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We consider the question of obtaining tight delay guarantees for throughout-optimal link scheduling in arbitrary topology wireless ad-hoc networks. Two classes of scheduling policies are considered: 1) a maximum queue-length weighted independent set scheduling policy and 2) a randomized independent set scheduling policy where the set scheduling probabilities are selected optimally. Both policies stabilize all queues for any set of feasible packet arrival rates, and are therefore throughput-optimal. For these policies, we show that the average packet delay is bounded by a constant that depends on the chromatic number of the interference graph, and the arrival slack in the system-a metric representing the overall load on the network. We prove that this upper bound is asymptotically tight in the sense that there exist classes of topologies where the expected delay attained by any scheduling policy is lower bounded by the same constant. We extend our upper bounds to the case of multi-hop sessions. Through simulations, we study how our analysis compares with actual delays computed for i.i.d., Markovian, and trace-driven packet arrival processes.