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We propose a new fair scheduling technique, called OCGRR (Output Controlled Grant-based Round Robin), for the support of DiffServ traffic in a core router. We define a stream to be the same-class packets from a given immediate upstream router destined to an output port of the core router. At each output port, streams may be isolated in separate buffers before being scheduled in a frame. The sequence of traffic transmission in a frame starts from higher-priority traffic and goes down to lower-priority traffic. A frame may have a number of small rounds for each class. Each stream within a class can transmit a number of packets in the frame based on its available grant, but only one packet per small round, thus reducing the intertransmission time from the same stream and achieving a smaller jitter and startup latency. The grant can be adjusted in a way to prevent the starvation of lower priority classes. We also verify and demonstrate the good performance of our scheduler by simulation and comparison with other algorithms in terms of queuing delay, jitter, and start-up latency.