Age of Gossip With Cellular Drone Mobility

TL;DR

This work analyzes information freshness in a cellular gossip network where a mobile drone disseminates updates across $f(n)$ cells containing $n$ nodes. The drone moves according to a continuous-time Markov chain with mobility rate $\lambda_m(n)$ and disseminates updates within the current cell at rate $\lambda_d(n)$, while nodes gossip fully within their cell; the version age of information (VAoI) is used to quantify freshness. The paper derives general results showing the drone's own VAoI remains $\Theta(1)$ w.h.p. and that the inter-update times to a cell depend on the stationary distribution of the drone's CTMC and $\lambda_d(n)$, independent of $\lambda_m(n)$. In the fully-connected mobility case, a dual-bottleneck emerges: the VAoI scales with the slower of $\lambda_m(n)$ and $\lambda_d(n)$, yielding $\Theta\left( \frac{f(n)}{\lambda_d(n)} \right)$ in the mobility-dominated regime and $\Theta\left( \frac{f(n)}{\lambda_m(n)} \right)$ in the dissemination-dominated regime, each plus a $\Theta(\log\frac{n}{f(n)})$ term from intra-cell gossip. These results inform how mobility and dissemination capabilities jointly determine freshness in UAV-assisted networks, with special cases recovering known logarithmic and max-type scalings.

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 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 $λ_m(n)$.

Figures (1)

• Figure 1: A gossiping network with cellular drone mobility. On the left, a source generates updates and shares them with a mobile drone. The drone moves between cells and disseminates information to all the nodes in a cell as a rate $\lambda_d(n)$ Poisson process. The nodes in each cell gossip as a fully-connected network, but do not gossip with nodes in a different cell. On the right, we see how the drone moves between cells. The top right figure shows which cell the drone can move to from cell $4$ based on the underlying CTMC shown on the bottom right. The holding time of each state of the CTMC has rate $\lambda_m(n)$.

Theorems & Definitions (6)

• Lemma 1
• Lemma 2
• Lemma 3
• Remark 1
• Remark 2
• Remark 3