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The development of delay-tolerant networks (DTNs) has attracted significant attention in the network research community. In this paper, we propose a new type of DTN - a homing-pigeon-based DTN (HoP-DTN). In the HoP-DTN, each node owns a dedicated messenger (called a pigeon). The only form of internode communication is for a pigeon to periodically carry a batch of messages originated at the home node, deliver them to the corresponding destination nodes, and return home. Clearly, given message-expiration times, some messages may not reach their destinations by the deadline. Through analysis and simulations, we study the relationship between key parameters of the system, including average message delay, expiration time, delivery ratio, arrival rate, and batch size of messages. Various simulations have been conducted to demonstrate the accuracy of our analysis. Our theoretical study and simulations present a deep insight into the characteristics of the proposed system. Some interesting observations from simulations are discussed in detail in this paper, and the results demonstrate that our proposed scheme performs better in terms of average message delay, message-delivery ratio, and cost-effectiveness.