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We consider an energy harvesting information update system where a sensor isallowed to choose a transmission mode for each transmission, where each modeconsists of a transmission power-error pair. We also incorporate the batteryphenomenon called battery recovery effect where a battery replenishes thedeliverable energy if kept idle after discharge. For an energy-limited age ofinformation (AoI) system, this phenomenon gives rise to the interestingtrade-off of recovering energy after transmissions, at the cost of increasedAoI. Considering two metrics, namely peak-age hitting probability and averageage as the worst-case and average performance indicators, respectively, wepropose a framework that formulates the optimal transmission scheme selectionproblem as a Markov Decision Process (MDP). We show that the gains obtained byconsidering both battery dynamics and adjustable transmission power togetherare much higher than the sum gain achieved if they are considered separately.We also propose a simple methodology to optimize the system performance takinginto account worst-case and average performances jointly.

Optimal Transmission Policies for Energy Harvesting Age of Information Systems with Battery Recovery