The Research Of Double Arrival Queue Syster Geom/Geom/(Geom/Geom)/H With Negative Customers

The discrete time queueing system has a wide range of application in the networkcommunication system. There have been modeling analysis for Peer-to-Peer(P2P)servicesystem with continuous queue system. According to characteristics of discrete timequeueing system, the use of discrete time queuing analysis P2P system will be more closeto the reality. This topic bases on the classical Geom/Geom/H queue. Then we build andanalysis the double arrival queue Geom/Geom/(Geom/Geom)/H. We get the queue indexand provide theoretical basis for performance analysis in network.First of all, we build the model which is the Geom/Geom/(Geom/Geom)/H doublearrival queue with random servers. The transition probability matrix of the system and itssub-block element, are deduced. And using iteration method, the rate matrix whichsatisfies the matrix equation is established. Using the Matrix-geometric solution method,the matrix geometry form of the probability distribution of the customer number in systemin steady-state is obtained. Further more, the average number of customers and servers areobtained. By some numerical examples, we analyze the parameters on the average numberof customers and servers.Secondly, based on the double arrival queue Geom/Geom/(Geom/Geom)/H, weanalyze the Geom/Geom/(Geom/Geom)/H queue with negative customer and Bernoullifeedback. Then the transition probability matrix which is the type of four diagonal matrixis deduced and the matrix equation is constructed. Using Matrix-geometric solution, wegive the steady-state distributions of the system and mean expression of customers andservers in the system. Through the numerical examples, we describe the variation curve ofthe parameters with the index and explain the main reason of the change trend.Finally, in order to make the model has more practical significance. We study theGeom/Geom/(Geom/Geom)/H queue with negative customer who can be served. In thetwo kinds of offset strategy, we get system transition probability matrix respectively.Using Matrix-geometric solution, we give the steady-state distributions for the number ofcustomers in the system. Furthermore, we gain the waiting number of customers, the average number of customers and servers in the system. At the last, we make programswith the Matrix Laboratory, and derive the figures which describe the changes inparameters with index. Then we observe that the influence of system performance isshowed by parameters in the system.In a word, based on the classical discrete time queueing system, we build a newqueuing model and use Matrix geometric solution method. We will get the correspondingsteady state index. Further more, the discrete time queueing system theory would beenriched.