We study a remote monitoring system in which a mutually independent and heterogeneous collection of finite-state irreducible continuous time Markov chain (CTMC) based information sources is considered. In this system, a common remote monitor queries the instantaneous states of the individual CTMCs according to a Poisson process with possibly different intensities across the sources, in order to maintain accurate estimates of the original sources. \color{black}Three information freshness models are considered to quantify the accuracy of the remote estimates: fresh when equal (FWE), fresh when sampled (FWS) and fresh when close (FWC). For each of these freshness models, closed-form expressions are derived for mean information freshness for a given source. Using these expressions, optimum sampling rates for all sources are obtained so as to maximize the weighted sum freshness of the monitoring system, subject to an overall sampling rate constraint. This optimization problem leads to a water-filling solution with quadratic worst case computational complexity in the number of information sources. Numerical examples are provided to validate the effectiveness of the optimum sampling policy in comparison to several baseline sampling policies.

翻译：我们研究一个远程监控系统，其中考虑了一组相互独立且异构的、基于有限状态不可约连续时间马尔可夫链的信息源。在该系统中，一个公共远程监视器根据泊松过程查询各个CTMC的瞬时状态（不同信源可能具有不同的查询强度），以维持对原始信源的准确估计。我们考虑了三种信息新鲜度模型来量化远程估计的准确性：相等时新鲜、采样时新鲜和接近时新鲜。针对每种新鲜度模型，我们推导了给定信源的平均信息新鲜度的闭式表达式。利用这些表达式，我们获得了所有信源的最优采样率，以在总体采样率约束下最大化监控系统的加权总新鲜度。该优化问题导出了一个注水式解决方案，其最坏情况计算复杂度在信息源数量上呈二次方增长。我们提供了数值算例，以验证最优采样策略相较于若干基线采样策略的有效性。