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Age of information cost minimization with no buffers, random arrivals and unreliable channels: A PCL-indexability analysis

José Niño-Mora

TL;DR

This paper addresses AoI cost minimization in a no-buffer, single-hop network with random packet arrivals and unreliable channels, formulated as a restless RMABP. It employs the PCL-indexability framework to prove indexability for both discounted and average cost criteria and derives closed-form Whittle index formulas, enabling threshold-based, low-complexity scheduling policies. The authors provide explicit index expressions for linear, quadratic, and threshold AoI costs and analyze how priority under Whittle's policy depends on arrival and success probabilities, offering practical insights for policy design. The work advances the applicability of Whittle index policies to broader AoI settings and suggests directions for extending the approach to more complex models, including buffers and online parameter estimation.

Abstract

Over the last decade, the Age of Information has emerged as a key concept and metric for applications where the freshness of sensor-provided data is critical. Limited transmission capacity has motivated research on the design of tractable policies for scheduling information updates to minimize Age of Information cost based on Markov decision models, in particular on the restless multi-armed bandit problem (RMABP). This allows the use of Whittle's popular index policy, which is often nearly optimal, provided indexability (index existence) is proven, which has been recently accomplished in some models. We aim to extend the application scope of Whittle's index policy in a broader AoI scheduling model. We address a model with no buffers incorporating random packet arrivals, unreliable channels, and nondecreasing AoI costs. We use sufficient indexability conditions based on partial conservation laws previously introduced by the author to establish the model's indexability and evaluate its Whittle index in closed form under discounted and average cost criteria. We further use the index formulae to draw insights on how scheduling priority depends on model parameters.

Age of information cost minimization with no buffers, random arrivals and unreliable channels: A PCL-indexability analysis

TL;DR

This paper addresses AoI cost minimization in a no-buffer, single-hop network with random packet arrivals and unreliable channels, formulated as a restless RMABP. It employs the PCL-indexability framework to prove indexability for both discounted and average cost criteria and derives closed-form Whittle index formulas, enabling threshold-based, low-complexity scheduling policies. The authors provide explicit index expressions for linear, quadratic, and threshold AoI costs and analyze how priority under Whittle's policy depends on arrival and success probabilities, offering practical insights for policy design. The work advances the applicability of Whittle index policies to broader AoI settings and suggests directions for extending the approach to more complex models, including buffers and online parameter estimation.

Abstract

Over the last decade, the Age of Information has emerged as a key concept and metric for applications where the freshness of sensor-provided data is critical. Limited transmission capacity has motivated research on the design of tractable policies for scheduling information updates to minimize Age of Information cost based on Markov decision models, in particular on the restless multi-armed bandit problem (RMABP). This allows the use of Whittle's popular index policy, which is often nearly optimal, provided indexability (index existence) is proven, which has been recently accomplished in some models. We aim to extend the application scope of Whittle's index policy in a broader AoI scheduling model. We address a model with no buffers incorporating random packet arrivals, unreliable channels, and nondecreasing AoI costs. We use sufficient indexability conditions based on partial conservation laws previously introduced by the author to establish the model's indexability and evaluate its Whittle index in closed form under discounted and average cost criteria. We further use the index formulae to draw insights on how scheduling priority depends on model parameters.
Paper Structure (25 sections, 21 theorems, 110 equations, 11 figures, 1 table)

This paper contains 25 sections, 21 theorems, 110 equations, 11 figures, 1 table.

Table of Contents

  1. Introduction
  2. AoI Minimization via Transmission Scheduling and Restless Bandit Framework
  3. Related Prior Work: AoI Cost Minimization via Whittle's Index Policy
  4. Contributions over Prior Work
  5. Structure of the Paper
  6. System Model and RMABP Formulation
  7. Indexability and Whittle Index
  8. PCL-Indexability Analysis: Discounted Cost Criterion
  9. A Verification Theorem for Threshold-Indexability
  10. Work Metric Analysis and Condition $($PCLI1$)$
  11. Cost Metric Analysis
  12. MP Index Analysis and Condition $($PCLI2$)$
  13. PCL-Indexability Analysis: Average Cost Criterion
  14. Work Metric Analysis and Condition $($PCLI1$)$
  15. Cost Metric Analysis
  16. ...and 10 more sections

Key Result

Proposition 1

Suppose that $\pi^* \in \Pi(N)$ solves (eq:lr) with $\nu^* \geqslant 0$, and that they satisfy CS. Then,

Figures (11)

  • Figure 1: System snapshot showing underutilization of channels.
  • Figure 2: System snapshot where a generated packet will be lost.
  • Figure 3: Discounted (a) and average (b) criterion Whittle index vs. AoI $i$ for linear AoI cost.
  • Figure 4: Discounted (a) and average (b) criterion Whittle index vs. $\lambda$ for linear AoI cost.
  • Figure 5: Discounted (a) and average (b) criterion Whittle indices vs. $\mu$ for linear AoI cost.
  • ...and 6 more figures

Theorems & Definitions (44)

  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Theorem 1
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • ...and 34 more