Power constrained DTNs: Risk MDP-LP approach

Delay Tolerant Networks (DTNs) have gained importance in the recent past, as cost-effective alternative, in scenarios where delays can be accommodated. They work well in discretely connected network, where there is no direct connectivity between some/all components of the system. But the mobility of nodes creates occasional contact opportunities. The randomly moving nodes cooperate to help a fixed source, in delivering message to a far away destination within the given time threshold. The objective is to optimize the delivery success probability, which turns out to be a risk sensitive cost. The success probability depends upon the contact rates, which in turn depend upon the power used by the nodes to remain visible. The more the power used by a node, the larger is the radius for which it is visible. However these nodes are power constrained. This leads to a constrained finite horizon, Risk sensitive Markov Decision Process (MDP). In this paper we propose a linear program (LP) based approach to solve the corresponding dynamic programming equations. This approach enables us in handling the constraints. We showed using numerical simulations that, given a hard power constraint, the solution of the constrained MDP performs significantly superior in comparison with a solution obtained by optimizing a joint cost.