Timely Gossip with Age-Dependent Networks

We study a class of gossip networks where a single source delivers fresh status updates through networks consisting of a set of gossiping nodes. Contrary to previous works, the source delivers updates to nodes subject to an age-dependent point process where the update rates are related to the age process at each node. We derive the closed-form expressions of stationary age moments for the disconnected networks, and demonstrate the general procedure of moment analysis in the age-dependent gossip networks based on stochastic hybrid systems (SHSs). Considering the analytical difficulties in solving the infinite-dimensional stationary moment equations in more complex topologies, we provide two numerical methods to solve for the numerical values of stationary age moments approximately, and verify the effectiveness of these methods on the first three age moments in ring networks.