Optimal Control of Epidemic Routing in Delay Tolerant Networks with Selfish Behaviors

Most routing algorithms in delay tolerant networks (DTN) need nodes serving as relays for the source to carry and forward message. Due to the impact of selfishness, nodes have no incentive to stay in the network after getting message (e.g., free riders). To make them be cooperative at specific time, the source has to pay certain reward to them. In addition, the reward may be varying with time. On the other hand, the source can obtain certain benefit if the destination gets message timely. This paper considers the optimal incentive policy to get the best trade-off between the benefit and expenditure of the source for the first time. To cope with this problem, it first proposes a theoretical framework, which can be used to evaluate the trade-off under different incentive policies. Then, based on the framework, it explores the optimal control problem through Pontryagin's maximum principle and proves that the optimal policy conforms to the threshold form in certain cases. Simulations based on both synthetic and real motion traces show the accuracy of the framework. Through extensive numerical results, this paper demonstrates that the optimal policy obtained above is the best.