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Steady and Fair Rate Allocation for Rechargeable Sensors in Perpetual Sensor Networks

Steady and Fair Rate Allocation for Rechargeable Sensors in Perpetual Sensor Networks. Zizhan Zheng Authors: Kai-Wei Fan, Zizhan Zheng and Prasun Sinha Department of Computer Science & Engineering The Ohio State University. Agenda. Motivation Centralized algorithm Distributed algorithm

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Steady and Fair Rate Allocation for Rechargeable Sensors in Perpetual Sensor Networks

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  1. Steady and Fair Rate Allocation for Rechargeable Sensorsin Perpetual Sensor Networks Zizhan Zheng Authors: Kai-Wei Fan, Zizhan Zheng and Prasun Sinha Department of Computer Science & Engineering The Ohio State University

  2. Agenda • Motivation • Centralized algorithm • Distributed algorithm • Evaluation • Conclusion and future work

  3. Perpetual Sensor Networks • Renewable Energy Source • Solar, wind, vibration, etc. • Replenish rechargeable batteries • Planning for renewable energy • Increase network lifetime • Optimize system performance • Goals • Perpetual Data Collection Service • Steady and Fair Data Collection

  4. L={8.6, 8.6, 6.4, 6.4} L={5, 5, 5, 5} L={10, 10, 10, 10} Rate Assignment Recharging Profiles

  5. Lexicographic Rate Assignment • Definition • A rate assignment L = {x1, x2, …, xn} is lexicographically optimal if xi can not be increased any further without reducing xj <= xi • Approaches • Centralized • Iteratively solving a maximization problem • Distributed • Fixed, unsplittable flows • Two-phase rate assignment

  6. Formulation - LP-Lex • Given a network G=(V, E) • : a recharging cycle is divided into slots • : amount of energy collected by node i in time slot t • : battery capacity of node i • : initial battery level of node i • : sensing, transmission, receiving energy consumption per packet

  7. LexRateAssignment Algorithm • Given a network G=(V, E). Let A = V • Find the maximum common rate C for A • Find the maximum single rate of each node in A assuming other nodes’ rates are C • Ac, = set of nodes whose maximum single rate is C • Remove Ac from A • Repeat step 1 until A is empty

  8. LexRateAssignment Algorithm • Parameters • Πi : Battery Capacity • Wi : Battery Level • : Recharging Rate Vector • Constraints: • Flow Constraints • Energy Constraints B A D C

  9. r r r r LexRateAssignment Algorithm • Find Maximum Common Rate r • Find Maximum Rate for each node assuming the rates of other nodes are 6 • <14, 14, 9, 6> • Fix the rate of nodes whose rates are 6 • Repeat the process for remaining nodes until rates of all nodes are fixed r=14 r=6 r B r=6 r=6 A D r=14 r=6 r C r=9 r=6

  10. Optimality of LexRateAssignment • Lemma: The optimal lexicographic rate assignment is unique • Theorem: LexRateAssignment computes the optimal lexicographic rate assignment.

  11. Distributed Algorithm • Assumptions: • Fixed Routes • Unsplittable Flows • Parameters • Πi : Battery Capacity • Wi : Battery Level • : Recharging Rate Vector • Constraints: • Flow Constraints • Energy Constraints B A D C

  12. DLEX Algorithm • For each node i : • Initialization: • Compute maximum achievable rate locally • Send the maximum achievable rate to its parent node p • When Receiving a Rate: • Compute and update rates • Send updated rates to parent node p • Sink notifies received rates to source nodes • Theorem: DLEX converges and computes the optimal lexicographic rate assignment

  13. Distributed Algorithm B A D C

  14. Experiment Results • Motelab: A network of 155 nodes • Random topology • Solar Energy Profiles • Field Experiments with Solar Panels • National Climatic Data Center • Evaluated Algorithm • DLEX: Distributed algorithm • DLEX-A: Distributed algorithm without considering initial battery level • NAVG: Average recharging rate

  15. Emulation Results • In NAVG, over 30% of nodes run out of energy for over 50% of the time; throughput is close to zero for about 2.5 hours.

  16. Experiment Results • Key Observations • Bottlenecks are 1-hop nodes • Balanced tree performs better

  17. Experiment Results - Overhead • Nodes closer to root have higher overhead • Running time varies from 50 to 244 seconds (depending on quality of selected links)

  18. Conclusion and Future work • Centralized Algorithm • Uniqueness of the optimal solution • Iteratively solving a maximization problem • Jointly solving routing and rate assignment problem • Distributed Algorithm • Two-phase rate assignment • Asynchronous computation • Only for fixed route, unsplittable flows • Future Work • Distributed algorithm for joint rate assignment and routing • Model link quality in the formulation

  19. DLEX Algorithm • Each node i maintains following • rjmax : Maximum feasible rate for flow j at node i • rj : Assigned rate for flow j at node i • R : The set contains flow j if rjmax < r • U : The set contains flow j if rjmax > r • Parameters • Ei: Available energy for node i • es: Energy consumption for sensing and transmitting • ef: Energy consumption for receiving and transmitting

  20. DLEX Algorithm • For each node i : • Compute maximum achievable rate locally • Send the maximum achievable rate to its parent node p • Update ri as when node ireceives rate updates from children nodes • Update rate for each flow j:rj = rjmax if jR rj = ri if jU • Send updated rates ris to parent node p • Sink notifies received rates to source nodes

  21. Rate Computation 30 Computation at node A 8 15 8 15 8 6 9 8 6 A B C D

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