Timely Monitoring of Markov Chains Under Sampling Rate Constraints

We study a pull-based monitoring system in which a common remote monitor queries the states of a collection of heterogeneous finite-state irreducible continuous time Markov chain (CTMC) based information sources, according to a Poisson process with different per-source sampling rates, in order to maintain remote estimates of the states. 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 each source, as a function of the sampling rate. Using these expressions, optimum sampling rates for all sources are obtained using water-filling based optimization for maximizing the weighted sum freshness of the monitoring system, under an overall sampling rate constraint. Numerical examples are presented to validate the effectiveness of the proposed method by comparing it to several baseline sampling policies.