In this paper, we analyze the performance of a statistical multiplexer for heterogeneous types of bursty traffic in an asynchronous transfer mode (ATM) network. We model each type of bursty traffic with a Markov-modulated Poisson process (MMPP), and represent different burstiness of each traffic by changing the parameters of the MMPP. Then, we use a finite queue multi-server model for analysis of the statistical multiplexer with multiple output channels. In order to consider the slottized operation of the ATM channel, we also assume that transmission of the cells queued in the buffer occurs at discrete time instants. With these traffic and system models, we obtain the cell delay distribution and the cell blocking probability for the superposed heterogeneous types of bursty traffic. We also investigate the performance of each traffic separately by obtaining the cell delay and the cell blocking probability. From numerical results, we show the effects of each traffic's characteristic on the performance of the statistical multiplexer. According to these results, it is noted that some efficiencies might be effected by dividing those types of traffic with comparable burstiness into segregated groups and allocate bandwidth to them exclusively.