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In this paper, we propose a cross-layer scheduling algorithm that achieves a throughput “ ε-close” to the optimal throughput in multihop wireless networks with a tradeoff of O([1/(ε)]) in average end-to-end delay guarantees. The algorithm guarantees finite buffer sizes and aims to solve a joint congestion control, routing, and scheduling problem in a multihop wireless network while satisfying per-flow average end-to-end delay constraints and minimum data rate requirements. This problem has been solved for both backlogged as well as arbitrary arrival rate systems. Moreover, we discuss the design of a class of low-complexity suboptimal algorithms, effects of delayed feedback on the optimal algorithm, and extensions of the proposed algorithm to different interference models with arbitrary link capacities.