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Delay requirement becomes a key problem for the time sensitive applications in wireless sensor networks besides the power conservation issue. This paper proposes a novel network utility maximization (NUM) model with constrained delay for real-time applications in wireless sensor networks. By using dual decomposition techniques, we present a distributed iterative price and rate adaption algorithm which converges to the global optimal solution. The presented algorithm can jointly control congestion and contention while meeting the delay requirement of each flow in the network. Numerical results validate our arguments.