Optimal forwarding in Delay Tolerant Networks with Multiple Destinations

International audienceWe 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

Delay and Energy Optimal Two-Hop Relaying in Delay Tolerant Networks

Abstract—We study the trade-off between delivery delay and energy consumption in delay tolerant mobile wireless networks that use two-hop relaying. The source may not have perfect knowledge of the delivery status at every instant. We formulate the problem as a stochastic control problem with partial information, and study structural properties of the optimal policy. We also propose a simple suboptimal policy. We then compare the performance of the suboptimal policy against that of the optimal control with perfect information. These are bounds on the performance of the proposed policy with partial information. Several other related open loop policies are also compared with these bounds. I

A Study on Throughput and Delay Performance Analysis in Two-Hop Relay Mobile Ad Hoc Networks

Tohoku University加藤寧課

Optimal Control of Epidemics in the Presence of Heterogeneity

We seek to identify and address how different types of heterogeneity affect the optimal control of epidemic processes in social, biological, and computer networks. Epidemic processes encompass a variety of models of propagation that are based on contact between agents. Assumptions of homogeneity of communication rates, resources, and epidemics themselves in prior literature gloss over the heterogeneities inherent to such networks and lead to the design of sub-optimal control policies. However, the added complexity that comes with a more nuanced view of such networks complicates the generalizing of most prior work and necessitates the use of new analytical methods. We first create a taxonomy of heterogeneity in the spread of epidemics. We then model the evolution of heterogeneous epidemics in the realms of biology and sociology, as well as those arising from practice in the fields of communication networks (e.g., DTN message routing) and security (e.g., malware spread and patching). In each case, we obtain computational frameworks using Pontryagin’s Maximum Principle that will lead to the derivation of dynamic controls that optimize general, context-specific objectives. We then prove structures for each of these vectors of optimal controls that can simplify the derivation, storage, and implementation of optimal policies. Finally, using simulations and real-world traces, we examine the benefits achieved by including heterogeneity in the control decision, as well as the sensitivity of the models and the controls to model parameters in each case