Summary: This paper analyzes the performance of an ATM cell multiplexer with a two level MMPP input on a discrete-time basis. We approximated the input process as a simple MMPP model. We developed an MMPP/D/1/K queueing model for the ATM cell multiplexer, and employed an analytic approach for the evaluation of cell loss probability. We verified the accuracy of the results using computer simulation. We applied the above analytic method to connection admission control (CAC) of the ATM network. The resulting connection admission control scheme employs the concept of the "effective bandwidth" and table-look-up procedure. We confirmed through a computer simulation that the proposed connection admission control scheme outperforms the peak bandwidth allocation scheme with respect to link utilization.