One of the fundamental challenges facing broadband information transport is to determine congestion control strategies to support multiple classes of traffic in the future Asynchronous Transfer Mode (ATM)-based Broadband Integrated Services Digital Networks (B-ISDN). To accomplish this in a flexible and a cost-effective manner, priority classes for the different services are commonly used. In this paper, we study priority queueing schemes implemented in statistical multiplexer with shared and separate buffers, whose input consists of superposition of voice and data traffic. A performance comparison is given for two buffer access schemes: the common Nested Threshold Cell Discarding (NTCD) with single shared buffer and NTCD with Multiple Buffers (NTCD-MB). The arrival process to the multiplexer is approximated using a Markov Modulated Poisson Process (MMPP). It is shown that when implementing the NTCD-MB priority scheme, the parameters of the switching node can be adjusted in such a way that the service quality is guaranteed for different classes of traffic. The improved performance as a result of implementing such scheme is investigated via simulations.