Optimal Forwarding in Delay-Tolerant Networks With Multiple Destinations

Abstract

Abstract-We study the trade-off between delivery delay and energy consumption in a delay tolerant network in which a message (or a file) has to be delivered to each of several destinations by epidemic relaying. In addition to the destinations, there are several other nodes in the network that can assist in relaying the message. We first assume that, at every instant, all the nodes know the number of relays carrying the message and the number of destinations that have received the message. We formulate the problem as a controlled continuous time Markov chain and derive the optimal closed loop control (i.e., forwarding policy). However, in practice, the intermittent connectivity in the network implies that the nodes may not have the required perfect knowledge of the system state. To address this issue, we obtain an ODE (i.e., a deterministic fluid) approximation for the optimally controlled Markov chain. This fluid approximation also yields an asymptotically optimal open loop policy. Finally, we evaluate the performance of the deterministic policy over finite networks. Numerical results show that this policy performs close to the optimal closed loop policy.Index Terms-Delay tolerant networks, epidemic relaying, optimal control, fluid approximation I. INTRODUCTION Delay tolerant networks (DTNs) [1] are sparse wireless ad hoc networks with highly mobile nodes. In these networks, the link between any two nodes is up when these are within each other's transmission range, and is down otherwise. In particular, at any given time, it is unlikely that there is a complete route between a source and its destination.We consider a DTN in which a short message (also referred to as a packet) needs to be delivered to multiple (say M ) destinations. There are also N potential relays that do not themselves "want" the message but can assist in relaying it to the nodes that do. At time t = 0, N 0 of the relays have copies of the packet. All nodes are assumed to be mobile. In such a network, a common technique to improve packet delivery delay is epidemic relaying [2]. We consider a controlled relaying scheme that works as follows. Whenever a node (relay or destination) carrying the packet meets a relay that does not have a copy of the packet, then the former has the option of either copying or not copying. When a node that

Optimal Beaconing Control in Delay-Tolerant Networks With Multiple Destinations

“…This makes the optimal controlling problem much more complex. The work in [17] considers the optimal controlling problem in DTNs with multiple destinations. However, this work is oriented to the optimal forwarding policy, which ignores the energy consumption in the beaconing process.…”

Energy constraint beaconing control in delay tolerant networks with multiple destinations

“…The work in explored the joint beaconing and activation control for the first activation control for the first time, but it used the simple two‐hop routing algorithm, which is just a special case of the original ER algorithm.The work in studied the optimal beaconing problem in DTN with ER algorithm, but it assumed that there was only one destination, and the energy consumption for the destination could be ignored in this case. In many applications, there may be multiple destinations . For example, the content provider pushes the advertisement to multiple consumers, and this can be seen as the multicasting case, which is an important problem in DTN.…”

“…Therefore, optimal control with multiple destinations is a complex problem. To our best knowledge, only the work in considered the optimal controlling problem in DTN with multiple destinations. However, the work in focused on the forwarding control, which ignored the beaconing energy.…”

“…To our best knowledge, only the work in considered the optimal controlling problem in DTN with multiple destinations. However, the work in focused on the forwarding control, which ignored the beaconing energy. The work in considered the optimal beaconing problem, but it just studied the trade‐off between the energy consumption and performance.…”

Adaptive Optimal Stochastic Control of Delay-Tolerant Networks

“…The optimization goal in [17] can be considered a relaxed version of our problem, e.g., the weighted sum of delivery time and energy consumption. Adopting that optimization goal, the authors of [19] provide a rigorous proof of the fact that the dynamics corresponding to the closed loop optimal control acting over a fluid approximation is the fluid limit -for large number of relays -of the optimal Markov decision process.…”