  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.
