1. Maximization of System Lifetime for Data-Centric Wireless Sensor Networks 指導教授：林永松 博士 具資料集縮能力無線感測網路 系統生命週期之最大化 研究生：郭文政 國立臺灣大學資訊管理學研究所碩士論文審查 民國 95 年 7 月 27 日

2. 2 Outline  Introduction Background Motivation  Problem Description & Formulation  Solution Approach Lagrangean Relaxation method  Getting Primal Feasible Solution  Computational Experiments  Conclusion and Future Work

3. 3 Introduction  Wireless sensor networks Sensing Computation Communication

4. 4 Introduction (cont’d)  Issues End-to-end delay Coverage Lifetime (Energy Consumption) Data Aggregation trees Clustering Spanning trees

5. 5 Background  Clustering LEACH (Low- Energy Adaptive Clustering Hierarchy) * Set-up phase Steady state phase  Spanning trees PEDAP(Power Efficient Data gathering and Aggregation Protocol) ** Minimum cost spanning tree: Prim’s algorithm PEDAP-PA (Power Efficient Data gathering and Aggregation Protocol- Power Aware) Remaining energy concept * W. Heinzelman, A. Chandrakasan and H. Balakrishnan, "Energy-Efficient Communication Protocol for Wireless Microsensor Networks", the 33rd Hawaii International Conference on System Sciences, Jan. 2000. ** H. O. Tan and I. Korpeoglu, “Power Efficient Data Gathering and Aggregation in Wireless Sensor Networks”, ACM SIGMOD Record, vol. 32, no. 4, pp. 66-71, 2003

6. 6 Motivation  How to energy-efficient construct the data aggregation trees to reduce the power consumption and further prolong the system lifetime? Event Source node Relay node Sink node

7. 7 Problem Description Source node Relay node Sink node Event  In the WSN, each event must be monitored by one awake data source node and the nodes transmit the sensed data to the sink node through aggregation trees.  Each aggregation tree is used for one or more rounds. The goal is to maximize the system lifetime under energy capacity constraints.

8. 8 Problem Description (cont’d) 25 Rounds 11 Rounds16 Rounds 52 Rounds

9. 9 Problem Description (cont’d)  Assumption Heterogeneous network Fixed sensing range and fixed transmission range Bidirectional links Error-free transmission within the transmission radius The sink node knows nodes all a priori  Given The network topology includes node set and link set The set of data source nodes The set of events The sink node Capacity for each node evaluated by residual power lifetime Transmission cost of each link with respect to energy consumption

10. 10 Problem Description (cont’d)  Objective To maximize the system lifetime of the sensor network  Subject to Event constraint: Each event must be monitored by one awake data source node and the awake data source nodes sense and transmit the sensed data to the sink node. Battery constraint: The total power consumption of a node can not exceed its initial energy level.  To determine The number of times that tree t is used

11. 11 Problem Formulation

12. 12 Problem Formulation (cont’d)  Objective Function max (IP)  subject to: (IP 1) (IP 2) (IP 3) (IP 4) (IP 5) (IP 6) (IP 7) (IP 8) Event constraints Tree constraints

13. 13 Problem Formulation (cont’d) (IP 9) (IP 10) (IP 11) (IP 12) (IP 13) (IP 14) (IP 15) (IP 16) (IP 17) (IP 18) = 0 or 1 Energy constraints

14. 14 Lagrangean Relaxation Method  Relax Constraints (3) 、 (5) 、 (7) 、 (8) 、 (11) 、 (12) and we can obtain the following Lagrangean relaxation problem (LR) Primal Problem Lagrangean Relaxation Problem Lagrangean Dual Problem Optimal Solution Adjust Multipliers

15. 15 Subproblem 1 (related to decision variable ) subject to: = 0 or 1 (Sub1 1.1) (Sub1 1.2) (Sub1 1.3) (Sub1 1.4) Firstly, set the decision variable to be 1 or 0 according to the corresponding coefficient. Then, solve the shortest path problem by Dijkstra’s algorithm if the decision variable is 1. Time complexity:

