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 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.