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From Timestamps to Versions: Version AoI in Single- and Multi-Hop Networks

Erfan Delfani, Nikolaos Pappas

TL;DR

This work addresses the problem of timely and informative data dissemination by studying the stationary distribution of Version AoI (VAoI) under rate-constrained updates in both single-hop and multi-hop networks. It develops discrete-time Markov chain models for randomized stationary, uniform, and threshold policies, deriving closed-form stationary distributions and average VAoI, and it shows that an optimal mixed-threshold policy minimizes VAoI under rate constraints. In the multi-hop setting, VAoI at the destination is expressed as a time-shifted copy of the first node's VAoI plus a random offset, leading to a simple additive formula for the average VAoI that scales with the number of hops and link reliabilities. Numerical results validate the theory and demonstrate that the threshold policy substantially reduces VAoI and transmission rates, offering practical guidelines for energy-efficient, semantics-aware network design.

Abstract

Timely and informative data dissemination in communication networks is essential for enhancing system performance and energy efficiency, as it reduces the transmission of outdated or redundant data. Timeliness metrics, such as Age of Information (AoI), effectively quantify data freshness; however, these metrics fail to account for the intrinsic informativeness of the content itself. To address this limitation, content-based metrics have been proposed that combine both timeliness and informativeness. Nevertheless, existing studies have predominantly focused on evaluating average metric values, leaving the complete distribution-particularly in multi-hop network scenarios-largely unexplored. In this paper, we provide a comprehensive analysis of the stationary distribution of the Version Age of Information (VAoI), a content-based metric, under various scheduling policies, including randomized stationary, uniform, and threshold-based policies, with transmission constraints in single-hop and multi-hop networks. We derive closed-form expressions for the stationary distribution and average VAoI under these scheduling approaches. Furthermore, for threshold-based scheduling, we analytically determine the optimal threshold value that minimizes VAoI and derive the corresponding optimal VAoI in closed form. Numerical evaluations verify our analytical findings, providing valuable insights into leveraging VAoI in the design of efficient communication networks.

From Timestamps to Versions: Version AoI in Single- and Multi-Hop Networks

TL;DR

This work addresses the problem of timely and informative data dissemination by studying the stationary distribution of Version AoI (VAoI) under rate-constrained updates in both single-hop and multi-hop networks. It develops discrete-time Markov chain models for randomized stationary, uniform, and threshold policies, deriving closed-form stationary distributions and average VAoI, and it shows that an optimal mixed-threshold policy minimizes VAoI under rate constraints. In the multi-hop setting, VAoI at the destination is expressed as a time-shifted copy of the first node's VAoI plus a random offset, leading to a simple additive formula for the average VAoI that scales with the number of hops and link reliabilities. Numerical results validate the theory and demonstrate that the threshold policy substantially reduces VAoI and transmission rates, offering practical guidelines for energy-efficient, semantics-aware network design.

Abstract

Timely and informative data dissemination in communication networks is essential for enhancing system performance and energy efficiency, as it reduces the transmission of outdated or redundant data. Timeliness metrics, such as Age of Information (AoI), effectively quantify data freshness; however, these metrics fail to account for the intrinsic informativeness of the content itself. To address this limitation, content-based metrics have been proposed that combine both timeliness and informativeness. Nevertheless, existing studies have predominantly focused on evaluating average metric values, leaving the complete distribution-particularly in multi-hop network scenarios-largely unexplored. In this paper, we provide a comprehensive analysis of the stationary distribution of the Version Age of Information (VAoI), a content-based metric, under various scheduling policies, including randomized stationary, uniform, and threshold-based policies, with transmission constraints in single-hop and multi-hop networks. We derive closed-form expressions for the stationary distribution and average VAoI under these scheduling approaches. Furthermore, for threshold-based scheduling, we analytically determine the optimal threshold value that minimizes VAoI and derive the corresponding optimal VAoI in closed form. Numerical evaluations verify our analytical findings, providing valuable insights into leveraging VAoI in the design of efficient communication networks.

Paper Structure

This paper contains 13 sections, 10 theorems, 36 equations, 14 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Works
  3. System Model
  4. Analysis of VAoI in a Single-hop Setup
  5. VAoI of randomized stationary policy
  6. VAoI of uniform policy
  7. VAoI of threshold policy
  8. Analysis of VAoI in a Multi-hop Setup
  9. Numerical Results
  10. Single-hop Setup
  11. Multi-hop Setup
  12. Conclusion
  13. Optimal On-Off Policy for the CMDP Problem

Key Result

Proposition 1

The steady-state probability of VAoI being in state $n$ under a randomized stationary policy with transmission probability $\alpha$ is given by: where $\beta=1-(1-\alpha p_s)(1-p_g)$.

Figures (14)

  • Figure 1: Single-hop status update system.
  • Figure 2: Multi-hop communication via LEO satellites.
  • Figure 3: Multi-hop communication in the presence of physical obstructions.
  • Figure 4: Evolution of VAoI compared to AoI over time.
  • Figure 5: Evolution of VAoI within the network over time.
  • ...and 9 more figures

Theorems & Definitions (27)

  • Proposition 1
  • proof
  • Lemma 1
  • proof
  • Proposition 2
  • proof
  • Proposition 3
  • proof
  • Lemma 2
  • proof
  • ...and 17 more