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Abstract-We address the problem of fair scheduling of packets in Internet routers with input-queued (IQ) switches. We present new performance metrics for IQ switches with unity speedup. Scheduling in IQ switches is formulated as tracking the behavior of an ideal output-queued (OQ) switch that provides optimal performance. We introduce several performance metrics that measure the difference between the ideal performance provided by an ideal OQ switch and an IQ switch with unity speedup. A key performance metric is the notion of ''lag" between an IQ switch and an ideal OQ switch. Using the proposed metric5 as design criteria, we present a suite of scheduling policies for IQ switches with unity speedup that provide better performance than existing scheduling policies in the literature, with comparable complexity.