When making decisions in a network, it is important to have up-to-date knowledge of the current state of the system. Obtaining this information, however, comes at a cost. In this paper, we determine the optimal finite-time update policy for monitoring the binary states of remote sources with a reporting rate constraint. We first prove an upper and lower bound of the minimal probability of error before solving the problem analytically. The error probability is defined as the probability that the system performs differently than it would with full system knowledge. More specifically, an error occurs when the destination node incorrectly determines which top-K priority sources are in the ``free'' state. We find that the optimal policy follows a specific ordered 3-stage update pattern. We then provide the optimal transition points for each stage for each source.

翻译：在网络决策中，实时掌握系统当前状态至关重要，但获取此类信息需要付出代价。本文针对具有报告速率约束的远程信源二元状态监测问题，确定了有限时间内的最优更新策略。我们首先证明了最小错误概率的上下界，进而对该问题进行了解析求解。其中，错误概率定义为系统表现与完全掌握系统信息时表现不一致的概率，具体而言，当目的节点错误判定前K个最高优先级信源处于"空闲"状态时即发生错误。研究发现，最优更新策略遵循特定的三阶段有序更新模式，并给出了每个信源在各阶段的最优转换点。