基于二进制新鲜度的闲聊
Gossiping with Binary Freshness Metric
摘要：
我们认为，由一个单一的源和$n$端节点，其中的端节点被允许与其他节点共享其存储的版本的源信息的八卦网络的二进制新鲜度度量。我们开发的递归方程，在任意连接的八卦网络使用随机混合系统（SHS）的方法来表征二进制新鲜度。接下来，我们研究了几个结构化的八卦网络，即断开，环和全连接网络中的二进制新鲜度。我们表明，对于断开和环形网络拓扑结构，当节点的数量变大，一个节点的二进制新鲜度下降到0为$n^{-1}$，但新鲜度严格较大的环形拓扑结构。我们还表明，对于全连接的拓扑结构，减少到0的速度较慢，它采取的形式$n^{-ρ}$的$ρ$小于1，当源节点和端节点的更新率是足够大的。最后，我们研究了集群八卦网络的二进制新鲜度度量，其中结构化八卦网络的多个集群通过指定的接入节点连接到源节点，即，集群头。我们在这样的网络中的二进制新鲜度的特点和数值研究如何最佳集群大小的变化相对于系统中的更新率。
英文摘要：
We consider the binary freshness metric for gossip networks that consist of a single source and $n$ end-nodes, where the end-nodes are allowed to share their stored versions of the source information with the other nodes. We develop recursive equations that characterize binary freshness in arbitrarily connected gossip networks using the stochastic hybrid systems (SHS) approach. Next, we study binary freshness in several structured gossip networks, namely disconnected, ring and fully connected networks. We show that for both disconnected 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 the freshness is strictly larger for the ring topology. We also show that for the fully connected topology, the rate of decrease to 0 is slower, and it takes the form of $n^{-ρ}$ for a $ρ$ smaller than 1, when the update rates of the source and the end-nodes are sufficiently large. Finally, we study the binary freshness metric for clustered gossip networks, where multiple clusters of structured gossip networks are connected to the source node through designated access nodes, i.e., cluster heads. We characterize the binary freshness in such networks and numerically study how the optimal cluster sizes change with respect to the update rates in the system.
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