Delay Guarantees for Throughput-Optimal Wireless Link Scheduling

We consider the question of obtaining tight delay guarantees for throughout-optimal link scheduling in arbitrary topology wireless ad-hoc networks. We consider two classes of scheduling policies: 1) a maximum queue-length weighted independent set scheduling policy, and 2) a randomized independent set scheduling policy where the independent 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 and i.i.d. packet arrivals, we show that the average packet delay is bounded by a constant that depends on the chromatic number of the interference graph, and the overall load on the network. We also 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. Through simulations we examine the scaling of the average packet delay with respect to the overall load on the network, and the chromatic number of the link interference graph.