We study an asynchronous transfer mode (ATM) multiplexer with selective cell discarding (SCD), and propose as a new traffic parameter the ratio of high and low priority cell streams when a cell stream multiplexed is classified by the cell loss priority (CLP) field in a cell header. By having loss priority control, it is possible to increase the multiplexing gain. For performance analysis we assume that an on-off bursty traffic is described with several traffic parameters and the proposed priority ratio, and is approximately modeled by a Markov-modulated deterministic process (MMDP). Assuming that several independent and homogeneous on-off bursty traffics with priority discrimination are multiplexed, we present an analytical procedure for the cell loss probability of each priority level in statistical cell multiplexing with loss priority control, and use the performance results for connection admission control (CAC). Also, we consider the effect of the proposed priority ratio. Although loss priority control increases the statistical multiplexing gain, it is not appropriate for the on-off bursty traffic to change the value of the high-priority ratio in order to obtain a larger multiplexing gain, since the admissible load is determined by the loss probability of low priority traffic for most cases and the values of the ratio in a certain range slightly affect it.