Timely Updating with Intermittent Energy and Data for Multiple Sources over Erasure Channels

A status updating system is considered in which multiple data sources generate packets to be delivered to a destination through a shared energy harvesting sensor. Only one source's data, when available, can be transmitted by the sensor at a time, subject to energy availability. Transmissions are prune to erasures, and each successful transmission constitutes a status update for its corresponding source at the destination. The goal is to schedule source transmissions such that the collective long-term average age-of-information (AoI) is minimized. AoI is defined as the time elapsed since the latest successfully-received data has been generated at its source. To solve this problem, the case with a single source is first considered, with a focus on threshold waiting policies, in which the sensor attempts transmission only if the time until both energy and data are available grows above a certain threshold. The distribution of the AoI is fully characterized under such a policy. This is then used to analyze the performance of the multiple sources case under maximum-age-first scheduling, in which the sensor's resources are dedicated to the source with the maximum AoI at any given time. The achievable collective long-term average AoI is derived in closed-form. Multiple numerical evaluations are demonstrated to show how the optimal threshold value behaves as a function of the system parameters, and showcase the benefits of a threshold-based waiting policy with intermittent energy and data arrivals.