Version Age of Information in Clustered Gossip Networks

TL;DR

This paper analyzes how the age of information metric scales in clustered gossip networks with various topologies, showing how increased connectivity and hierarchy can improve information freshness as network size grows.

Contribution

It provides a comprehensive characterization of version age scaling laws in clustered gossip networks with different topologies and hierarchical structures, introducing new bounds and hierarchical strategies.

Findings

Disconnection, ring, and full connectivity achieve different age scalings: O(√n), O(n^{1/3}), and O(log n).

Adding gossip among cluster heads improves age scaling to O(n^{1/3}), O(n^{1/4}), and O(log n).

Hierarchical structures can achieve age scaling of O(n^{1/(2h)}) with h levels, without dedicated cluster heads.

Abstract

We consider a network consisting of a single source and $n$ receiver nodes that are grouped into equal-sized clusters. We use cluster heads in each cluster to facilitate communication between the source and the nodes within that cluster. Inside clusters, nodes are connected to each other according to a given network topology. Based on the connectivity among the nodes, each node relays its current stored version of the source update to its neighboring nodes by $local$ $gossiping$. We use the $version$ $age$ metric to assess information freshness at the nodes. We consider disconnected, ring, and fully connected network topologies for each cluster. For each network topology, we characterize the average version age at each node and find the average version age scaling as a function of the network size $n$. Our results indicate that per node average version age scalings of $O(\sqrt{n})$, $O(n^{\frac{1}{3}})$, and $O(\log n)$ are achievable in disconnected, ring, and fully connected cluster models, respectively. Next, we increase connectivity in the network and allow gossiping among the cluster heads to improve version age at the nodes. With that, we show that when the cluster heads form a ring network among themselves, we obtain per node average version age scalings of $O(n^{\frac{1}{3}})$, $O(n^{\frac{1}{4}})$, and $O(\log n)$ in disconnected, ring, and fully connected cluster models, respectively. Next, focusing on a ring network topology in each cluster, we introduce hierarchy to the considered clustered gossip network model and show that when we employ two levels of hierarchy, we can achieve the same $O(n^{\frac{1}{4}})$ scaling without using dedicated cluster heads. We generalize this result for $h$ levels of hierarchy and show that per user average version age scaling of $O(n^{\frac{1}{2h}})$ is achievable in the case of a ring network in each cluster across all hierarchy levels.