Space division switching fabrics, like the buffered crossbar, are required to meet the forwarding capacity requirements of Gigabit and Terabit packet switches. These fabrics use fast-operating arbitration algorithms to achieve high utilization under heavy traffic loads. However, Next Generation Network (NGN) switches also need to provide throughput guarantees. A new scheduling system is proposed in this paper that can achieve both of these goals. Primarily, backlogged traffic is serviced in a manner that meets throughput guarantees, after which, the excess capacity is serviced in a manner that achieves high switch utilization.