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Optimization of Low-Power Energy Harvesting Devices Using Predictable and Stochastic Profiles

This research explores energy harvesting devices in networking, focusing on resource allocation algorithms that adapt to varying energy profiles. It introduces a model that combines predictable and stochastic energy profiles to optimize energy spending and communication rates across devices. By employing measurements of indoor irradiance and adapting algorithms based on energy storage types and environmental conditions, this study aims to improve the efficiency of data transmission while addressing fairness and energy decision-making in wireless networks.

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Optimization of Low-Power Energy Harvesting Devices Using Predictable and Stochastic Profiles

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  1. Networking Low-Power Energy Harvesting Devices: Measurements and Algorithm Gorlatova M., Wallwater A., Zussman G. INFOCOM 2011

  2. Outline • Introduction • Model • Measurement • Energy profile • Algorithm for predictable profile and stochastic profile • Result

  3. Introduction • Achieve time-fair resource allocation since energy varies among different time • Other research focus on fairness • Data generation rate (SenSys08) • among nodes (JSAC06) • Proposed energy allocation algorithms across the different time slot to optimize • energy spending rate for single node • energy communication rate for a link • Indoor irradiance measurements study.

  4. Dimensions of algorithm design • Environmental energy model • Energy storage type • Ratio of energy storage capacity to energy harvested • Time granularity • nodes characterize received energy • Make decision from sec ~days • Problem /Network size • energy harvesting affects nodes’ decisions • Link decisions, routing, rate adaptation

  5. Environmental energy model • Predictable profiles • Ideal • Accurate for the future • Partially predictable • Stochastic • Model-free

  6. Energy storage type • Rechargeable battery • Ideal linear model • Changes of stored energy vs harvested power • Capacitor • Non-linear model • Power harvested depend both on the energy provided and on the amount of energy stored

  7. Contributions • Indoor : partially-predictable energy model • Time granularity : day, improving prediction • Fair allocation of resources along the time • Energy spending rate for a node • Data rate for a link • Predictable energy profiles • Lexicographic maximization • Utility maximization • Stochastic model • Markov Decision Process

  8. Model • K slots time i = {0,1,…K-1} • D=AηH • Q(i)=q(D(i),B(i)) for capacitor

  9. Objective • Optimization energy spending rate s(i) for single node • Optimization energy communication rate ru(i), rv(i) for a link • Utility maximization frame work to find • spending rate s(i) • communication rate ru(i), rv(i) • α-fair function U(s(i)) = s(i)1-α/(1-α), for α>0, α≠1 log(s(i)), for α=1 • Consider predictable profile energy model

  10. Dynamic programming-based algorithm • h(i,B(i))=max[ U(s(i)) + h(i+1,min(B(i)+Q(i)-s(i),C))] • Determine vector {s(0),…s(K-1)} maximizes h(0,B0) • Running time O(K[C/△]2)

  11. For linear storage q(D(i),B(i)) = D(i) • Progressive Filling algorithm • Running time O(K[K+QT/△]),QT= ΣQ(i)+(B0-BK) • If linear storage is large, s(i) = QT/K

  12. Measurement • Long-term measurement of indoor irradiance • Office buildings at Columbia Uni. since 2009/6 • TAOS TSL230rd photometric sensors • LabJack U3 DAQ

  13. Hd: mean of the daily irradiation • σ : standard deviation • r : bit rate, throughout a day when exposed Hd • r = A(10cm2) x η(1%) x Hd /(3600x24)/(10e-9) • EnHANTs costs 1nJ/bit

  14. How to predict Hd? • Exponentially weighted moving-average (EWMA) • Error is relatively high • For L-1, avg. prediction error > 0.4Hd • L-2, avg. prediction error > 0.5Hd • Outdoor, avg. prediction error = 0.3Hd • Weather forecast [secon10] may be improved • For L-1, correlation coefficient of Hd and weather = 0.35 • For L-6, correlation coefficient =0.8

  15. Work week pattern • For L-2, student office, on shelf far from window • Hd= 1.63 on weekdays, Hd=0.37 on weekend • 9.7hr/day lighting on weekday, <1hr on weekend • Avg. error prediction error 0.5Hd -> 0.26Hd if separate weekdays and weekends. • L-1 and L-5, correlation coefficient =0.58 • L-1 and L-5 facing same direction, correlation coefficient =0.71

  16. Short term energy profiles • HT, T= 0.5 hr • L-3, daylight-dependent variations • L-2, either 0 or 45uW/cm2 • partially predictable energy model

  17. Mobile measurements • mobile device carried around indoor and outdoor locations • Indoor : 70uW/cm2 • Outdoor : 32mW/cm2 • Poorly predictable • Stochastic energy model

  18. Link: optimizing Data rate

  19. ru(i) = rv(i) = r(i)

  20. Extension of TFR algorithm • {ru(0),..ru(K-1)}, {rv(0,..rv(K-1)} maximize h(0,B0u,B0v) • Complexity : • For linear storage, LPF algo.,

  21. Decoupled Rate Control algorithm • DRC algorithm • Determine su(i), sv(i) independently using PF algorithm • r(i) = min(su(i), sv(i))/(ctx + crx)

  22. Stochastic Energy model • Energy harvested in a slot is and i.i.d (identical independent distribution)random variable D • [d1,..dM] with probability [p1,…pM] • Spending Policy Determination (SPD) problem • Given distribution D, determine s(i) • Markov Decision Process(MDP)

  23. Apply dynamic programming, from i=K-1 for each {i,B(i)} • For each storage B(i), s(i) approached optimal • Running time

  24. Link Spending Policy Determination Problem(LSPD) • Apply dynamic programming • For each {i, Bu(i), Bv(i)} • Maximization is over all {ru(i), rv(i)}, such that • ctxru(i) + crxrv(i) = su(i) ≤ Bu(i) • ctxrv(i) + crxru(i) =sv(i) ≤ Bv(i) • Complexity: O([Cu/△]2[Cv/]2MuMvK)

  25. Numerical results • Energy profile L-3 input • s(i) are obtained by PF algorithmfor linear storage(left) • s(i) for TFU problem for nonlinear storage (right)

  26. L-1, L-2 energy profile • Optimal communication rate {ru(i), rv(i)}

  27. Optimal energy spending policies (SPD) • L-1 profile as random variable D • Optimal s(i) • Optimal communication rateru(i), rv(i)

  28. Conclusion • First long-term indoor radiant energy measurements campaign that provides useful traces • Developed algorithms for predictable environment that uniquely determine the spending policies for linear and non-linear energy storage models • Developed algorithms for stochastic environments that can provide nodes with simple pre-computed decisions policies

  29. Alpha ->0, globally optimize • Alpha ->1, proportional fairness • ->2, harmonic mean fairness • -> infinite , generalized max min allocation

  30. Introduction • Perpetual energy harvesting wireless device • Solar, piezoelectric and thermal energy harvesting • Ultra-low-power wireless communication • Rechargeable sensor networks • Focus on devices that harvest environmental light energy • Energy-harvesting-aware algorithm and system • Lack of data and analysis of energy availability for indoor/outdoor environment • 16 months indoor light energy measurement • light measurement and resource allocation

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