Age of Information and its Distribution Properties in Energy Harvesting WSN

This paper studies the age of information (AoI) and its distributional properties for a dual-source status update system with transmitters characterized by energy constraints. Specially, the two sources send their sensed measurements in the form of status updates to the destination through a server powered by energy harvesting (EH). Meanwhile, arrivals times of the status update packets and the harvesting energy units at the transmitter are assumed to be random according to independent Poisson processes. The service time of each packet is assumed to be exponentially distributed. Firstly, we construct a three-dimensional state vector to track the occupancy of energy buffer, server and data buffer. Furthermore, by describing a multi-dimensional random process of AoI evolution representing all possible state transitions of the system, we could use the stochastic hybrid system (SHS) to characterize the moment generating function (MGF) of AoI. Therefore, we further derive closed-form expressions for the first and second moments of AoI by solving the differential equations. The numerical results illustrate that in the design and optimization process of the dual-source sensor status update system, it is necessary to incorporate the second-order moment and even higher-order moments of AoI.