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arxiv: 2510.23820 · v2 · pith:BPFSCEHNnew · submitted 2025-10-27 · 📡 eess.SY · cs.SY

MDP-based Energy-aware Task Scheduling for Battery-less IoT

Shahab Jahanbazi , Mateen Ashraf , Onel L. A. L\'opez This is my paper

Pith reviewed 2026-05-21 20:07 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords battery-less IoTenergy harvestingMarkov decision processtask schedulingthreshold policyunichain MDP
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The pith

An MDP for battery-less IoT scheduling is unichain with an optimal threshold policy that yields a simple OSTB scheduler.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper casts periodic task scheduling for battery-less IoT devices as a long-term average-reward Markov decision process that tracks capacitor voltage, task ordering, and safe execution windows under i.i.d. energy arrivals. It proves the MDP is unichain and that its optimal stationary policy has a threshold structure, which directly produces an implementable optimal stationary threshold-based scheduler. Rewards are designed to favor reliable full-chain completion while penalizing low-energy risks. The same framework applies to a finite-state Markov correlated harvesting model under conservative conditions. Numerical comparisons show the resulting scheduler raises full-chain completion rates and cuts power failures and latency relative to representative baselines, especially when energy is scarce.

Core claim

The considered MDP is unichain and the optimal stationary policy has a threshold structure, which leads to an optimal stationary threshold-based (OSTB) scheduler.

What carries the argument

The unichain property of the MDP together with the threshold structure of its optimal stationary policy, which reduces the scheduler to simple voltage-based decisions.

If this is right

  • The OSTB scheduler achieves higher long-term rates of completing the full sensing-computing-transmitting chain.
  • Power failures and task latency decrease compared with non-threshold policies when harvested energy is limited.
  • The MDP framework extends to correlated energy harvesting under stated conservative sufficient conditions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The threshold rule could be hardcoded on microcontrollers, avoiding repeated MDP solves at runtime.
  • Analogous threshold proofs may simplify scheduling in other energy-harvesting systems with timing deadlines.
  • Hardware tests with measured solar or RF traces would check whether the i.i.d. model captures essential behavior.

Load-bearing premise

Energy arrivals are independent and identically distributed.

What would settle it

A computed optimal policy from value iteration on the MDP that fails to switch actions at a single threshold per state under i.i.d. arrivals would disprove the structural result.

Figures

Figures reproduced from arXiv: 2510.23820 by Mateen Ashraf, Onel L. A. L\'opez, Shahab Jahanbazi.

Figure 1
Figure 1. Figure 1: System model: a battery-less IoT device powered by am [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: An illustrative representation of the scheme descri [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Reward values from (13) and (14) with β = 15 and θ ∈ 0.7, 0.9, 0.95 as functions of voltage for states in S1 with action sensing (top) and states in S2 with action transmitting (bottom), with C = 2.7mF, Vout = 2.4V, and ih has an i.i.d. uniform distribution as U[0, 3]mA. A. Objective Function The objective is to develop a scheduling policy that ef￾fectively utilizes the available energy to maximize the tas… view at source ↗
Figure 4
Figure 4. Figure 4: The average expected reward defined in equation (15) v [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Average number of completed tasks per time unit for th [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
read the original abstract

