Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Version Innovation Age and Age of Incorrect Version for Monitoring Markovian Sources

Mehrdad Salimnejad, Marios Kountouris, Anthony Ephremides, Nikolaos Pappas

TL;DR

This work introduces Version Innovation Age (VIA) and Age of Incorrect Version (AoIV) as semantics-aware metrics for real-time monitoring of a two-state Markov source over unreliable channels. It develops DTMC-based analytical expressions for VIA, AoIV, and AoII under change-aware, semantics-aware, and randomized stationary sampling policies, and formulates a constrained optimization to minimize VIA subject to sampling-cost and reconstruction-error constraints. The authors compare policies and identify regimes where randomized stationary, change-aware, or semantics-aware policies perform best, highlighting the balance between timeliness, content significance, and resource constraints. The results enable design guidelines for version-aware monitoring in industrial and autonomous systems.

Abstract

In this paper, we propose two new performance metrics, coined the Version Innovation Age (VIA) and the Age of Incorrect Version (AoIV) for real-time monitoring of a two-state Markov process over an unreliable channel. We analyze their performance under the change-aware, semantics-aware, and randomized stationary sampling and transmission policies. We derive closed-form expressions for the distribution and the average of VIA, AoIV, and AoII for these policies. We then formulate and solve an optimization problem to minimize the average VIA, subject to constraints on the time-averaged sampling cost and time-averaged reconstruction error. Finally, we compare the performance of various sampling and transmission policies and identify the conditions under which each policy outperforms the others in optimizing the proposed metrics.

Version Innovation Age and Age of Incorrect Version for Monitoring Markovian Sources

TL;DR

This work introduces Version Innovation Age (VIA) and Age of Incorrect Version (AoIV) as semantics-aware metrics for real-time monitoring of a two-state Markov source over unreliable channels. It develops DTMC-based analytical expressions for VIA, AoIV, and AoII under change-aware, semantics-aware, and randomized stationary sampling policies, and formulates a constrained optimization to minimize VIA subject to sampling-cost and reconstruction-error constraints. The authors compare policies and identify regimes where randomized stationary, change-aware, or semantics-aware policies perform best, highlighting the balance between timeliness, content significance, and resource constraints. The results enable design guidelines for version-aware monitoring in industrial and autonomous systems.

Abstract

In this paper, we propose two new performance metrics, coined the Version Innovation Age (VIA) and the Age of Incorrect Version (AoIV) for real-time monitoring of a two-state Markov process over an unreliable channel. We analyze their performance under the change-aware, semantics-aware, and randomized stationary sampling and transmission policies. We derive closed-form expressions for the distribution and the average of VIA, AoIV, and AoII for these policies. We then formulate and solve an optimization problem to minimize the average VIA, subject to constraints on the time-averaged sampling cost and time-averaged reconstruction error. Finally, we compare the performance of various sampling and transmission policies and identify the conditions under which each policy outperforms the others in optimizing the proposed metrics.
Paper Structure (13 sections, 4 theorems, 44 equations, 9 figures)

This paper contains 13 sections, 4 theorems, 44 equations, 9 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Performance Metrics
  4. Version Innovation Age (VIA)
  5. Age of Incorrect Version (AoIV)
  6. Age of Incorrect Information
  7. Optimization Problem
  8. Numerical Results
  9. Conclusion
  10. Proof of Lemma \ref{['Lemma_Pij']}
  11. Proof of Lemma \ref{['theorem_VAoI']}
  12. Proof of Lemma \ref{['piijk_VAoII_RS']}
  13. Proof of Lemma \ref{['AoIIDistribution_RS']}

Key Result

Lemma 1

For the randomized stationary policy, the transition probability $P_{i,j}, \forall i,j\in \{0,1,\cdots\}$ is given by Note that $\pi_{0,i}$ and $\pi_{1,i}$ in Lemma Lemma_Pij are the probabilities obtained from the stationary distribution of the two-dimensional DTMC describing the joint status of the original source regarding the current state of the VIA, i.e., $(X(t), {\text{VIA}}(t))$.

Figures (9)

  • Figure 1: Real-time monitoring of a Markovian source over a wireless channel.
  • Figure 2: DTMC describing the evolution of the VIA.
  • Figure 3: Minimum average VIA in a constrained optimization problem as a function of $p$ and $q$.
  • Figure 4: Minimum average VIA in an unconstrained optimization problem as a function of $p$ and $q$.
  • Figure 5: Average AoIV as a function of $p$ and $q$.
  • ...and 4 more figures

Theorems & Definitions (7)

  • Lemma 1
  • Lemma 2
  • Remark 1
  • Remark 2
  • Lemma 3
  • Lemma 4
  • Remark 3