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In multi-hop wireless networks, maximizing network utility by joint congestion control and scheduling has drawn much research interest, and significant progress has been made that has yielded much insight. However, in attempting to maximize network utilization, most scheduling mechanisms proposed in earlier works are too complicated to be implemented in wireless devices. One traditional approach to address complexity is to approximate the optimal but complex solution by a feasible solution that can provide a certain performance guarantee. In this paper, we suggest an alternative approach that simplifies the optimization problem itself in such a way that the solution of the new problem is guaranteed to be a fraction of the optimal solution of the original problem. The fraction depends on the Â¿interference degreeÂ¿ of the network. Based on the simplified model, we propose a scheme which combines congestion control and random access MAC. We subsequently analyze its theoretical performance, and prove that the algorithm guarantees stability, and asymptotically converges to the near-optimal operational point. Future work is needed to investigate the mechanism by which such a scheme can be implemented.