In this work, we study the real-time tracking and reconstruction of an information source with the purpose of actuation. A device monitors the state of the information source and transmits status updates to a receiver over a wireless erasure channel. We consider two models for the source, namely an $N$-state Markov chain and an $N$-state Birth-Death Markov process. We investigate several joint sampling and transmission policies, including a semantics-aware one, and we study their performance with respect to a set of metrics. Specifically, we investigate the real-time reconstruction error and its variance, the cost of actuation error, the consecutive error, and the cost of memory error. These metrics capture different characteristics of the system performance, such as the impact of erroneous actions and the timing of errors. In addition, we propose a randomized stationary sampling and transmission policy and we derive closed-form expressions for the aforementioned metrics. We then formulate two optimization problems. The first optimization problem aims to minimize the time-averaged reconstruction error subject to time-averaged sampling cost constraint. Then, we compare the optimal randomized stationary policy with uniform, change-aware, and semantics-aware sampling policies. Our results show that in the scenario of constrained sampling generation, the optimal randomized stationary policy outperforms all other sampling policies when the source is rapidly evolving. Otherwise, the semantics-aware policy performs the best. The objective of the second optimization problem is to obtain an optimal sampling policy that minimizes the average consecutive error with a constraint on the time-averaged sampling cost. Based on this, we propose a \emph{wait-then-generate} sampling policy which is simple to implement.

翻译：本文研究以驱动为目的的信息源实时跟踪与重构问题。设备监测信息源状态，并通过无线擦除信道向接收器发送状态更新。我们考虑了两种源模型，即N状态马尔可夫链和N状态生灭马尔可夫过程。我们研究了多种联合采样与传输策略（包括一种语义感知策略），并根据一组指标评估其性能。具体而言，我们考察了实时重构误差及其方差、驱动误差成本、连续误差以及记忆误差成本。这些指标反映了系统性能的不同特征，例如错误操作的影响及错误发生的时间分布。此外，我们提出了一种随机平稳采样与传输策略，并推导了上述指标的闭式表达式。随后我们构建了两个优化问题。第一个优化问题旨在最小化时间平均重构误差，同时满足时间平均采样成本约束。然后，我们将最优随机平稳策略与均匀采样策略、变化感知采样策略及语义感知采样策略进行比较。结果表明，在采样生成受限场景下，当信源快速演化时，最优随机平稳策略优于所有其他采样策略；反之，语义感知策略表现最佳。第二个优化问题的目标是获得一个最优采样策略，以在时间平均采样成本约束下最小化平均连续误差。基于此，我们提出了一种易于实现的"等待-生成"采样策略。