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Shengbo Chen, Prasun Sinha, Ness Shroff, Changhee Joo

A Simple Asymptotically Optimal 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 networks]. Applications

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Shengbo Chen, Prasun Sinha, Ness Shroff, Changhee Joo

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  1. A Simple Asymptotically Optimal 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 networks] Applications Environment monitoring:earthquake, structural, soil, glacial Unattended operability for long periods Opportunity Harvesting and storing renewable energy (like solar or wind) Challenges Full battery means no opportunity to harvest renewable energy Unpredictable and time-varying renewable energy Goal: develop control mechanism to maximize the total utility for a sensor network with energy replenishment

  3. Outline Model Problem statement Related Literature Our approach Simulation results Conclusion

  4. Model[Rechargeable sensor node] • Rechargeable sensor node r(t) B(t) B(t+1) e(t) M M: Battery size B(t): Battery level in time slot t e(t): allocated energy in time slot t r(t): harvested energy in time slot t • Rate-power function Nondecreasing and strictly concave Amount of data transmitted with spending units of energy

  5. Problem Statement • Sensor network with renewable energy • Assume the date rate is low • Ignore interference from other nodes • Problem: utility maximization amount of data from source to destination in slot t is a strictly concave utility function Convex optimization problem: Joint energy allocation and routing Requires full knowledge of the replenishment profile Time coupling property: have to optimize all time slots simultaneously Flow 1 Flow 2

  6. Related Literature • Finite horizon • [S. Chen, P. Sinha and N. B. Shroff], INFOCOM, 2011. • [A. Fu, E. Modiano and J. Tsitsiklis], TON, 2003. • Dynamic programming • Infinite horizon • [L. Lin, N. B. Shroff, and R. Srikant], TON, 2007. • Asymptotically optimal competitive ratio • [Z. Mao, C. E. Koksal, N. B. Shroff ],TAC, 2011 • Finite battery size • [M. Gatzianas, L. Georgiadis, and L. Tassiulas], TWC, 2010. • Maximize a function of the long-term rate per link • [L. Huang, M. Neely],Mobihoc, 2011 • Asymptotically optimal utility Lyapunov optimization technique Our focus: Infinite horizon Our contribution: develop a low-complexity solution

  7. Our approach • Construct a fictitious infeasible energy allocation and routing scheme • Prove that its performance forms an upper bound on • Develop a low-complexity online scheme • Prove that the performance achieved by the online scheme can get arbitrarily close to the upper bound as tends to infinity

  8. Assumption Replenishment process has a finite mean value Infinite battery capacity Upper bound for the optimum Jensen’s Inequality: is an upper bound Single node case[Throughput maximization] Spending energy at the average rate is the best

  9. Single node case (cont’d) [Throughput maximization] • Consider the energy allocation scheme • In each time slot, the estimated average replenishment rate • The allocated energy in each slot where is an arbitrary parameter Intuition: spend energy at a rate close to the mean Theorem 1: The scheme above achieves the throughput performance arbitrarily close to by choosing to be sufficiently small as tends to infinity

  10. Upper bound on the optimum Consider a fictitiousinfeasible scheme For each node i, energy allocation in each slot Routing decision in each slot Network Case [fictitious scheme] • Energy allocation and routing decoupled • Time decoupled • 3. Time homogeneous Spend a little more energy than the average harvested Theorem 2: is upper bounded by

  11. Consider the online scheme Energy allocation (same as the single node case) The estimated average replenishment rate The allocated energy in each slot Routing decision in each slot Network Case (cont’d) [Online scheme] Theorem 3: The scheme achieves the performance arbitrarily close to by choosing to be sufficiently small as tends to infinity

  12. Distributed algorithm • Duality based • At each time slot, source s generates data at rate by solving • Routing • Lagrange multipliers are updated as

  13. Simulation Setup • Network topology: • 100 nodes and three flows in 1×1 field • Link available if distance is less than 0.2 • Using real traces of solar energy and wind energy [3] • June 5th, 2011-July 5th, 2011 [3]. “National Renewable Energy Laboratory,” http://www.nrel.gov.

  14. Simulation results ESA: Infinite-horizon based scheme in [1] [1] L. Huang, M. Neely, “Utility Optimal Scheduling in Energy Harvesting Networks,” in Proceedings of Mobihoc, May 2011. minute minute

  15. Conclusion • Study the joint problem of energy allocation and routing to maximize total utility in a sensor network with energy replenishment. • Develop a low-complexity online solution that is asymptotically optimal with general energy replenishment profiles. • Evaluate the performance using real traces

  16. Thank you! 16

  17. Simulation results for one node ESA: Infinite-horizon based scheme in [1] [1] L. Huang, M. Neely, “Utility Optimal Scheduling in Energy Harvesting Networks,” in Proceedings of Mobihoc, May 2011.

  18. Finite battery size Required battery size

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