Asynchronous Transfer Mode (ATM) Broadband Networks are expected to provide a large number of services and applications. A predominant service will be the support of multimedia traffic applications that integrate different types of traffic (e.g., video, voice and data) over the same connection. The heterogeneous traffic-types differ, widely, not only in their individual bit-rates but also in their corresponding correlations and burstiness parameters. Access flow control algorithms are required to enforce and maintain a specific QOS for each type of traffic. In this paper, we present an effective access flow control algorithm that can be applied at the user to network interface (UNI). The scheme is based upon a preventive control principle and uses a control signal, that is function of the buffer occupancy level, to control the source coder sampling rate. The scheme avoids congestion and enhances the statistical multiplexing gain, consequently providing a higher bandwidth utilization for each QOS. We provide a performance analysis study, supported by simulations, of the access node multiplexer. We studied the resulting Quasi Birth Death queueing process, with state dependant arrivals, using matrix-geometric techniques, and found that both MMPP/Er/1/K and the Poisson Process approximations provided very close results for an ATM multiplexer with small buffer size and access control.