1.  Tree in Sensor Network Patrick Y.H. Cheung, and Nicholas F. Maxemchuk, Fellow, IEEE 3 rd New York Metro Area Networking Workshop (NYMAN 2003)

2. Columbia University 2 NYMAN 03 xxxxx xxx... Overview Routing Problem in Sensor Network The  Tree Algorithm Performance Evaluation Work in Progress

3. 1. Routing Problem in Sensor Network

4. Columbia University 4 Routing Problem in Sensor Network Introduction Data Processing Center Sensor Sink Network Infrastructure Data Flow

5. Columbia University 5 Routing Problem in Sensor Network Introduction Sensor Network vs. Conventional Network Perform data collectionPoint-to-point communications Compress data on the wayData is transparent Impulse arrival process triggered by an event Poisson arrival process Sensor NetworkConventional Network

6. Columbia University 6 Routing Problem in Sensor Network Introduction If the paths are not carefully provisioned, popular routes may run out of energy before the transmission of the impulse is complete. Two competing effects:  On one hand concentrating the data on a small number of paths increases the compression and reduces the energy.  On the other hand it increases the energy expended by those nodes and decreases the network lifetime.

7. Columbia University 7 Routing Problem in Sensor Network The Routing Problem Objective: To choose paths through the sensor network to the sinks that maximize the lifetime of the network by minimizing energy consumption.

8. Columbia University 8 Routing Problem in Sensor Network Phase 1: Minimize the total energy, taking into account the amount of aggregation that can be performed along the paths. Phase 2: Avoid overloading the popular paths by considering the energy expended by the intermediate nodes. Our Approach

9. Columbia University 9 Routing Problem in Sensor Network Phase 3: Take into account congestion and energy deficits and use deflection routing to move packets in directions that are preferable based on actual network use. The  tree algorithm is a response to the challenge in Phase 1. Our Approach

10. 2. The  Tree Algorithm

11. Columbia University 11 The  Tree Algorithm It is the same as the Dijkstra’s Algorithm, except that we label the next closest node with   (distance to the destination) The parameter  (0<  <1) is adjusted according to the data aggregation performance, in order to find topologies which minimize total energy costs. Basic Concepts

12. Columbia University 12 The  Tree Algorithm Consider the extreme cases:  No data reduction Optimal topology: Minimum Depth Tree (MDT)   = 1  100% data reduction (i.e. two msgs. in, one msg. out) Optimal topology: Minimum Spanning Tree (MST)   = 0 In general,  decreases as the amount of compression increases. Effects of 

13. Columbia University 13 The  Tree Algorithm How  affects the “shape” of a tree. Effects of  MDT (  = 1)MST (  = 0)  Tree

14. Columbia University 14 The  Tree Algorithm A Routing Example MDT (  = 1) 4 2 1 2 34 3 4 5.5 [0][0] [2][2] [5.5] MST (  = 0)  Tree (  = 0.5) 1 2 34 3 4 4 2 5.5 [0][0] [2][2] [5.5] 1 2 34 3 4 4 2 5.5 [0][0] [2][2] [5.5]

15. Columbia University 15 The  Tree Algorithm A Routing Example 4 [0] 1 2 34 3 4 2 5.5 [0][0] [5.5][5][5] 1 2 34 3 4 4 2 5.5 [0] [2 .5] [5.5] [1][1] 1 2 34 3 4 4 2 5.5 [0] [2][2] [5.5][6][6][4][4][4][4][5][5] MDT (  = 1)MST (  = 0)  Tree (  = 0.5)

16. Columbia University 16 [5 .5] The  Tree Algorithm A Routing Example [2.5] 3 [0] 1 2 3 4 4 4 2 5.5 [5] [1] 1 2 3 4 3 4 4 2 5.5 [0] [2] [5.5][6][4] 4 2 1 2 3 4 3 4 5.5 [0] [0][0][3][3] MDT (  = 1)MST (  = 0)  Tree (  = 0.5)

17. Columbia University 17 [5 .5] The  Tree Algorithm A Routing Example 3 [2.5] [0] [2.5] 1 2 34 4 4 2 5.5 [1] 1 2 34 3 4 4 2 5.5 [0] [2] [5.5][6][6] 3 1 2 34 4 4 2 5.5 [0] [0][0] MDT (  = 1)MST (  = 0)  Tree (  = 0.5)

18. Columbia University 18 The  Tree Algorithm A Routing Example 1 2 34 4 4 2 1 2 34 4 2 5.5 3 1 2 34 4 2 MDT (  = 1)MST (  = 0)  Tree (  = 0.5)

