The Queueing System With Negative Customers And Vacations And Its Application In Signal Transmission

With the quick development of the communication systems and computer techniques,there are many kinds of complicated queuing systems. Especially the application value of queueing model with negative customers and priority is more practical.In this paper, three finite buffer queuing systems with negative customers,balking,priority, batch arrival and single working vacation are analyzed. They are expansions of other models in the documents. The main result of this paper has three parts.Firstly, we investigate a finite buffer M/M/1/N queuing system with negative customers,balking and single working vacation. The matrix form solution of the steady-state probability was derived by the Markfoy process method, by writing the transition rate matrix as block matrix, we get the matrix form solution of the steady-state probabilities,some performance measures of the system such as the expected number of customers in the system or in the queue and the average rate of the customer balking are also presented. Finally, taking N=3 as an example,we analyze the influence of the parameters of the system to the system performance measures.Secondly, we investigate a finite buffer MX/M/1/N queuing system with negative customers, balking, batch arrival and single working vacation. The matrix form solution of the steady-state probability was derived by the Markfoy process method, by writing the transition rate matrix as block matrix, we get the matrix form solution of the steady-state probabilities,some performance measures of the system such as the expected number of customers in the system or in the queue and the average rate of the customer balking are also presented. Finally, taking N=3 as an example,we analyze the influence of the parameters of the system to the system performance measures.Finally, we investigate a finite buffer M/M/1/N queuing system with negative customers, priority and multiple vacations. The matrix form solution of the steady-state probability was derived by the Markfoy process method.The steady-state probability vector iteration formulas of the system are derived. Some performance measures of the system such as the expected number of customers in the system or in the queue and the average loss rate of the customer are also presented. Finally, taking N=3 as an example,we analyze the influence of the parameters of the system to the system performance measures.