α–β AoI Penalty in Wireless-Powered Status Update Networks
Huimin Hu, Ke Xiong, Yang Lu, Bo Gao, Pingyi Fan, Khaled B. Letaief · IEEE Internet of Things Journal · 2021
In multiservice systems, multiple different Age of Information (AoI) penalty functions and corresponding algorithms are required to be deployed, which may result in high deployment complexity. Motivated by this, we propose a universal function$f(t)=\beta e^{\alpha t} -\beta $called$\alpha $-$\beta $AoI penaltyfunction to characterize different nonlinear forms of AoI penalty. With the presented$\alpha $-$\beta $AoI penalty function, we analyze the performance of wireless-powered communication networks (WPCNs), where a sensor first harvests energy from a wireless power station (WPS) and then transmits the generated update to its data collector. The sensor is equipped with a battery of limited energy capacity. When the battery of the sensor node is fully charged, the sensor generates a status update and uses all available energy to transmit it. A closed-form expression of the system average$\alpha $-$\beta $AoI penalty is derived by using some limit methods. In order to minimize the average$\alpha $-$\beta $AoI penalty of the system, an optimization problem is formulated to optimize the battery capacity. Simulation results demonstrate the correctness of our theoretical analysis results and show that there is a unique optimal battery capacity that optimizes the system AoI performance. Moreover, when the system is with the exponential-shape AoI penalty function ($\beta >0$and$\alpha >0$), with the increment of$\alpha $and$\beta $increase, the average$\alpha $-$\beta $AoI penalty also increases. Differently, when the system is with the logarithmic-shape AoI penalty function ($\beta < 0$and$\alpha < 0$), with the increment of$\alpha $and$\beta $, the average$\alpha $-$\beta $AoI penalty decreases.