Age Optimal Information Gathering and Dissemination on Graphs

Vishrant Tripathi, Rajat Talak, Eytan H. Modiano

Abstract: We consider the problem of timely exchange of updates between a central station and a set of ground terminals $V$ , via a mobile agent that traverses across the ground terminals along a mobility graph $G = (V, E)$ . We design the trajectory of the mobile agent to minimize average-peak and average age of information (AoI), two recently proposed metrics for measuring timeliness of information. We consider randomized trajectories, in which the mobile agent travels from terminal $i$ to terminal $j$ with probability $P_{i,j}$ . For the information gathering problem, we show that a randomized trajectory is average-peak age optimal and factor- $8\mathcal {H}$ average age optimal, where $\mathcal {H}$ is the mixing time of the randomized trajectory on the mobility graph $G$ . We also show that the average age minimization problem is NP-hard. For the information dissemination problem, we prove that the same randomized trajectory is factor- $O(\mathcal {H})$ average-peak and average age optimal. Moreover, we propose an age-based trajectory, which utilizes information about current age at terminals, and show that it is factor-2 average age optimal in a symmetric setting.