Techniques for performing user-configurable traffic management functions on streams of packets. The functions include multicasting, discard, scheduling, including shaping, and segmentation and reassembly. In the techniques, the functions are not performed directly on the packets of the stream, but instead on descriptors that represent stored packets. Output of descriptors from all traffic queues, including discard traffic queues, is scheduled. Scheduling is done using a hierarchy of schedulers. The form of the hierarchy and the scheduling algorithms used by the schedulers in the hierarchy are both user configurable. As disclosed, the techniques are implemented in a traffic management coprocessor integrated circuit. The traffic manager coprocessor is used with a digital communications processor integrated circuit that performs switching functions. The buffers for the packets are in the digital communications processor. Also disclosed are a modified partial packet discard algorithm and a frame based deficit round robin scheduling algorithm.