Joint Optimization of Expected Age-of-Information and Its Variance in UAV-Assisted Networks

Unmanned Aerial Vehicles (UAVs) have emerged as dynamic relays for collecting data from Internet of Things (IoT) devices and maintaining information freshness in wireless networks. Prior research has primarily focused on optimizing the average Age-of-Information (AoI) or its peak values to maintain data freshness. This work, however, presents a novel framework that addresses not only the expected AoI minimization but also the minimization of its variance, which reduces the overall AoI variability across the network. To this end, we first derive the closed-form expressions for the expected AoI and its variance. The joint optimization of AoI expectation and variance is then formulated as a bi-objective problem with quality-of-service constraints, where UAVs' trajectories and data transmission probabilities are optimized. To solve the resulting non-convex problem, we leverage Geometric Programming (GP), a robust optimization technique that reformulates the problem into a sequence of convex subproblems using logarithmic transformations. An efficient iterative algorithm is devised to refine UAV trajectories and transmission probabilities, ensuring rapid convergence to an optimal solution. Our simulation results demonstrate the superiority of the proposed GP-based solution over conventional methods. Specifically, the expected AoI achieved by our GP approach significantly outperforms the interior point and Sequential Quadratic Programming (SQP) methods. This reflects a remarkable improvement of over 88% compared to these traditional techniques. Additionally, our framework effectively minimizes AoI variability, ensuring more predictable network performance.