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We consider the binary freshness metric for gossip networks that consist of asingle source and $n$ end-nodes, where the end-nodes are allowed to share theirstored versions of the source information with the other nodes. We developrecursive equations that characterize binary freshness in arbitrarily connectedgossip networks using the stochastic hybrid systems (SHS) approach. Next, westudy binary freshness in several structured gossip networks, namelydisconnected, ring and fully connected networks. We show that for bothdisconnected and ring network topologies, when the number of nodes gets large,the binary freshness of a node decreases down to 0 as $n^{-1}$, but thefreshness is strictly larger for the ring topology. We also show that for thefully connected topology, the rate of decrease to 0 is slower, and it takes theform of $n^{-\rho}$ for a $\rho$ smaller than 1, when the update rates of thesource and the end-nodes are sufficiently large. Finally, we study the binaryfreshness metric for clustered gossip networks, where multiple clusters ofstructured gossip networks are connected to the source node through designatedaccess nodes, i.e., cluster heads. We characterize the binary freshness in suchnetworks and numerically study how the optimal cluster sizes change withrespect to the update rates in the system.

Gossiping with Binary Freshness Metric