We investigate information accuracy in timeliness-based gossip networks where the source evolves according to a continuous-time Markov chain (CTMC) with $M$ states and disseminates status updates to a network of $n$ nodes. In addition to direct source updates, nodes exchange their locally stored packets via gossip and accept incoming packets solely based on whether the incoming packet is fresher than their local copy. As a result, a node can possess the freshest packet in the network while still not having the current source state. To quantify the amount of accurate information flowing in the network under such a gossiping scheme, we introduce two accuracy metrics, average accuracy, defined as the expected fraction of nodes carrying accurate information in any given subset, and freshness-based accuracy, defined as the accuracy of the freshest node in any given subset. Using a stochastic hybrid systems (SHS) framework, we first derive steady-state balance equations and obtain matrix-valued recursions that characterize these metrics in fully connected gossip networks under binary CTMCs. We then extend our analysis to the general multi-state information source using a joint CTMC approach. Finally, we quantify the fraction of nodes whose information is accurate due to direct source pushes versus gossip exchanges. We verify our findings with numerical analyses and provide asymptotic insights.

翻译：本文研究了基于时效性的谣言网络中的信息准确性，其中信源根据具有$M$个状态的连续时间马尔可夫链（CTMC）演化，并向一个包含$n$个节点的网络传播状态更新。除了直接接收信源更新外，节点还通过谣言交换其本地存储的数据包，并且仅当接收到的数据包比其本地副本更新时才接受。因此，一个节点可能拥有网络中最新鲜的数据包，但仍未掌握信源的当前状态。为了量化在此类谣言传播方案下网络中流动的准确信息量，我们引入了两个准确性度量：平均准确性（定义为任意给定子集中携带准确信息的节点比例的期望值）和基于新鲜度的准确性（定义为任意给定子集中最新鲜节点的准确性）。利用随机混合系统（SHS）框架，我们首先推导出稳态平衡方程，并获得了在完全连接的谣言网络中针对二元CTMC表征这些度量的矩阵值递归关系。随后，我们通过联合CTMC方法将分析扩展到一般的多状态信源。最后，我们量化了因信源直接推送与谣言交换而获得准确信息的节点比例。我们通过数值分析验证了研究结果，并提供了渐近性见解。