Nail Akar, Sennur Ulukus

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 remote monitor samples the states of the individual CTMCs according to a Poisson process with possibly different per-source sampling rates, in order to maintain remote estimates of the states of each of the sources. 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 under an overall sampling rate constraint. This optimization problem possesses 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 sampler in comparison to several baseline sampling policies.