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We consider the delay properties of one-hop networks with general interference constraints and multiple traffic streams with time-correlated arrivals. We first treat the case when arrivals are modulated by independent finite state Markov chains. We show that the well known maximal scheduling algorithm achieves average delay that grows at most logarithmically in the largest number of interferers at any link. Further, in the important special case when each Markov process has at most two states (such as bursty ON/OFF sources), we prove that average delay is independent of the number of nodes and links in the network, and hence is order-optimal. We provide tight delay bounds in terms of the individual auto-correlation parameters of the traffic sources. These are perhaps the first order-optimal delay results for controlled queueing networks that explicitly account for such statistical information. Our analysis treats cases both with and without flow control.