Fluid Model Driven By An M/M/1Vacation Queue With Negative Customer

With the rapid development of computer technology and network technology matures,the Internet gradually goes into the people’s production and life. However, on the basis ofATM broadband ISDN and other high-speed communication network performanceanalysis, with heavy tailed (non index) reached communication environment and businesshours interval distribution are distance dependent and sudden, In order to reveal the heavytailed conditions that influence the system performance indexes. the traditional queuingmodel to describe the practical problems appear significant limitations. But in flowqueuing model, its input and output buffer is a continuous flow with random variation rate,that is to say, the buffer capacity is continuously changing. Preliminary research resultshows that the random flow queuing system is more suitable for the moderncommunication system and production system modeling.In this theory, fluid model driven by a M/M/1vacations queue with negativecustomer is studied, negative customers need not accept service and remove positivecustomers only one by one at the end when they are served, which is called RCE-policy.The main content is as follows:First, considering a fluid model driven by a Markov arrival queuing system withnegative customers, the fluid rate of input and output was controlled by the state in theprocess of driving system. Given infinitesimal generator, the joint distribution ofinventories and the captain process of LT, have a kind of matrix geometric structure, usingthe matrix geometric solution method, and given a smooth buffer content distribution ofLST and the average buffer content formula.Second, considering a fluid model driven by an M/M/1queuing system with multiplevacation and negative customer, the fluid rate of input and output rate is controlled by thestate in the process of driving system. Using the matrix geometric solution method, andgiven a smooth buffer content distribution of LST and the average buffer content formula.Finally, the numerical results of the model are presented, which straightlydemonstrates the effect of different system parameters on the probability of empty buffer and buffer content in this paper.