N-stage Tandem Open Queuing Network System Analysis

The tandem open queueing network system has a wide application in actual production and living. It has been studied by many researchers and a lot of results have been obtained in recent years. In this paper we make a further research on this system. We study the multi-node tandem open queueing network system with feedback and set-up time. In this case it will satisfy the need of actual production and living better.For this reason ,this paper mainly studies two kinds of queueing models.The first is N-node tandem open queueing network system with feedback and server vacation. The generator matrix of Markov process is given in recurrence formulation. The steady-state distribution and other relative index of the system are obtained by means of matrix analysis theory and probability theory. The other is N-node tandem open queueing network system with set-up time. We get the generator matrix in recurrence formulation of the system too, and gain the probability solution of the system ,the distribution of stay-time and the busy time distribution and so on. Since the operation of matrix and recursion are easy to perform on computers, the conclusions of this paper can be conveniently applied.