Timely Status Updating Over Erasure Channels Using an Energy Harvesting Sensor: Single and Multiple Sources

Abstract

A status updating system is considered in which data from multiple sources are sampled by an energy harvesting sensor and transmitted to a remote destination through an erasure channel. The goal is to deliver status updates of all sources in a timely manner, such that the cumulative long-term average <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">age-of-information</i> (AoI) is minimized. The AoI for each source is defined as the time elapsed since the generation time of the latest successful status update received at the destination from that source. Transmissions are subject to energy availability, which arrives in units according to a Poisson process, with each energy unit capable of carrying out one transmission from only one source. The sensor is equipped with a unit-sized battery to save the incoming energy. A scheduling policy is designed in order to determine which source is sampled using the available energy. The problem is studied in two main settings: 1) no erasure status feedback and 2) perfect instantaneous feedback. For the case of one source, it is shown that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">renewal policies</i> are optimal, in which successful status update instances form a renewal process. In the setting without feedback, it is further shown that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">threshold-based policies</i> are optimal, in which the source is sampled only if the time until a new energy unit arrives exceeds a certain threshold. In the setting with feedback, threshold-greedy policies are investigated, in which the source is sampled according to a threshold-based policy following successful transmissions, and instantaneously whenever energy is available following failed transmissions. The optimal thresholds are found in closed-form in terms of the erasure probability. Such threshold-based policies are then extended for the case of multiple sources, combined with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">round robin</i> scheduling in the setting without feedback, in which sources are sampled in the same repeating order; and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">maximum-age-first</i> scheduling in the setting with feedback, in which sources with maximum AoI are given priority. In both settings, the achieved cumulative long-term average AoI is derived in closed-form in terms of the threshold, the erasure probability and the number of sources.