19. Columbia University 19 The  Tree Algorithm It makes a pioneer attempt on relating data aggregation performance to the generation of routing topologies which minimize the total energy cost for data funneling. It can easily adapt to the variations in aggregation performances through the adjustment of a single parameter. Impacts

20. 3. Performance Evaluation

21. Columbia University 21 Performance Evaluation In order to evaluate the performance of the  tree algorithm, we need a data aggregation model. A data aggregation model describes the amount of data reduction that can be achieved in a network. As a ground work, we begin with the simple Fixed-Ratio Data Aggregation Model. Introduction

22. Columbia University 22 Performance Analysis In the fixed-ratio model, data is always compressed by the same ratio c at each forwarding node. Introduction LcLc2Lc2LciLciL … 01i2

23. Columbia University 23 Performance Analysis  tree can always find the network topology with the minimum energy cost if we assume: (1) a fixed-ratio data aggregation model (2) link weight = (distance between two nodes) n, where n is the path loss exponent Optimality of  Tree for Fixed-Ratio Model

24. Columbia University 24 Performance Analysis Proof: wKwK w K-1 w K-2 w1w1 … KK-11K-2 0 Let w i = (distance between nodes i and i-1) n  transmission power on the link Optimality of  Tree for Fixed-Ratio Model

25. Columbia University 25 Performance Analysis By the definition of the  tree algorithm, the distance from node K to node 0 D K = w K +  D K-1 = w K +  (w K-1 +  D K-2 ) … = w K +  w K-1 +  2 w K-2 + … +  K-1 w 1 ………… (1) wKwK w K-1 w K-2 w1w1 … KK-11K-2 0 Optimality of  Tree for Fixed-Ratio Model

26. Columbia University 26 Performance Analysis With a fixed compression ratio c, the total energy for sending a unit of data from node K to node 0 E K =  Energy consumed on each link  [w K + cw K-1 + c 2 w K-2 + … + c K-1 w 1 ] ………… (2) 1cc2c2 c K-1 wKwK w K-1 w K-2 w1w1 … KK-11K-2 0 Optimality of  Tree for Fixed-Ratio Model

27. Columbia University 27 Performance Analysis D K = w K +  w K-1 +  2 w K-2 + … +  K-1 w 1 ………… (1) E K  [w K + cw K-1 + c 2 w K-2 + … + c K-1 w 1 ] ………… (2) By comparing Eqns. (1) and (2), we find that D K  E K if  is chosen to be c. Therefore, we can prove the optimality of  tree for the fixed-ratio model. Optimality of  Tree for Fixed-Ratio Model

28. Columbia University 28 Performance Analysis Simulation Results Simulation Settings  200 sensors are spread randomly over a 30  30 region with a sink at the center  Compression ratio = 0.8 Define the total energy cost of a topology as  (Distance) n No. of bits transmitted on a link after data aggregation No. of bits in a message Energy Cost =  all links

29. Columbia University 29 Performance Analysis The total energy costs are summarized as follows: Simulation Results Path Loss Exp. (n)  = 0 MST  = 1 MDT  = 0.8 22302 (8.7%)2763 (30.5%)2118 34360 (6.3%)5512 (34.3%)4103 48892 (3.7%)10033 (17%)8574

30. Columbia University 30 Performance Analysis  Tree Topology with  = 0.8 and path loss exponent = 4 Simulation Results

31. 4. Work in Progress

32. Columbia University 32 Work in Progress Apply information theory to defining a generic data aggregation model, taking into consideration possible temporal and spatial correlations.

33. Columbia University 33 Work in Progress Overlapping-Area Data Aggregation Model Sensing Range R Sensor Common Data among the Three Sensors Larger R → Longer range of spatial correlation

34. Columbia University 34 Work in Progress Based on the refined data aggregation model, evaluate the performance of  tree. E.g. Percentage reduction on total energy cost with respect to node density and sensor-to-sink ratio, as compared to MST and MDT. Investigate the relationship between the choice of  and the data aggregation performances.

35. Columbia University 35 Work in Progress Study the overhead in generating  trees. Find out the response of the algorithm at different levels of node mobility. Use optimal routing to generate optimal trees and compare these trees with best  trees.

36. Columbia University 36 References D. Bertsekas and R. Gallager. Data Networks. Prentice- Hall, Upper Saddle River, NJ, 1992. N.F. Maxemchuk. Video Distribution on Multicast Networks. IEEE JSAC, 15(3): 357-372, April 1997.