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

This paper discusses an energy allocation and routing scheme for rechargeable sensor networks, focusing on the challenges of energy allocation in networks with and without replenishment opportunities. The study involves motivation, problem statements, related literature review, and a three-step approach.

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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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