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We analyze the delay performance of a multihop wireless network with a fixed route between each source-destination pair. We develop a new queue grouping technique to handle the complex correlations of the service process resulting from the multihop nature of the flows. A general set-based interference model is assumed that imposes constraints on links that can be served simultaneously at any given time. These interference constraints are used to obtain a fundamental lower bound on the delay performance of any scheduling policy for the system. We present a systematic methodology to derive such lower bounds. For a special wireless system, namely the clique, we design a policy that is sample-path delay-optimal. For the tandem queue network, where the delay-optimal policy is known, the expected delay of the optimal policy numerically coincides with the lower bound. We conduct extensive numerical studies to suggest that the average delay of the back-pressure scheduling policy can be made close to the lower bound by using appropriate functions of queue length.