Battery-less Internet of Things (IoT) devices rely on ambient energy harvesting and therefore require scheduling policies that jointly account for energy intermittency and hard timing constraints. This challenge is especially acute in periodic monitoring applications, where a sensing--computing--transmitting task chain must be completed within each reporting cycle. In this paper, we formulate this problem within a setting characterized by independently and identically distributed (i.i.d.) energy arrivals as a long-term average-reward Markov decision process (MDP) that explicitly captures capacitor-voltage evolution, task ordering, permissible start windows, and safe-execution requirements. We further propose rewards that promote reliable task completion while penalizing risky low-energy execution. We prove that the considered MDP is unichain and that the optimal stationary policy has a threshold structure, which leads to an optimal stationary threshold-based (OSTB) scheduler. To account for more realistic energy sources, we additionally study a correlated harvesting model based on a finite-state Markov process and show that the proposed framework can be applied to this richer setting under conservative sufficient conditions. Finally, numerical results show that OSTB outperforms representative baselines in terms of long-term full-chain completion rate, power failures, and latency, particularly when harvested energy is scarce.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript formulates energy-aware scheduling of periodic sensing-computing-transmitting task chains on battery-less IoT devices as a long-term average-reward MDP whose state tracks discretized capacitor voltage, current task phase, and permissible start windows, with actions constrained by safe-execution voltage thresholds. Under i.i.d. energy arrivals it proves the MDP is unichain and that every optimal stationary policy has a threshold structure, yielding the OSTB scheduler; the framework is extended to a finite-state Markov energy-harvesting model under conservative conditions, and numerical experiments compare OSTB against baselines on full-chain completion rate, power-failure frequency, and latency.

Significance. If the unichain and threshold-structure results are valid, the work supplies a rigorous existence proof for optimal stationary policies in an intermittent-energy setting that is directly relevant to sustainable IoT design. The explicit reward construction that trades off completion reliability against low-energy risk, together with the extension to correlated harvesting, constitutes a concrete methodological contribution; the numerical validation under scarce energy further strengthens the practical relevance.

major comments (2)
  1. [Section 4 (unichain proof)] Unichain proof (Section 4): the connectivity argument that i.i.d. energy arrivals guarantee escape from every low-voltage state regardless of task phase must explicitly state the minimal support condition on the energy distribution. When the support is bounded (e.g., P(E=0) close to 1 or increments too small to satisfy safe-execution thresholds), a policy that idles in a low-voltage phase can induce a separate recurrent class unreachable from other phases, violating unichain and thereby undermining the existence of a constant gain and of an optimal stationary policy.
  2. [Section 4 (threshold-structure proof)] Threshold-structure proof (Section 4): the induction or coupling argument establishing monotonicity of the optimal action with respect to voltage must be checked against the precise definition of the reward function and the safe-execution constraint; if the reward penalizes low-voltage execution only when an action is taken, the threshold may shift with the current task phase in a way not captured by a single global threshold.
minor comments (2)
  1. [Abstract and Introduction] The abstract and introduction should cite the exact theorem numbers for the unichain and threshold results so readers can locate the proofs without scanning the entire section.
  2. [Numerical results] Numerical-results section: the energy-arrival distributions, capacitor capacitance values, and task-phase durations used in the simulations should be tabulated so that the reported performance gains can be reproduced.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on the proofs in Section 4. We address each major comment below and indicate planned revisions to strengthen the presentation.

read point-by-point responses

  1. Referee: [Section 4 (unichain proof)] Unichain proof (Section 4): the connectivity argument that i.i.d. energy arrivals guarantee escape from every low-voltage state regardless of task phase must explicitly state the minimal support condition on the energy distribution. When the support is bounded (e.g., P(E=0) close to 1 or increments too small to satisfy safe-execution thresholds), a policy that idles in a low-voltage phase can induce a separate recurrent class unreachable from other phases, violating unichain and thereby undermining the existence of a constant gain and of an optimal stationary policy.

    Authors: We agree that an explicit minimal support condition on the energy distribution is necessary to guarantee the unichain property. The manuscript implicitly relies on the assumption that energy arrivals have sufficient support to allow positive probability of escaping any low-voltage state and satisfying safe-execution thresholds, independent of task phase. We will revise Section 4 to state this condition formally (i.e., that the support of the energy random variable includes increments large enough to cross the relevant voltage thresholds with positive probability from every discretized level). Under this condition the connectivity argument holds and the MDP remains unichain. We will also note the limitation when the condition is violated. revision: yes

  2. Referee: [Section 4 (threshold-structure proof)] Threshold-structure proof (Section 4): the induction or coupling argument establishing monotonicity of the optimal action with respect to voltage must be checked against the precise definition of the reward function and the safe-execution constraint; if the reward penalizes low-voltage execution only when an action is taken, the threshold may shift with the current task phase in a way not captured by a single global threshold.

