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This paper considers a real-time status update system in which an energyharvesting (EH)-powered transmitter node observes some physical process, andsends its sensed measurements in the form of status updates to a destinationnode. The status update and harvested energy packets are assumed to arrive atthe transmitter according to independent Poisson processes, and the servicetime of each status update is assumed to be exponentially distributed. Wequantify the freshness of status updates when they reach the destination usingthe concept of Age of Information (AoI). Unlike most of the existing analysesof AoI focusing on the evaluation of its average value when the transmitter isnot subject to energy constraints, our analysis is focused on understanding thedistributional properties of AoI through the characterization of its momentgenerating function (MGF). In particular, we use the stochastic hybrid systems(SHS) framework to derive closed-form expressions of the MGF of AoI underseveral queueing disciplines at the transmitter, including non-preemptive andpreemptive in service/waiting strategies. Using these MGF results, we furtherobtain closed-form expressions for the first and second moments of AoI in eachqueueing discipline. We demonstrate the generality of this analysis byrecovering several existing results for the corresponding system with no energyconstraints as special cases of the new results. Our numerical results verifythe analytical findings, and demonstrate the necessity of incorporating thehigher moments of AoI in the implementation/optimization of real-time statusupdate systems rather than just relying on its average value.

Closed-form Characterization of the MGF of AoI in Energy Harvesting Status Update Systems