Age of incorrect information (AoII) has recently been proposed as an alternative to existing information freshness metrics for real-time sampling and estimation problems involving information sources that are tracked by remote monitors. Different from existing metrics, AoII penalizes the incorrect information by increasing linearly with time as long as the source and the monitor are de-synchronized, and is reset when they are synchronized back. While AoII has generally been investigated for discrete time information sources, we develop a novel analytical model in this paper for push- and pull-based sampling and transmission of a continuous time Markov chain (CTMC) process. In the pull-based model, the sensor starts transmitting information on the observed CTMC only when a pull request from the monitor is received. On the other hand, in the push-based scenario, the sensor, being aware of the AoII process, samples and transmits when the AoII process exceeds a random threshold. The proposed analytical model for both scenarios is based on the construction of a discrete time MC (DTMC) making state transitions at the embedded epochs of synchronization points, using the theory of absorbing CTMCs, and in particular phase-type distributions. For a given sampling policy, analytical models to obtain the mean AoII and the average sampling rate are developed. Numerical results are presented to validate the analytical model as well as to provide insight on optimal sampling policies under sampling rate constraints.

翻译：错误信息年龄（AoII）是近期提出的新型信息新鲜度度量，旨在解决涉及远程监控信息源的实时采样与估计问题。与现有度量不同，AoII对错误信息的惩罚机制表现为：当信息源与监控器状态不同步时，其值随时间线性递增；当两者恢复同步时立即重置。尽管现有研究主要针对离散时间信息源分析AoII，本文针对连续时间马尔可夫链（CTMC）过程，分别提出推送与拉取两种采样传输模式下的新型解析模型。在拉取模式下，传感器仅在接收到监控器的拉取请求后启动CTMC状态信息传输；而在推送模式下，传感器自主监测AoII过程，当其超过随机阈值时执行采样与传输。两类场景的解析模型均基于吸收CTMC理论（尤其相位型分布），通过构建在同步点嵌入时刻发生状态转移的离散时间马尔可夫链（DTMC）实现建模。针对给定采样策略，本文开发了平均AoII与平均采样率的解析计算方法。通过数值结果验证了解析模型的有效性，并揭示了采样率约束下的最优采样策略。