In this paper, we analyze a new type of delay tolerant networks (DTN) where each node owns multiple dedicated messengers, called pigeons. The only form of inter- node communication is for a pigeon to periodically carry a batch of messages originated at the home node, deliver to the corresponding destination nodes and return home. We name this as homing-pigeon (HoP) based routing mechanism, which is an effective way to overcome end-to-end disconnection in DTN. In this work, we model the HoP mechanism analytically with a periodic pigeon scheduling algorithm. Our analysis focuses on understanding the pigeon departure frequency from the home node while keeping the message delivery ratio above a given threshold. Simulation results are given to validate our analysis.