    Authors: The induction argument in the proof shows monotonicity of the optimal action in the voltage coordinate for each fixed task phase, taking into account that the reward penalizes low-voltage execution only upon action selection and that safe-execution constraints restrict the feasible action set. Consequently the optimal policy is threshold-based with respect to voltage, but the threshold value is permitted to depend on the current task phase. We will revise the manuscript to clarify that the OSTB scheduler employs phase-dependent voltage thresholds (rather than a single global threshold) and to make the dependence on task phase explicit in the policy description. This clarification does not change the validity of the structural result. revision: partial

Circularity Check

0 steps flagged

No circularity; standard MDP theory applied to domain-specific formulation

full rationale

The paper formulates the IoT scheduling problem as an average-reward MDP with states capturing capacitor voltage, task phases, and safe-execution constraints under an i.i.d. energy arrival model. It states a proof that the MDP is unichain and that the optimal stationary policy has a threshold structure, leading to the OSTB scheduler. These steps rely on established MDP results for unichain processes (constant gain, existence of optimal stationary policies) rather than any self-definitional equations, fitted parameters renamed as predictions, or load-bearing self-citations. The correlated harvesting extension is handled under conservative conditions without reducing claims to tautologies. Numerical comparisons to baselines are external evaluations. No step in the provided derivation chain reduces by construction to its own inputs; the analysis is self-contained against external MDP benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption of i.i.d. energy arrivals and on standard MDP properties such as the existence of optimal stationary policies for unichain processes; no free parameters or invented entities are identified from the abstract.

axioms (1)
  • domain assumption Energy arrivals are independently and identically distributed.
    Explicitly stated in the abstract as characterizing the main setting.

pith-pipeline@v0.9.0 · 5758 in / 1282 out tokens · 71499 ms · 2026-05-21T20:07:08.777473+00:00 · methodology

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Reference graph

Works this paper leans on

28 extracted references · 28 canonical work pages

  1. [1]

    Energy-sustainable I oT connec- tivity: Vision, technological enablers, challenges, and f uture directions,

    O. L. A. L ´ opez, O. M. Rosabal, D. E. Ruiz-Guirola, P . Ragh uwanshi, K. Mikhaylov, L. Lov´ en, and S. Iyer, “Energy-sustainable I oT connec- tivity: Vision, technological enablers, challenges, and f uture directions,” IEEE Open Journal of the Communications Society , vol. 4, pp. 2609– 2666, 2023

    work page 2023

  2. [2]

    Foundations for energ y-aware zero-energy devices: From energy sensing to adaptive proto cols,

    O. L. A. L ´ opez, M. Ashraf, S. Nasser, G. M. de Jesus, R. K. Singh, M. C. Filippou, and J. Famaey, “Foundations for energ y-aware zero-energy devices: From energy sensing to adaptive proto cols,” 2025. [Online]. Available: https://arxiv.org/abs/2507.22740

    work page arXiv 2025

  3. [3]

    Real-ti me scheduling for energy harvesting sensor nodes,

    C. Moser, D. Brunelli, L. Thiele, and L. Benini, “Real-ti me scheduling for energy harvesting sensor nodes,” Real-Time Syst., vol. 37, no. 3, p. 233–260, Dec. 2007

    work page 2007

  4. [4]

    Energy-aware sensing on battery-less LoRaW AN d evices with energy harvesting,

    A. Sabovic, C. Delgado, D. Subotic, B. Jooris, E. De Poort er, and J. Famaey, “Energy-aware sensing on battery-less LoRaW AN d evices with energy harvesting,” Electronics, vol. 9, no. 6, 2020. [Online]. Available: https://www.mdpi.com/2079-9292/9/6/904

    work page 2020

  5. [5]

