Random-Access Monitoring of Markov Sources: Analytical Characterization of Uncertainty

Abstract

We study the remote monitoring of two-state Markov sources over a shared wireless channel with destructive collisions. System performance is measured in terms of state estimation entropy (SEE) and state estimation error probability (SEEP), which quantify the receiver's uncertainty and decision error regarding the source state, respectively. We consider two transmission policies: a random strategy, where nodes access the channel independently of their state, and a reactive strategy, where transmissions occur only upon state changes. Our main contribution is a simple and explicit analytical characterization of the long-term average SEE and SEEP under both policies using a renewal–reward framework, alternative to the density evolution approach introduced in [1]. For random transmission, both metrics admit closed-form representations as expectations over the geometric steady-state age-of-information distribution. For reactive transmission, we show that estimation uncertainty and error accumulate exclusively through collision events, and derive their long-term averages via a collision-indexed Markov reward recursion.