N Series Leave Open Queuing Network System Analysis

Multi-node tandem open queueing network system with server vacation is analyzed in this paper. The multi-node tandem open queueing network system has been studied by many researchers and a lot of results have been obtained. However, multi-node tandem open queueing network system with server vacation has not been studied seen in open literatures.For this reason , the paper considers N-node tandem open queueing network system with finite capacity 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. At the same time, computational algorithms to obtain numerical solutions of the system in steady state are developed. The paper also analyses this model based on numerical observation. Since the operation of matrix and recursion are easy to perform on computers, the conclusions of this paper can be conveniently applied.