    An energy-aware task scheduler for energy-harvesting bat teryless IoT devices,

    A. Sabovic, A. K. Sultania, C. Delgado, L. D. Roeck, and J. Famaey, “An energy-aware task scheduler for energy-harvesting bat teryless IoT devices,” IEEE Internet of Things Journal , vol. 9, no. 22, pp. 23 097– 23 114, 2022

    work page 2022

  6. [6]

    Optimal Energy-Aware Task Sch eduling for Batteryless IoT Devices,

    C. Delgado and J. Famaey, “Optimal Energy-Aware Task Sch eduling for Batteryless IoT Devices,” IEEE Transactions on Emerging Topics in Computing, vol. 10, no. 3, pp. 1374–1387, 2022

    work page 2022

  7. [7]

    A Robust Transmission Scheduling Approach for Internet of Things Se nsing Service with Energy Harvesting,

    J. Hao, J. Chen, R. Wang, Y . Zhuang, and B. Zhang, “A Robust Transmission Scheduling Approach for Internet of Things Se nsing Service with Energy Harvesting,” Sensors, vol. 19, no. 14, 2019

    work page 2019

  8. [8]

    Optima l task scheduling policy in energy harvesting wireless senso r networks,

    V . S. Rao, R. V . Prasad, and I. G. M. M. Niemegeers, “Optima l task scheduling policy in energy harvesting wireless senso r networks,” in 2015 IEEE Wireless Communications and Networking Conferen ce (WCNC), 2015, pp. 1030–1035

    work page 2015

  9. [9]

    Batter yless LoRaW AN communications using energy harvesting: Modeling and characterization,

    C. Delgado, J. M. Sanz, C. Blondia, and J. Famaey, “Batter yless LoRaW AN communications using energy harvesting: Modeling and characterization,” IEEE Internet of Things Journal , vol. 8, no. 4, pp. 2694–2711, 2021

    work page 2021

  10. [10]

    Clank: Architectural support for intermitt ent computation,

    M. Hicks, “Clank: Architectural support for intermitt ent computation,” in 2017 ACM/IEEE 44th Annual International Symposium on Compu ter Architecture (ISCA), 2017, pp. 228–240

    work page 2017

  11. [11]

    Flexicheck: A n adaptive checkpointing architecture for energy harvesting devices ,

    P . Singla, S. S. Singh, and S. R. Sarangi, “Flexicheck: A n adaptive checkpointing architecture for energy harvesting devices ,” in 2019 Design, Automation & Test in Europe Conference & Exhibition (DATE), 2019, pp. 546–551

    work page 2019

  12. [12]

    Handling power depletion in e nergy har- vesting iot devices,

    Y .-m. Kang and Y .-s. Lim, “Handling power depletion in e nergy har- vesting iot devices,” Electronics, vol. 13, no. 14, 2024

    work page 2024

  13. [13]

    A decentralized optimi zation frame- work for energy harvesting devices,

    A. Biason, S. Dey, and M. Zorzi, “A decentralized optimi zation frame- work for energy harvesting devices,” IEEE Transactions on Mobile Computing, vol. 17, no. 11, pp. 2483–2496, 2018

    work page 2018

  14. [14]

    Real-t ime task scheduling on intermittently powered batteryless devices ,

    M. Karimi, H. Choi, Y . Wang, Y . Xiang, and H. Kim, “Real-t ime task scheduling on intermittently powered batteryless devices ,” IEEE Internet of Things Journal , vol. 8, no. 17, pp. 13 328–13 342, 2021

    work page 2021

  15. [15]

    Fault-tolerant and real-time schedulin g for mixed- criticality systems,

    R. M. Pathan, “Fault-tolerant and real-time schedulin g for mixed- criticality systems,” Real-Time Syst. , vol. 50, no. 4, p. 509–547, Jul

    work page

  16. [16]

    Available: https://doi.org/10.1007/s11 241-014-9202-z

    [Online]. Available: https://doi.org/10.1007/s11 241-014-9202-z

    work page doi:10.1007/s11

  17. [17]

