Analysis of a two-node closed queueing network with vacation and non-renewal arrival

We give a two-node closed queueing model with vacation and MMPP (Markov–Modulated Poisson Process) arrival. The model also fits some communication networks with feedback and a type of self-adapted productive systems with finite jobs, etc. By use of the phase-decomposition principle, the hidden Markovian renewal process, and the analysis of a two-node closed queue with Poisson arrival and state dependent vacation policy, we present the steady states and the cyclic time of the model. It is another attempt to solve the problems of this type of closed systems by using the related existing models.