In this paper, we design a greedy routing on networks of mobile agents. In the greedy routing algorithm, every time step a packet in agent $i$ is delivered to the agent $j$ whose distance from the destination is shortest among searched neighbors of agent $i$. Based on the greedy routing, we study the traffic dynamics and traffic-driven epidemic spreading on networks of mobile agents. We find that the transportation capacity of networks and the epidemic threshold increase as the communication radius increases. For moderate moving speed, the transportation capacity of networks is the highest and the epidemic threshold maintains a large value. These results can help controlling the traffic congestion and epidemic spreading on mobile networks.
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