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Finite-Horizon Energy Allocation and Routing Scheme in Rechargeable Sensor Networks

Finite-Horizon Energy Allocation and Routing Scheme in Rechargeable Sensor Networks. Shengbo Chen, Prasun Sinha, Ness Shroff, Changhee Joo Electrical and Computer Engineering & Computer Science and Engineering. Introduction [Rechargeable sensor network]. Environment monitoring

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Finite-Horizon Energy Allocation and Routing Scheme in Rechargeable Sensor Networks

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  1. Finite-Horizon Energy Allocation and Routing Scheme in Rechargeable Sensor Networks Shengbo Chen, Prasun Sinha, Ness Shroff, Changhee Joo Electrical and Computer Engineering & Computer Science and Engineering

  2. Introduction[Rechargeable sensor network] • Environment monitoring • Earthquake, structural, soil, glacial • Unattended Operability for long periods • Battery with renewable energy (like solar or wind) • Challenge: energy allocation • Sensor Network without replenishment: full battery is desirable feature • Sensor Network with replenishment: no opportunity to harvest energy

  3. Introduction(cont’)[Rechargeable sensor network] r(t) B(t) B(t+1) e(t) M M: Battery size B(t): Battery level at time slot t e(t): allocated energy at time slot t r(t): harvested energy at time slot t

  4. Motivation • Rate-power function • Nondecreasing and strictly concave • Data transmission with spending units of energy • How to design

  5. Motivation(cont’) • Example 1: • r(1)=4, r(2)=2, r(3)=0 • e*(1)=2, e*(2)=2, e*(3)=2 r(2) r(1) Average replenishment rate is the best because of Jensen’s inequality

  6. Motivation(cont’) Example 2: r(1)=2, r(2)=0, r(3)=4 r(3) r(2) r(1) Average replenishment rate is infeasible

  7. Problem Statement • Sensor Network with renewal energy • Assumption • No interference from other nodes • Problem: throughput maximization where, is the amount of data from source to the destination at time slot t

  8. Problem Statement (cont’) • Convex optimization problem • Joint energy allocation and routing • Complex due to the “time coupling property” • Concave rate-power function

  9. Related Literatures • Finite horizon • A. Fu, E. Modiano and J. Tsitsiklis, 2003. • Dynamic programming • Infinite horizon • L. Lin, N. B. Shroff, and R. Srikant, 2007 • Asymptotically optimal competitive ratio • M. Gatzianas, L. Georgiadis, and L. Tassiulas, 2010. • Maximize a function of the long-term rate per link • L. Huang, Neely • Asymptotically optimal

  10. Three-step Approach • One node with full knowledge of replenishment profile • One node with estimation of replenishment profile • Multiple-node network

  11. Three-step Approach • One node with full knowledge of replenishment profile • One node with estimation of replenishment profile • Multiple-node network

  12. One node with full knowledge of replenishment profile • Finite time horizon: T time slots • Assumption: replenishment profile is known • Constraints: • Cumulative used no greater than cumulative harvested • Residual no greater than the battery size

  13. Result 1 Shortest path S(t): curve that connects two points (0, 0) and (T,K) in the domain D with least Euclidean length • Theorem 1: The energy allocation scheme , satisfying s(t) = S(t) − S(t − 1), is the optimal energy allocation scheme K R(t) Cumulative Energy D R(t)-M T time

  14. Three-step Approach • One node with full knowledge of replenishment profile • One node with estimation of replenishment profile • Multiple-node network

  15. One node with estimation of replenishment profile • Assumption relaxed • Replenishment profile is unknown • Estimation replenishment rate • Actual replenishment rate

  16. Online algorithm Theorem 2: The throughput U of the online algorithm, achieves fraction of the optimal throughput Calculate e(t) from the lower-bound of the estimated replenishment profile by the shortest-path solution The allocated energy is determined as e(t) = e(t) + r(t) − r(t) K R(t) (1+β2)R(t) Cumulative Energy (1-β1)R(t) T time

  17. Three-step Approach • One node with full knowledge of replenishment profile • One node with estimation of replenishment profile • Multiple-node network

  18. Heuristic scheme: NetOnline • Throughput maximization • Decouple energy allocation and routing： • Energy allocation of each node follows the online algorithm • Routing:

  19. Result 3 • Theorem 3: The heuristic scheme is optimal if all nodes have the same replenishment profile and perfect estimation.

  20. Simulations

  21. Simulations (cont’)

  22. Simulations (cont’) • NRABP: Infinite-horizon based scheme in Gatzianas’s paper

  23. Future work • Considering interference in the model • Replenishment rate is known with some distribution, what is the best strategy? • Infinite horizon but only finite period of estimation

  24. Thank you! 24

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