In this paper, a novel rate control scheme is presented. The main aim of this scheme is to regulate the flow of traffic through a high-speed backbone network interconnecting multiple LANs. The scheme is implemented at the interconnection devices (bridges) where the traffic from each source-destination LAN pair is monitored and enforced. This scheme aims to provide a fair sharing of the network resources. LAN/MAN systems are of particular interest as the deployment of this kind of systems is seen as the first step to the development of the future Broadband-ISDN.