Age of Gossip With Cellular Drone Mobility

Abstract

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 drone receives source updates 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). We evaluate the impact of the number of cells $f(n)$, drone speed $\lambda_m(n)$ and drone dissemination rate $\lambda_d(n)$ on the information freshness of nodes in the network. We use the version age of information metric to quantify information freshness. We observe that the expected duration between two drone-to-cell service times depends on the stationary distribution of the underlying CTMC and $\lambda_d(n)$, but not on $\lambda_m(n)$. However, the version age instability makes high probability analysis for a general underlying CTMC difficult. Therefore, we focus on the fully-connected drone mobility model. Under this model, we uncover a dual-bottleneck, by leveraging stochastic equivalence between drone mobility and drone dissemination speed: the version age is constrained by the slower of these two processes. If $\lambda_d(n) \gg \lambda_m(n)$, then the version age scaling of nodes is dominated by the inverse of $\lambda_m(n)$ and is independent of $\lambda_d(n)$. If $\lambda_m(n) \gg \lambda_d(n)$, then the version age scaling of nodes is dominated by the inverse of $\lambda_d(n)$ and is independent of $\lambda_m(n)$.