16. 16 Subproblem 2 (related to decision variable ) subject to: (Sub2 2.1) (Sub2 2.2) (Sub2 2.3)= 0 or 1 Compute the coefficient of each link. Pick up at most one outgoing link of each node and at least one incoming link of the sink node according to the corresponding coefficient. Time complexity:

17. 17 Subproblem 3 (related to decision variable ) = 0 or 1 (Sub3 3.1) (Sub3 3.2) (Sub3 3.3) (Sub3 3.4) subject to: Firstly, solve the spanning tree problem by Prim’s algorithm. Then, calculate the sum of the rounds each tree t is used. Time complexity:

18. 18 Subproblem 4 (related to decision variable ) subject to: = 0 or 1 (Sub4 4.1) Set the decision variable to be 1 or 0 according to the corresponding coefficient. Time complexity:

19. 19 Getting Primal Feasible Solutions  By applying Lagrangean Relaxation method and the subgradient method to solve the problem, we can obtain A theoretical lower bound of the primal problem Some hints to get a feasible solution to the primal problem  Two major primal decision variables

20. 20 Getting Primal Feasible Solution (Tree1)(Tree2)(Tree3) 22 Rounds31 Rounds43 Rounds 55 Rounds

21. 21 Experiment Scenarios  Random network  Grid network

22. 22 Evaluation of Lifetime (Random Network) Evaluation of Lifetime (Rounds) (Small Network, No. of Nodes = 25)

23. 23 Evaluation of Lifetime (Random Network) Evaluation of Lifetime (Rounds) (Medium Network, No. of Nodes = 49)

24. 24 Evaluation of Lifetime (Random Network) Evaluation of Lifetime (Rounds) (Large Network, No. of Nodes = 81)

25. 25 Evaluation of Lifetime (Grid Network) Evaluation of Lifetime (Rounds) (Small Network, No. of Nodes = 25)

26. 26 Evaluation of Lifetime (Grid Network) Evaluation of Lifetime (Rounds) (Medium Network, No. of Nodes = 49)

27. 27 Evaluation of Lifetime (Grid Network) Evaluation of Lifetime (Rounds) (Large Network, No. of Nodes = 81)

28. 28 Discussion  The bottleneck of system lifetime The relay nodes around the sink node The source nodes Articulation points Source node Relay node Sink node Event

29. 29 Conclusion  Contribution Propose a mathematical formulation to model this complicated problem Devise a simple heuristic algorithm to obtain good solutions which outperforms PEDAP and PEDAP-AP  Bottleneck of System Lifetime

30. 30 Future Work  End-to-end Delay  Clustering

31. 31 Q & A -Thanks for your listening

32. 32 Problem Formulation

33. 33 Problem Formulation (cont’d)

34. 34 Problem Formulation (cont’d)

35. 35 Getting Primal Feasible Solution  The proposed heuristic algorithm is described as follows Step 1: Construct candidate trees based on the solutions to (Sub3) and select the data source nodes to transmit sensed data based on the solutions to (Sub1). Step 2: Sort the candidate trees in ascending order with the cost, the total energy consumption in the aggregation tree. Step 3: Use the tree to transmit the sensed data to the sink node from candidate trees, if satisfied with all constraints, if not, select another tree from the candidate trees. Repeat step2 until the candidate trees are exhausted. Step 4: Construct a new tree to transmit the sensed data to the sink node based on remaining energy of nodes. Repeat step3 until we can not construct a tree. Step 5: Compute the lifetime

36. 36 Lagrangean Relaxation method  Relax Constraints (3) 、 (5) 、 (7) 、 (8) 、 (11) 、 (12) and we can obtain the following Lagrangean relaxation problem (LR) (LR)

37. 37 Lagrangean Relaxation method (cont’d) subject to: (LR 1) (LR 3) (LR 4) (LR 5) (LR 6) (LR 2)

38. 38 Lagrangean Relaxation method (cont’d) (LR 7) (LR 8) (LR 9) (LR 10) (LR 11) (LR 12) = 0 or 1 We can decomposed this LR problem into 4 subproblems.