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This paper introduces a protocol for scheduling of packets in high-capacity switches, termed weighted sequential greedy scheduling (WSGS). WSGS is a simple, greedy algorithm that uses credits to reserve bandwidth for input-output pairs. By using a pipeline technique, WSGS implemented by the current technology readily supports a switching capacity exceeding 1 Tb/s. Admission control is straightforward, allowing bandwidth reservations on a submillisecond time scale. Namely, the central controller readily determines if the newly requested bandwidth can be assigned to the given input-output pair. We have shown that a newly requested bandwidth should be assigned if both the input and output have enough capacity, which requires checking of only two inequalities. Therefore, WSGS is well suited for switching in data networks where sessions might require high bit rates and last for a short time. The WSGS allows bandwidth reservations with fine granularity, e.g., bandwidth can be reserved for individual web sessions, video streams, etc.