Index-based Update Policy for Minimizing Information Mismatch with Markovian Sources

We consider a scenario where a base station collects time-varying state information from multiple sources, and makes system decisions based on the collected information. When the information update is constrained to one source at a time, the state information at the base station can be stale and different from actual state of the sources, in which case the base station can make a false decision due to the information mismatch (or error). In this paper, we assume that the update decisions are made at the base station without current state information, and consider the problem of minimizing the information mismatch under limited communication capability. For two-state Markovian source, we consider two different types of estimators at the base station, and characterize the optimal update policy. For the symmetric case, we can obtain the closed-form average cost. Further, with multiple symmetric sources, we show that the problem is indexable and obtain the close-form Whittle’s index for the two different types of estimator.