  This paper characterizes the structure of the Age of Information
(AoI)-optimal policy in wireless powered communication systems while accounting
for the time and energy costs of generating status updates at the source nodes.
In particular, for a single source-destination pair in which a radio frequency
(RF)-powered source sends status updates about some physical process to a
destination node, we minimize the long-term average AoI at the destination
node. The problem is modeled as an average cost Markov Decision Process (MDP)
in which, the generation times of status updates at the source, the
transmissions of status updates from the source to the destination, and the
wireless energy transfer (WET) are jointly optimized. After proving the
monotonicity property of the value function associated with the MDP, we
analytically demonstrate that the AoI-optimal policy has a threshold-based
structure w.r.t. the state variables. Our numerical results verify the
analytical findings and reveal the impact of state variables on the structure
of the AoI-optimal policy. Our results also demonstrate the impact of system
design parameters on the optimal achievable average AoI as well as the
superiority of our proposed joint sampling and updating policy w.r.t. the
generate-at-will policy.
