Age of Information in Gossip Networks: A Friendly Introduction and Literature Survey

Gossiping is a communication mechanism, used for fast information dissemination in a network, where each node of the network randomly shares its information with the neighboring nodes. To characterize the notion of fastness in the context of gossip networks, age of information (AoI) is used as a timeliness metric. In this article, we summarize the recent works related to timely gossiping in a network. We start with the introduction of randomized gossip algorithms as an epidemic algorithm for database maintenance, and how the gossiping literature was later developed in the context of rumor spreading, message passing and distributed mean estimation. Then, we motivate the need for timely gossiping in applications such as source tracking and decentralized learning. We evaluate timeliness scaling of gossiping in various network topologies, such as, fully connected, ring, grid, generalized ring, hierarchical, and sparse asymmetric networks. We discuss age-aware gossiping and the higher order moments of the age process. We also consider different variations of gossiping in networks, such as, file slicing and network coding, reliable and unreliable sources, information mutation, different adversarial actions in gossiping, and energy harvesting sensors. Finally, we conclude this article with a few open problems and future directions in timely gossiping.

Age of Gossip on Generalized Rings

We consider a gossip network consisting of a source forwarding updates and $n$ nodes placed geometrically in a ring formation. Each node gossips with $f(n)$ nodes on either side, thus communicating with $2f(n)$ nodes in total. $f(n)$ is a sub-linear, non-decreasing and positive function. The source keeps updates of a process, that might be generated or observed, and shares them with the nodes in the ring network. The nodes in the ring 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. Prior to this work, it was shown that the version age scales as $O(n^{\frac{1}{2}})$ in a ring network, i.e., when $f(n)=1$, and as $O(\log{n})$ in a fully-connected network, i.e., when $2f(n)=n-1$. In this paper, we find an upper bound for the average version age for a set of nodes in such a network in terms of the number of nodes $n$ and the number of gossiped neighbors $2 f(n)$. We show that if $f(n) = \Omega(\frac{n}{\log^2{n}})$, then the version age still scales as $\theta(\log{n})$. We also show that if $f(n)$ is a rational function, then the version age also scales as a rational function. In particular, if $f(n)=n^\alpha$, then version age is $O(n^\frac{1-\alpha}{2})$. Finally, through numerical calculations we verify that, for all practical purposes, if $f(n) = \Omega(n^{0.6})$, the version age scales as $O(\log{n})$.

Age of Gossip on a Grid

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 $O(n^{\frac{1}{3}})$.