The Satellite Internet of Things (S-IoT) enables global connectivity for remote sensing devices that must operate energy-efficiently over long time spans. We consider an S-IoT system consisting of a sender-receiver pair connected by a data channel and a feedback channel and capture its dynamics using a Markov Decision Process (MDP). To extend battery life, the sender has to decide on deep-sleep durations. Deep-sleep scheduling is the primary lever to reduce energy consumption, since sleeping devices consume only a fraction of their idle power. By choosing its deep-sleep duration online, the sender has to find a trade-off between energy consumption and data quality degradation at the receiver, captured by a weighted sum of costs. We quantify data quality degradation via the recently introduced Goal-Oriented Tensor (GoT) metric, which can take both age and content of delivered data into account. We assume a Markovian observed process and Markov channels with time-varying delay and erasure rates. The challenge is that content awareness of the GoT metric makes periodic transmissions inherently inefficient. Additionally, optimal sleep durations depends on the (unknown) future states of the observed process and the channels, both of which must be inferred online. We propose a novel algorithm using probabilistic simulation-based optimization (PSBO). With PSBO, the sensor forecasts future states based on estimated transition probabilities, and uses these forecasts to select the optimal deep-sleep duration. Extensive simulations and experiments with S-IoT hardware demonstrate superior performance of PSBO under diverse conditions.

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