Age of Gossip With Cellular Drone Mobility

We consider a cellular network containing $n$ nodes where nodes within a cell gossip with each other in a fully-connected fashion and a source shares updates with these nodes via a mobile drone. The mobile drone receives updates directly from the source and shares them with nodes in the cell where it currently resides. The drone moves between cells according to an underlying continuous-time Markov chain (CTMC). In this work, we evaluate the impact of the number of cells $f(n)$, drone speed $λ_m(n)$ and drone dissemination rate $λ_d(n)$ on the freshness of information of nodes in the network. We utilize the version age of information metric to quantify the freshness of information. We observe that the expected duration between two drone-to-cell service times depends on the stationary distribution of the underlying CTMC and $λ_d(n)$, but not on $λ_m(n)$. However, the version age instability in slow moving CTMCs makes high probability analysis for a general underlying CTMC difficult. Therefore, next we focus on the fully-connected drone mobility model. Under this model, we uncover a dual-bottleneck between drone mobility and drone dissemination speed: the version age is constrained by the slower of these two processes. If $λ_d(n) \gg λ_m(n)$, then the version age scaling of nodes is dominated by the inverse of $λ_m(n)$ and is independent of $λ_d(n)$. If $λ_m(n) \gg λ_d(n)$, then the version age scaling of nodes is dominated by the inverse of $λ_d(n)$ and is independent of $λ_m(n)$.