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 p. 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 p as well as the optimal time dependent value of p. 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.