In this paper, we study the cell loss performances of an asynchronous transfer mode (ATM) multiplexer with loss priority control, whose input consists of variable bit rate (VBR) homogeneous bursty traffic. Among a variety of traffic models, we consider an on-off model and a high-low activity model, which are modeled by a Markov-modulated deterministic process (MMDP). We assume that the parameter values of the on-off model are given, but the parameter values of the high-low activity model are obtained from those of a stepwise VBR video traffic model. Here, we present a procedure of approximating to the two-state MMDP stepwise VBR traffic of the Markov process of a non-birth-death process type having more than two states. For the cell loss performance, we use some approximations to make analysis tractable. Also, for loss priority control we use the statistics of the priority ratio as a traffic parameter, and consider two different methods of assigning cell priority for the high-low activity model. By numerical examples, we show that the performance of the on-off model is different from that of our high-low activity model, because the high-low activity model chosen here has less bursty characteristics, resulting from the parameter values of the stepwise VBR video traffic model. Selective cell discarding by the partial buffer scheme increases the admissible load for the on-off model, while it increases or does not affect the admissible load for our approximated high-low activity model for different priority assignment methods and performance requirements.