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We present a novel fair queueing scheme, which we call Smoothed Round Robin (SRR). Ordinary round-robin schedulers are well known for the burstiness of their scheduling output. In order to overcome this problem, SRR codes the weights of the flows into binary vectors to form a Weight Matrix and then uses a Weight Spread Sequence (WSS), which is specially designed to distribute the output more evenly, to schedule packets by scanning a Weight Matrix. By using the WSS and the Weight Matrix, SRR emulates the Generalized Processor Sharing (GPS) well. SRR possesses better short-term fairness and scheduling delay properties in comparison with various existing round-robin schedulers. At the same time, SRR preserves O(1) time complexity by avoiding the time-stamp maintenance employed in various fair queueing schedulers. Simulation and implementation experiments show that SRR provides good mean end-to-end delay for soft real-time services. SRR can be implemented in high-speed networks to provide quality of service due to its simplicity and low time complexity.