Abstract
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.
Highlights
With the increasing of mobile operating systems, such as iPhone OS, Android, and Windows Phone OS, mobile phones have already evolved from simple voice communication means into powerful devices able to provide a variety of services to users
Through Pontryagin’s maximum principle, we explore the optimal control problem and prove that the optimal policy conforms to the threshold form in some cases
If above conditions can be satisfied, the optimal policy conforms to the threshold form and has at most one jump
Summary
With the increasing of mobile operating systems, such as iPhone OS, Android, and Windows Phone OS, mobile phones have already evolved from simple voice communication means into powerful devices able to provide a variety of services to users. The source has the incentive to push the message to other nodes timely To achieve this goal, it has to pay certain reward to the relay nodes to make them be cooperative. If the remaining lifetime of message is shorter, they may think that the source is eager to transmit the message as soon as possible, so they think that their goods (e.g., the forwarding service) are important for the source In this case, they may increase the price. The price of the goods (e.g., the forwarding service) may be varying with time In this environment, whether to make nodes be cooperative at specific time is an important problem for the source. We compare the performance of the optimal policy with other policies through extensive numerical results and find that the optimal policy obtained by our model is the best
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