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.
翻译:我们考虑一个由单一源和美元接收器节点组成的网络, 将其分组成等尺寸的组群 。 我们使用每个组组的组头, 以便利该组内源和节点之间的通信。 内部组, 节点根据给定的网络型态相互连接。 根据节点之间的连接, 每个节点将其当前存储的源更新版本转至相邻节点, 以美元为本地美元 。 我们用美元 来评估节点的信息新鲜度 。 我们认为每个组群头的断、 环和完全连接的网络表层 。 根据我们的结果, 每节节节节点之间的平均版本缩放 $( =QQ), 以美元=1 =1 = =1 = = 美元, 以美元 美元 =1 = = = =1 = 美元, 以评估节点点点点点的信息新鲜度 。 我们认为, 每个组群点、 环 和完全连接的网络结构模式可以实现 $ 。 接下来, 显示每个组群点的网络的连 = 。