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In this paper, we propose a time-sensitive utility model for delay tolerant networks (DTNs), in which each message has an attached time-sensitive benefit that decays over time. The utility of a message is the benefit minus the transmission cost incurred by delivering the message. This model is analogous to the postal service in the real world, which inherently provides a good balance between delay and cost. Under this model, we propose a Time-sensitive Opportunistic Utility-based Routing (TOUR) algorithm. TOUR is a single-copy opportunistic routing algorithm, in which a time-sensitive forwarding set is maintained for each node by considering the probabilistic contacts in DTNs. By forwarding messages via nodes in these sets, TOUR can achieve the optimal expected utilities. We show the outstanding performance of TOUR through extensive simulations with several real DTN traces. To the best of our knowledge, TOUR is the first utility-based routing algorithm in DTNs.