A proper performance evaluation of ATM (Asynchronous Transfer Mode) multiplexer is essential for stable management of ATM networks. We model the on/off traffics entering to the ATM switch as a Markov renewal process (MRP) and propose a performance evaluation method of ATM multiplexer by modeling the system as a discrete time MR/D/1/B queueing system, whose input process is the superposed MRP and present a performance analysis by finding CLP(Cell Loss Probability).