Fair and Efficient Scheduling for Sensor Networks via Online Whittle Index Policy

Abstract: Wake-Up Radio (WUR) enables resource-constrained, battery-powered sensor nodes to remain in a low-power deep sleep state while continuously listening for a Wake-Up Signal (WUS). Sensor nodes only wake and transmit data after receiving the WUS, significantly reducing energy consumption. However, polling nodes whose transmitted data provides little or no meaningful update to the remote monitor can still result in unnecessary energy usage and increased storage overhead. To address this issue, this paper uses the Age of Incorrect Information (AoII) metric to prioritise the polling of nodes that provide informative updates to the remote monitor. Determining the optimal set of nodes to poll based on AoII can be formulated as a Restless Multi-Armed Bandit (RMAB) problem, which traditionally requires prior knowledge of the monitored process transition dynamics. Since such dynamics are often unknown in practical deployments, we propose an online learning framework based on state estimation to derive Whittle Index AoII (WAoII) and Fair Whittle Index AoII (FWAoII) policies without assuming known transition probabilities. The proposed policies efficiently schedule node polling while adapting to unknown process behaviour. Experimental evaluation using both real-world and synthetic datasets demonstrates that the proposed online WAoII policy can reduce packet transmissions by up to 70\% compared to the widely used Round Robin (RR) polling strategy, while maintaining Root Mean Squared Error (RMSE) values within acceptable application error tolerances. These results demonstrate the effectiveness of WAoII and FWAoII as energy-efficient polling techniques for low-power WUR sensor networks.

• The paper demonstrates that online Whittle index methods can minimize the Age of Incorrect Information (AoII) without requiring explicit transition models.
• It introduces fairness constraints and adaptive penalty tuning to balance polling and energy efficiency, reducing packet transmissions by up to 70%.
• Experimental results on synthetic and real-world sensor data show network lifetime improvements of 1.8–2.5× compared to traditional and RL-based scheduling.

Fair and Efficient Scheduling in Sensor Networks Using Online Whittle Index Policy

Introduction and Problem Statement

This work addresses the fundamental trade-off between information freshness and energy efficiency in Wireless Sensor Networks (WSNs), with a focus on systems equipped with Wake-Up Radio (WUR) modules. Standard approaches (e.g., Round Robin (RR) scheduling) often result in redundant transmissions and do not account for the value or relevance of the transmitted information. To mitigate this, the paper leverages the Age of Incorrect Information (AoII) as a prioritization metric and formulates the scheduling problem as a Restless Multi-Armed Bandit (RMAB), aiming to select which of the $N$ sensor nodes to poll (subject to a channel constraint $M < N$) so as to minimize the expected long-term AoII.

The principal challenge is that transition dynamics—needed for classical Whittle index policies—are typically unknown or non-stationary in practical settings. The paper circumvents this by introducing online learning-based index policies (WAoII and Fair WAoII, termed FWAoII) using only state estimations at the sink, and further enforces fairness constraints to ensure unbiased data collection.

Methodological Contributions

The key methodological advances are as follows:

1. Online Whittle Index Policy for AoII The authors prove that AoII-based RMAB scheduling is indexable, enabling threshold-based Whittle index solutions. By using real-time state estimation (via edge mining, specifically the L-SIP protocol), the sink can maintain estimates of each sensor’s state (value and rate of change) without knowledge of explicit transition dynamics, and directly apply the Whittle index policy.
2. Fairness-Enhanced Scheduling Prior approaches can result in certain nodes being perpetually starved due to persistent low index values. By enforcing a fairness window, FWAoII mandates that every node is scheduled at least once every $n$ rounds, ensuring timely updates from all sensors while minimizing suboptimality.
3. Real-Time Adaptive Penalty Tuning Since the optimal penalty threshold for index policies is rarely known a priori, the paper introduces an online adaptive algorithm that dynamically updates the scheduling penalty, maintaining optimality in terms of energy-efficiency/information freshness trade-off.

Theoretical Analysis

• Indexability The paper provides formal proof of the indexability of the AoII scheduling problem, a nontrivial extension due to the continuous and data-driven evolution of AoII. Given the explicit update rules, the authors show that increasing the penalty $\lambda$ monotonically enlarges the passive set, ensuring the applicability of Whittle index solutions.
• Optimality Bounds Incorporation of fairness constraints introduces a controlled, theoretically bounded loss of optimality, depending on the window parameter $n$ and the real-time distribution of index values.
• Computational Complexity Unlike RL or Q-learning variants for RMAB, the WAoII and FWAoII policies scale as $O(N\log N)$, suitable for dense sensor deployments, and do not require explicit model training or hyperparameter tuning.

Experimental Results

Synthetic Data Evaluation

Comprehensive scenarios with multi-category sensor deployments (ranging from slow to highly dynamic processes) confirm:

• Significant transmission reduction: WAoII reduces packet transmissions by up to 70% relative to RR, with FWAoII achieving comparable reductions while enforcing fairness.
• Estimation fidelity: Despite aggressive down-sampling, reconstruction errors (RMSE) remain within acceptable bounds of the original process, even under abrupt changes in process dynamics.
• Adaptive behavior: Both WAoII and FWAoII rapidly adapt to non-stationarity. FWAoII is more robust to abrupt reversals and node failures due to periodic polling guarantees.

Real-World Sensor Data

Experiments with the Intel Berkeley research lab dataset (54-node, multimodal) yield:

• Network lifetime improvement: Under typical energy models, WAoII/FWAoII increase network lifetime by factors of 1.8–2.5× compared to RR and AoI-based policies.
• Polling distribution: RR and AoI sampling remain uniform, while WAoII and FWAoII concentrate efforts on high-value, rapidly-varying nodes.
• Comparison to RL-based scheduling: WAoII matches or slightly outperforms Whittle-Index Q-Learning (WIQL) methods for AoII minimization but at lower computational cost and without online exploration phases.

Fairness/Energy Trade-off

As the fairness window narrows (lower $n$), more equitable polling is achieved at a modest increase in transmissions and RMSE—highlighting a controllable trade-off space between strict optimality and unbiased information acquisition.

Implications and Future Directions

The WAoII/FWAoII approach decouples the scheduling policy from a priori knowledge of process models, enabling deployment in heterogeneous, highly dynamic IoT environments with non-stationary behaviors. While the technique is demonstrated on WUR-based networks, the underlying methodology is applicable across a broad spectrum of resource-constrained polling applications.

Potential extensions include:

• Explicit handling of strongly nonlinear system dynamics via advanced state estimation and local linearization techniques.
• Integration with uncertainty-aware filtering (e.g., particle filtering) to improve robustness in highly noisy environments.
• Full-stack implementation and evaluation in operational sensor platforms—quantifying wall-time energy savings and latency metrics under true protocol stacks.

Conclusion

This paper establishes that effective, adaptive, and fair scheduling for energy-harvesting or battery-powered sensor networks can be achieved without model knowledge, by leveraging online Whittle index policies on AoII. The technique yields substantial gains in information relevance, energy efficiency, and network longevity, with computational complexity amenable to embedded deployment. The introduction of fairness constraints directly addresses key practical concerns in real-world WSNs and IoT deployments, supporting their use in critical infrastructure and industrial contexts. The methods proposed herein offer a principled foundation for future goal-oriented and semantics-aware networked sensing paradigms (2605.08674).