When Fresh Information Is Not Enough: Age-of-Actuation-Optimal Scheduling for Energy-Harvesting Actuators

Abstract: We study transmission scheduling in an energy-harvesting actuation system where an actuation requires both a received update and available energy. While age of information (AoI) measures information freshness, age of actuation (AoA) measures the time elapsed since the latest completed actuation. The transmitter observes the receiver's AoA and battery state and decides whether to transmit a fresh update in each slot. We formulate average-AoA minimization as a Markov decision process and establish an AoA-threshold property for an optimal policy. We also derive the average AoA in closed form under the AoI-optimal policy, which is always-transmit. Numerical results show that AoA-aware scheduling can improve actuation freshness while reducing the number of transmissions, although information freshness may deteriorate. The two policies coincide for some pairs of channel success and energy-arrival probabilities. For a one-unit battery, the transmission rate under the AoA-optimal policy can vary nonmonotonically with the energy-arrival probability.