  In this work, we investigate the use of epidemic routing in energy
constrained Delay Tolerant Networks (DTNs). In epidemic routing, messages are
relayed by intermediate nodes at contact opportunities, i.e., when pairs of
nodes come within the transmission range of each other. Each node needs to
decide whether to forward its message upon contact with a new node based on its
own residual energy level and the age of that message. We mathematically
characterize the fundamental trade-off between energy conservation and a
measure of Quality of Service as a dynamic energy-dependent optimal control
problem. We prove that in the mean-field regime, the optimal dynamic forwarding
decisions follow simple threshold-based structures in which the forwarding
threshold for each node depends on its current remaining energy. We then
characterize the nature of this dependence. Our simulations reveal that the
optimal dynamic policy significantly outperforms heuristics.
