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Utility-based routing is a special routing approach, which takes the reliability and transmission costs into account at the same time. However, the existing utility-based routing algorithms have not yet considered the delivery delay. Thus, they cannot work well in duty-cycle wireless sensor networks (WSNs) since delay is an important factor in such WSNs. In this paper, we propose a novel utility model time-sensitive utility model. Unlike previous work, the utility of a message delivery in our model is not only affected by the reliability and transmission costs but also by the delivery delay. Under the time-sensitive utility model, we derive an iterative formula to compute the time-varying utility of each message delivery. Based on the formula, we propose an optimal time-sensitive utility-based routing algorithm. The theoretical analysis and simulation results show that our proposed algorithm can maximize the average utility of message deliveries, which makes a good tradeoff among reliability, delay, and cost.