there. A specific method of discrete-time queuing matrix geometric solution also be found,which laid solid foundation for further research.Secondly,the main context,which explains the feature of discrete-time Geom/Geom/l model with multiple working vacation and set-up and closed-down period,is specifically described in this chapter. byembedding Markov chain at the corresponding point of time,one-step transfer probability matrix can be given explicitly using Markov property.The matrix geometric solution helps us to deduce the steady-state queuing length and some important factors,such as the length of the whole queue,the average queuing length and so on.