Dual-Regime Absorbing Markov Chain Theory in Remote Estimation: Age-Minimizing Push Policies
2026-06-30 • Information Theory
Information TheoryNetworking and Internet Architecture
AI summaryⓘ
The authors study how to keep information fresh and accurate in systems where updates about a changing source are sent to a remote monitor. They focus on a metric called Age of Incorrect Information (AoII), which measures how outdated the monitor's estimate is. To reduce AoII and transmission energy, they develop a strategy where updates are sent only when AoII crosses certain thresholds. Their approach uses advanced mathematical models called semi-Markov decision processes and a new tool called dual-regime absorbing Markov chain to find the best update policy. They tested their method through simulations and showed it performs well compared to other strategies.
Age of Incorrect Information (AoII)Markov ChainDiscrete-Time Phase-Type DistributionSemi-Markov Decision Process (SMDP)Remote EstimationDual-Regime Absorbing Markov Chain (DR-AMC)Threshold PolicyEnergy ConsumptionStochastic Modeling
Authors
Ismail Cosandal, Sennur Ulukus, Nail Akar
Abstract
For a remote estimation system, we study the optimization of age of incorrect information (AoII), which is a recently proposed semantic-aware information freshness metric. In particular, we assume an information source that observes a discrete-time finite-state Markov chain (DTMC), and occasionally transmits status update packets to a remote monitor which is tasked with remote estimation of the source. For the forward channel from the source to the monitor, we assume the channel delay to be modeled by a general discrete-time phase-type (DPH) distribution, whereas the reverse channel from the monitor to the source is assumed to be perfect, ensuring that the source has perfect information on the AoII and the remote estimate at the monitor, at all times. Push-based transmissions are initiated when AoII exceeds a threshold depending on the current estimation value, i.e., multi-threshold policy. In this very general setting, our goal is to minimize a weighted sum of the time average of a polynomial function of AoII, depending on the remote estimate, and energy consumption from transmissions. We formulate the problem as a semi-Markov decision process (SMDP) with the same state-space of the original DTMC to obtain the optimal multi-threshold policy, whereas the parameters of the SMDP are obtained by using a novel stochastic tool called dual-regime absorbing Markov chain (DR-AMC), and its corresponding absorption time distribution named as dual-regime DPH (DR-DPH). The proposed method is validated with numerical examples using comparisons against other policies obtained by exhaustive search, and also various benchmark policies.