This paper studies efficient data management and timely information dissemination for real-time monitoring of an $N$-state Markov process, enabling accurate state estimation and reliable actuation decisions. First, we analyze the Age of Incorrect Information (AoII) and derive closed-form expressions for its time average under several scheduling policies, including randomized stationary, change-aware randomized stationary, semantics-aware randomized stationary, and threshold-aware randomized stationary policies. We then formulate and solve constrained optimization problems to minimize the average AoII under a time-averaged sampling action constraint, and compare the resulting optimal sampling and transmission policies to identify the conditions under which each policy is most effective. We further show that directly using reconstructed states for actuation can degrade system performance, especially when the receiver is uncertain about the state estimate or when actuation is costly. To address this issue, we introduce a cost function, termed the Cost of Actions under Uncertainty (CoAU), which determines when the actuator should take correct actions and avoid incorrect ones when the receiver is uncertain about the reconstructed source state. We propose a randomized actuation policy and derive a closed-form expression for the probability of taking no incorrect action. Finally, we formulate an optimization problem to find the optimal randomized actuation policy that maximizes this probability. The results show that the resulting policy substantially reduces incorrect actuator actions.

翻译：本文研究面向N状态马尔可夫过程实时监测的高效数据管理与及时信息传播，以实现精确的状态估计与可靠的驱动决策。首先，我们分析错误信息年龄（AoII），并推导出它在多种调度策略下时间平均值的闭式表达式，这些策略包括随机平稳策略、变化感知随机平稳策略、语义感知随机平稳策略以及阈值感知随机平稳策略。随后，我们构建并求解在时间平均采样动作约束下以最小化平均AoII为目标的约束优化问题，通过比较所得的最优采样与传输策略，明确每种策略效能最优的条件。进一步研究表明，直接利用重构状态进行驱动会降低系统性能，尤其在接收器对状态估计不确定或驱动成本高昂时。针对此问题，我们引入一种名为“不确定性下的动作成本（CoAU）”的成本函数，该函数确定当接收器对重构源状态存在不确定性时，执行器应如何采取正确动作并避免错误动作。我们提出一种随机驱动策略，并推导出不执行任何错误动作概率的闭式表达式。最后，构建优化问题以求解最大化该概率的最优随机驱动策略。结果表明，所得策略能显著减少错误驱动动作。