Broadband networks are required to support multimedia applications that will have stringent requirements in terms of the quality of service. For instance, a video coding scheme has the ability to distinguish a given cell in the same connection as being a high-or low-priority cell by approprite packetization. Thus, the design of a multi-connection shaper and enforcer architecture which deals with different traffic parameters and cell priorities is important. In this paper, we propose algorithms and the architecture of a GCRA-based multiple-connection prioritized traffic shaper and enforcer. Simulation results reveal that the GCRA scheme is more suitable for shaping and UPC functions than conventional leaky-bucket schemes. (C) 1997 Elsevier Science B.V.