Age of Gossip With Time-Varying Topologies

TL;DR

This paper studies how time-varying network topologies, modeled by a Markov chain, affect information freshness in gossip networks, showing that certain conditions preserve logarithmic age scaling despite topology changes.

Contribution

It introduces a framework for analyzing age of information in networks with dynamic topologies governed by a Markov chain, demonstrating conditions under which age scaling is maintained.

Findings

Age scales logarithmically with number of nodes when fully connected state exists.

Topology changes do not affect age scaling if the network can be fully connected.

Numerical simulations explore effects of different topologies and transition rates.

Abstract

We consider a gossiping network, where a source node sends updates to a network of $n$ gossiping nodes. Meanwhile, the connectivity topology of the gossiping network changes over time, among a finite number of connectivity ''states,'' such as the fully connected graph, the ring graph, the grid graph, etc. The transition of the connectivity graph among the possible options is governed by a finite state continuous time Markov chain (CTMC). When the CTMC is in a particular state, the associated graph topology of the gossiping network is in the way indicated by that state. We evaluate the impact of time-varying graph topologies on the freshness of information for nodes in the network. We use the version age of information metric to quantify the freshness of information at the nodes. Using a method similar to the first passage percolation method, we show that, if one of the states of the CTMC is the fully connected graph and the transition rates of the CTMC are constant, then the version age of a typical node in the network scales logarithmically with the number of nodes, as in the case if the network was always fully connected. That is, there is no loss in the age scaling, even if the network topology deviates from full connectivity, in this setting. We perform numerical simulations and analyze more generally how having different topologies and different CTMC rates (that might depend on the number of nodes) affect the average version age scaling of a node in the gossiping network.