A new generation of systems called Networked Multimedia Systems are currently being the subject of intense study. These systems require a high throughput and QoS guarantees. The Broadband Integrated Service Digital Network (B-ISDN) based on the Asynchronous Transfer Mode (ATM) provides these requirements in an efficient manner. A new ATM service category, the Available Bit Rate (ABR) service, will systematically and dynamically allocate available bandwidth to users by controlling the flow of traffic with a closed-loop feedback mechanism. The ABR service was initially design to support data traffic but recently there has been muchinterest in using ABR to support voice and video applications . In this scenario, the voice and video connections, which may require small delays, and the bursty data connections are multiplexed on different queues at the switches. An admission control policy over the real-time connections is usually required to guarantee that the end to end delay is kep..