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We study a remote monitoring system in which a collection of ergodic,aperiodic, mutually independent, and heterogeneous continuous time Markov chain(CTMC) based information sources is considered. In this system, a common remotemonitor samples the states of the individual CTMCs according to a Poissonprocess with possibly different per-source sampling rates, in order to maintainremote estimates of the states of each of the sources. Three informationfreshness models are considered to quantify the accuracy of the remoteestimates: fresh when equal (FWE), fresh when sampled (FWS) and fresh whenclose (FWC). For each of these freshness models, closed-form expressions arederived for mean information freshness for a given source. Using theseexpressions, optimum sampling rates for all sources are obtained so as tomaximize the weighted sum freshness of the monitoring system under an overallsampling rate constraint. This optimization problem possesses a water-fillingsolution with quadratic worst case computational complexity in the number ofinformation sources. Numerical examples are provided to validate theeffectiveness of the optimum sampler in comparison to several baseline samplingpolicies.

Optimum Monitoring of Heterogeneous Continuous Time Markov Chains