On the Output of Two-Stage Cyclic Queue

Throughout this paper we analyze the system at output point t of two stage cyclic queueing model. Our main result characterize the stochastic process (X$^{o}$ , T$^{o}$ ), the system at output point, as a Markov renewal process. The subsequent lemma exhibits the semi-Markov kernel of (X$^{o}$ , T$^{o}$ ) with state dependent feedback, the possibility of a reducible state space arises. A simple necessary and sufficient condition for the irreducibility of (X$^{o}$ , T$^{o}$ was determinded. This irreducibility implied that (X$^{o}$ , T$^{o}$ ) was aperiodic.