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We consider a class of wireless networks with general interference constraints on the set of links that can be served simultaneously at any given time. We restrict the traffic to be single-hop, but allow for simultaneous transmissions as long as they satisfy the underlying interference constraints. We begin by proving a lower bound on the delay performance of any scheduling scheme for this system. We then analyze a large class of throughput optimal policies which have been studied extensively in the literature. The delay analysis of these systems has been limited to asymptotic behavior in the heavy traffic regime and order results. We obtain a tighter upper bound on the delay performance for these systems. We use the insights gained by the upper and lower bound analysis to develop an estimate for the expected delay of wireless networks with mutually independent arrival streams operating under the well-known maximum weighted matching (MWM) scheduling policy. We show via simulations that the delay performance of the MWM policy is often close to the lower bound, which means that it is not only throughput optimal, but also provides excellent delay performance.