Timely Updates in Energy Harvesting Two-hop Networks: Offline and Online Policies

A two-hop energy harvesting communication network is considered, in which measurement updates are transmitted by a source to a destination through an intermediate relay. Updates are to be sent in a timely fashion that minimizes the age of information, defined as the time elapsed since the most recent update at the destination was generated at the source. The source and the relay communicate using energy harvested from nature, which is stored in infinite-sized batteries. Both nodes use fixed transmission rates, and hence updates incur fixed delays (service times). Two problems are formulated: an offline problem, in which the energy arrival information is known a priori, and an online problem, in which such information is revealed causally over time. In both problems, it is shown that it is optimal to transmit updates from the source just in time as the relay is ready to forward them to the destination, making the source and the relay act as one combined node. A recurring theme in the optimal policy is that updates should be as uniformly spread out over time as possible, subject to energy causality and service time constraints. This is perfectly achieved in the offline setting, and is achieved almost surely in the online setting by a best effort policy.