    Effectively schedulin g hard and soft real-time tasks on multiprocessors,

    F. M. S. Nascimento and G. Lima, “Effectively schedulin g hard and soft real-time tasks on multiprocessors,” in 2021 IEEE 27th Real-Time and Embedded Technology and Applications Symposium (RTAS) , 2021, pp. 210–222

    work page 2021

  18. [18]

    Cyense: Cyclic ener gy-aware scheduling for energy-harvested embedded systems,

    E. Aerabi, M. Fazeli, and D. H´ ely, “Cyense: Cyclic ener gy-aware scheduling for energy-harvested embedded systems,” Microprocessors and Microsystems , vol. 89, p. 104421, 2022. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0141933121005597

    work page 2022

  19. [19]

    Earliest deadline first schedu ling for real- time computing in sustainable sensors,

    M. Chetto and R. El Osta, “Earliest deadline first schedu ling for real- time computing in sustainable sensors,” Sustainability, vol. 15, no. 5,

    work page

  20. [20]

    Available: https://www.mdpi.com/2071-1 050/15/5/3972

    [Online]. Available: https://www.mdpi.com/2071-1 050/15/5/3972

    work page 2071

  21. [21]

    Energy prediction for energy-harvesting wireless sensor: A syste matic mapping study,

    Z. Y uan, Y . Ge, J. Wei, S. Y uan, R. Liu, and X. Mo, “Energy prediction for energy-harvesting wireless sensor: A syste matic mapping study,” Electronics, vol. 12, no. 20, 2023. [Online]. Available: https://www.mdpi.com/2079-9292/12/20/4304

    work page 2023

  22. [22]

    A priority-aware dynamic scheduling algor ithm for ensuring data freshness in 5g networks,

    B.-S. Kim, “A priority-aware dynamic scheduling algor ithm for ensuring data freshness in 5g networks,” Future Generation Computer Systems, vol. 163, p. 107542, 2025. [Online]. Available: https: //www.sciencedirect.com/science/article/pii/S0167739X24005065

    work page 2025

  23. [23]

    Age-based scheduling: Improvin g data freshness for wireless real-time traffic,

    N. Lu, B. Ji, and B. Li, “Age-based scheduling: Improvin g data freshness for wireless real-time traffic,” ser. Mobihoc ’18 . New Y ork, NY , USA: Association for Computing Machinery, 2018, p. 191– 200. [Online]. Available: https://doi.org/10.1145/3209582. 3209602

    work page doi:10.1145/3209582 2018

  24. [24]

    M. L. Puterman, Markov Decision Processes: Discrete Stochastic Dy- namic Programming, 2nd ed. US: Wiley, 2005

    work page 2005

  25. [25]

    Online Learning Sc hemes for Power Allocation in Energy Harvesting Communications,

    P . Sakulkar and B. Krishnamachari, “Online Learning Sc hemes for Power Allocation in Energy Harvesting Communications,” IEEE Trans- actions on Information Theory , vol. 64, no. 6, pp. 4610–4628, 2018

    work page 2018

  26. [26]

    S. M. Ross, Introduction to Stochastic Dynamic Programming . CA, USA: Academic, 1983

    work page 1983

  27. [27]

    Re NEW: A Prac- tical Module for Reliable Routing in Networks of Energy-Har vesting Wireless Sensors,

    R. V . Prasad, V . S. Rao, C. Sarkar, and I. Niemegeers, “Re NEW: A Prac- tical Module for Reliable Routing in Networks of Energy-Har vesting Wireless Sensors,” IEEE Transactions on Green Communications and Networking, vol. 5, no. 3, pp. 1558–1569, 2021. JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2021 13

    work page 2021

  28. [28]

    Networkin g low-power energy harvesting devices: Measurements and algorithms,

    M. Gorlatova, A. Wallwater, and G. Zussman, “Networkin g low-power energy harvesting devices: Measurements and algorithms,” IEEE Trans- actions on Mobile Computing , vol. 12, no. 9, pp. 1853–1865, 2013

    work page 2013