Optimal monotone forwarding policies in delay tolerant mobile ad-hoc networks

We study fluid approximations for a class of monotone relay policies in delay tolerant ad-hoc networks. This class includes the epidemic routing and the two-hops routing protocols. We enhance relay policies with probabilistic forwarding, i.e., a message is forwarded to a relay with some probability pp. We formulate an optimal control problem where a tradeoff between delay and energy consumption is captured and optimized. We compute both the optimal static value of pp as well as the optimal time dependent value of pp. We show that the time-dependent problem is optimized by threshold type policies, and we compute explicitly the value of the optimal threshold for some special classes of relay policies.