Age Optimal Information Gathering and Dissemination on Graphs

We consider the problem of timely exchange of updates between a central station and a set of ground terminalsV, 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 terminalito terminaljwith probabilityPi,j. For the information gathering problem, we show that a randomized trajectory is average-peak age optimal and factor-8Haverage age optimal, whereHis the mixing time of the randomized trajectory on the mobility graphG. 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(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.