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Age of Information for Constrained Scheduling with Imperfect Feedback

Yuqing Zhu, Yuan-Hsun Lo, Yan Lin, Yijin Zhang

TL;DR

The paper addresses AoI minimization in downlink scheduling with multiple sources and users under imperfect feedback and constrained transmission rates. It develops a zero-feedback lower bound for GAW traffic and an offline rate-splitting policy to attain it, plus a drift-plus-penalty (DPP) policy for Bernoulli zero-feedback with a threshold structure and performance guarantees. The DPP framework is extended to general imperfect feedback using Bayes-based AoI estimation without increasing online complexity, enabling practical deployment. Numerical results validate the theoretical findings, showing significant AoI gains over state-of-the-art policies, and highlighting the benefits of robust feedback mechanisms and rate constraints in AoI-optimized networks.

Abstract

This paper considers a downlink system where an access point sends the monitored status of multiple sources to multiple users. By jointly accounting for imperfect feedback and constrained transmission rate, which are key limited factors in practical systems, we aim to design scheduling algorithms to optimize the age of information (AoI) over the infinite time horizon. For zero feedback under the generate-at-will traffic, we derive a closed-form lower bound of achievable AoI, which, to the best of our knowledge, reflects the impact of zero feedback for the first time, and propose a policy that achieves this bound in many cases by jointly applying rate splitting and modular arithmetic. For zero feedback under the Bernoulli traffic, we develop a drift-plus-penalty (DPP) policy with a threshold structure based on the theory of Lyapunov optimization and provide a closed-form performance guarantee. Furthermore, we extend the design of this DPP policy to support general imperfect feedback without increasing the online computational complexity. Numerical results verify our theoretical analysis and the AoI advantage of the proposed policies over state-of-the-art policies.

Age of Information for Constrained Scheduling with Imperfect Feedback

TL;DR

The paper addresses AoI minimization in downlink scheduling with multiple sources and users under imperfect feedback and constrained transmission rates. It develops a zero-feedback lower bound for GAW traffic and an offline rate-splitting policy to attain it, plus a drift-plus-penalty (DPP) policy for Bernoulli zero-feedback with a threshold structure and performance guarantees. The DPP framework is extended to general imperfect feedback using Bayes-based AoI estimation without increasing online complexity, enabling practical deployment. Numerical results validate the theoretical findings, showing significant AoI gains over state-of-the-art policies, and highlighting the benefits of robust feedback mechanisms and rate constraints in AoI-optimized networks.

Abstract

This paper considers a downlink system where an access point sends the monitored status of multiple sources to multiple users. By jointly accounting for imperfect feedback and constrained transmission rate, which are key limited factors in practical systems, we aim to design scheduling algorithms to optimize the age of information (AoI) over the infinite time horizon. For zero feedback under the generate-at-will traffic, we derive a closed-form lower bound of achievable AoI, which, to the best of our knowledge, reflects the impact of zero feedback for the first time, and propose a policy that achieves this bound in many cases by jointly applying rate splitting and modular arithmetic. For zero feedback under the Bernoulli traffic, we develop a drift-plus-penalty (DPP) policy with a threshold structure based on the theory of Lyapunov optimization and provide a closed-form performance guarantee. Furthermore, we extend the design of this DPP policy to support general imperfect feedback without increasing the online computational complexity. Numerical results verify our theoretical analysis and the AoI advantage of the proposed policies over state-of-the-art policies.

Paper Structure

This paper contains 32 sections, 7 theorems, 69 equations, 6 figures, 3 tables.

Table of Contents

  1. Introduction
  2. System Model
  3. Network description
  4. Problem Formulation
  5. Zero-Feedback Scenarios: GAW Traffic
  6. Lower Bound
  7. Optimal Policy for Many Cases
  8. Zero-Feedback Scenarios: Bernoulli Traffic
  9. Hybrid Lyapunov Function
  10. DPP Function
  11. Queue Stability
  12. Performance Guarantee
  13. Policy Structure
  14. Extension to Imperfect-Feedback Scenarios
  15. ACKs Mechanism
  16. ...and 17 more sections

Key Result

Lemma 1

For each $n\in \mathcal{N}$, the minimum of ${f_n}({\hat{\bm{X}}_n})$ is

Figures (6)

  • Figure 1: Considered downlink scenario.
  • Figure 2: An example of evolution of $h_{n,t}$ for a generic point-to-point system $n$ under the GAW traffic. The symbol $\color{red}{\times}$ indicates the transmission failed, whereas $\color{blue}{\checkmark}$ indicates the transmission was successful.
  • Figure 3: An example of a splitting tree.
  • Figure 4: EWSAoI vs. priority ratio in imperfect-feedback scenarios with Bernoulli traffic for $12$ sources.
  • Figure 5: EWSAoI in imperfect-feedback scenarios with Bernoulli traffic for $12$ sources.
  • ...and 1 more figures

Theorems & Definitions (24)

  • Lemma 1
  • proof
  • Remark 1
  • Theorem 2
  • proof
  • Remark 2
  • Theorem 3
  • Remark 3
  • Remark 4
  • Lemma 4
  • ...and 14 more