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In this paper, we consider a status update system, where an access pointcollects measurements from multiple sensors that monitor a common physicalprocess, fuses them, and transmits the aggregated sample to the destinationover an erasure channel. Under a typical information fusion scheme, thedistortion of the fused sample is inversely proportional to the number ofmeasurements received. Our goal is to minimize the long-term average age whilesatisfying the average energy and general age-based distortion requirements.Specifically, we focus on the setting in which the distortion requirement isstricter when the age of the update is older. We show that the optimal policyis a mixture of two stationary, deterministic, threshold-based policies, eachof which is optimal for a parameterized problem that aims to minimize theweighted sum of the age and energy under the distortion constraint. We thenderive analytically the associated optimal average age-cost function andcharacterize its performance in the large threshold regime, the results ofwhich shed critical insights on the tradeoff among age, energy, and thedistortion of the samples. We have also developed a closed-form solution forthe special case when the distortion requirement is independent of the age,arguably the most important setting for practical applications.

Age Minimization with Energy and Distortion Constraints