Distributional Properties of Age of Information in Energy Harvesting Status Update Systems
Mohamed A. Abd-Elmagid, Harpreet S. Dhillon · 2021
This paper considers an energy harvesting (EH) real-time status update system in which an EH-powered transmitter node sends status updates about some physical process of interest to a destination node. The status update and harvested energy packets are assumed to arrive at the transmitter according to independent Poisson processes, and the service time of each status update is assumed to be exponentially distributed. We quantify the freshness of status updates when they reach the destination using the concept of Age of Information (AoI). Unlike most of the existing analyses of AoI that focus on characterizing its average when the transmitter has a reliable energy source and is hence not powered by EH (referred henceforth as a non-EH transmitter), our analysis is focused on understanding the distributional properties of AoI through the characterization of its moment generating function (MGF). In particular, we use the stochastic hybrid systems (SHS) framework to derive closed-form expressions of the MGF of AoI under both nonpreemptive and preemptive in service queueing disciplines at the transmitter. We demonstrate the generality of this analysis by recovering several known results for the corresponding system with a non-EH transmitter as special cases of the new results. Our numerical results verify the analytical findings, and demonstrate the importance of incorporating the higher moments of AoI in the implementation/optimization of real-time status update systems rather than just relying on its average value.