Optimal Routing Control in Delay Tolerant Networks with Time-Varying Fees

Due to the uncertainty of the connections in delay tolerant networks, the source may need help from other nodes and make these nodes serve as relays to forward the messages to the destination. To further improve the performance, the source may also make these nodes serve as agents, which can help the source to make other nodes serve as relays. However, nodes may not be willing to help the source without any reward because of the selfish nature. This means that the source has to pay certain reward to the nodes that provide help. Furthermore, such fees may be varying with time. For example, if the nodes guess that the source is eager to transmit the message to the destination, they may ask for more reward. In addition, the reward that the source obtains from the destination may be varying with time, too. For example, the sooner the destination gets the message, the more reward may be. In such complex case, it may not be good for the source to request help all the time. This paper proposes a unifying theoretical framework based on Ordinary Differential Equations to evaluate the total reward that the source can obtain. Then, based on the framework, we study the optimal control problem by Pontryagin’s Maximum Principle and prove that the optimal policy confirms to the threshold form in some cases. Simulations based on both synthetic and real motion traces show the accuracy of the framework. Furthermore, we demonstrate that the performance of the optimal policy is the best through extensive numerical results.