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We address the problem of fair scheduling of packets in Internet routers with input-queued switches. The goal is to ensure that packets of different flows leave a router in proportion to their reservations under heavy traffic. First, we examine the problem when fair queuing is applied only at output link of a router, and verify that this approach is ineffective. Second, we propose a flow-based iterative deficit-round-robin (iDRR) fair scheduling algorithm for the crossbar switch that supports fair bandwidth distribution among flows, and achieves asymptotically 100% throughput under uniform traffic. Since the flow-based algorithm is hard to implement in hardware, we finally propose a port-based version of iDRR (called iPDRR) and describe its hardware implementation.