Age of Gossip on a Grid

TL;DR

This paper analyzes the age of information in a grid gossip network, establishing that the average version age scales as O(n^{1/3}), which is an improvement over ring networks and extends understanding beyond fully-connected graphs.

Contribution

It provides the first age scaling result for a grid network, showing how increased connectivity reduces information age compared to ring networks.

Findings

Average age scales as O(n^{1/3}) in grid networks

Higher connectivity reduces age from O(n^{1/2}) to O(n^{1/3})

First analysis of age scaling in grid topology beyond ring and fully-connected networks

Abstract

We consider a gossip network consisting of a source generating updates and $n$ nodes connected in a two-dimensional square grid. The source keeps updates of a process, that might be generated or observed, and shares them with the grid network. The nodes in the grid network communicate with their neighbors and disseminate these version updates using a push-style gossip strategy. We use the version age metric to quantify the timeliness of information at the nodes. We find an upper bound for the average version age for a set of nodes in a general network. Using this, we show that the average version age at a node scales as $O(n^{\frac{1}{3}})$ in a grid network. Prior to our work, it has been known that when $n$ nodes are connected on a ring the version age scales as $O(n^{\frac{1}{2}})$, and when they are connected on a fully-connected graph the version age scales as $O(\log n)$. Ours is the first work to show an age scaling result for a connectivity structure other than the ring and fully-connected networks that represent two extremes of network connectivity. Our work shows that higher connectivity on a grid compared to a ring lowers the age experience of each node from $O(n^{\frac{1}{2}})$ to $O(n^{\frac{1}{3}})$.