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Many wormhole interconnection networks for parallel systems, and more recently system area networks, implement virtual channels to provide a number of services including improved link utilization and lower latencies. The forwarding of flits from the virtual channels on to the physical channel is typically accomplished using flit-based round-robin (FBRR) scheduling. This paper presents a novel scheduling strategy, anchored opportunity queueing (AOQ), which preserves the throughput and fairness characteristics of FBRR while significantly reducing the average delay experienced by packets. The AOQ scheduler achieves lower average latencies by trying, as far as possible, to complete the transmission of a complete packet before beginning the transmission of flits from another packet. The AOQ scheduler achieves provable fairness in the number of opportunities it offers to each of the virtual channels for transmissions of flits over the physical channel. We prove this by showing that the relative fairness bound, a popular measure of fairness, is a small finite constant in the case of the AOQ scheduler. Finally, we present simulation results comparing the delay characteristics of AOQ with other schedulers for virtual channels. The AOQ scheduler is simple to implement in hardware, and also offers a practical solution in other contexts such as in scheduling ATM cells in Internet backbone switches.