1. On the Topology of Wireless Sensor Networks Sen Yang, Xinbing Wang, Luoyi Fu Department of Electronic Engineering, Shanghai Jiao Tong University, China Email: {twood,xwang8,fly}@sjtu.edu.cn

2. 2 Outline Introduction  Motivations  Objectives System Models Topology of Heterogeneous WSNs Without Obstacles Topology of Heterogeneous WSNs With Obstacles Summary On the Topology of Wireless Sensor Networks 2

3. Motivation [1] P. Gupta and P. R. Kumar, “The capacity of wireless networks”, in IEEE Transaction on Information Theory, 2000. [2] P. Li and Y. Fang, “The Capacity of heterogeneous wireless networks,” in Proc. IEEE INFOCOM, 2010. On the Topology of Wireless Sensor Networks 3

4. 4 Motivation  Network Topology  We investigate throughput capacity of networks with the following topologies and then generalize the results to get some useful conclusions. Uniform DistributionCentralized DistributionMulti-centralized Distribution

5. Motivation  In practice, sensor nodes may not be placed uniformly, which could have a huge impact on network performance, including the capacity [3]. [3] G. Alfano, M. Garetto, E. Leonardi, “Capacity Scaling of Wireless Networks with Inhomogeneous Node Density: Upper Bounds,” IEEE Journal on Selected Areas in Communications, vol. 27, no. 7, Sept. 2009. On the Topology of Wireless Sensor Networks 5 Wireless Networks with Inhomogeneous Node Density. [3]

6. Motivation  In practice, sensor nodes may not be placed uniformly, which could have a huge impact on network properties, including the capacity [3].  Also, sensor networks are often deployed in complex environments, such as battle fields or mountainous areas, and there are often many obstacles distributed in these regions. [3] G. Alfano, M. Garetto, E. Leonardi, “Capacity Scaling of Wireless Networks with Inhomogeneous Node Density: Upper Bounds,” IEEE Journal on Selected Areas in Communications, vol. 27, no. 7, Sept. 2009. On the Topology of Wireless Sensor Networks 6 What are the best network topologies for given network regions, especially for networks with obstacles?

7. On the Topology of Wireless Sensor Networks 7 Objective  We study  How does the node distribution influence the throughput capacity?  What’s the optimal nodes distribution on given conditions?  We obtain  Some guidelines on generating the optimal topology for flat network areas.  An algorithm of linear complexity to generate optimal sensor nodes’ topologies for any given obstacle distributions.

8. 8 Outline Introduction System Models Topology of Heterogeneous WSNs Without Obstacles Topology of Heterogeneous WSNs With Obstacles Summary On the Topology of Wireless Sensor Networks 8

9. 9 System Model

10. On the Topology of Wireless Sensor Networks 10 System Model  Here, “blocked” has two implications:  No sensor node can be distributed in these cells;  Nodes’ communication cannot cross them directly.

11. On the Topology of Wireless Sensor Networks 11 System Model [2] P. Li and Y. Fang, “The Capacity of heterogeneous wireless networks,” in Proc. IEEE INFOCOM, 2010.

12. On the Topology of Wireless Sensor Networks 12 System Model  Network Topology  We investigate throughput capacity of networks with the following topologies and then generalize the results to get some useful conclusions. Uniform DistributionCentralized DistributionMulti-centralized Distribution

13. On the Topology of Wireless Sensor Networks 13 System Model  Routing Strategies  Routing Strategy I - for networks without obstacles: [2] P. Li and Y. Fang, “The Capacity of heterogeneous wireless networks,” in Proc. IEEE INFOCOM, 2010.

14. On the Topology of Wireless Sensor Networks 14 System Model  Routing Strategies  Routing Strategy II - for networks with obstacles:

15. On the Topology of Wireless Sensor Networks 15 System Model  Routing Strategies  Routing Strategy II - for networks with obstacles:

16. On the Topology of Wireless Sensor Networks 16 Introduction System Models Topology of Heterogeneous WSNs Without Obstacles  Capacity of Heterogeneous WSNs without Obstacles  General Properties of “Combined Networks”  Impact of Network Topology on Throughput Capacity Topology of Heterogeneous WSNs With Obstacles Summary

17. On the Topology of Wireless Sensor Networks 17 Capacity of WSNs w.o. Obstacles  Achievable throughput in normal mode [2] P. Li and Y. Fang, “The Capacity of heterogeneous wireless networks,” in Proc. IEEE INFOCOM, 2010. Maximal number of flows across a cell Virtual destination nodes

18. On the Topology of Wireless Sensor Networks 18 Capacity of WSNs w.o. Obstacles  Achievable throughput in helping mode  In the first phase  In the second phase  In the third phase [2] P. Li and Y. Fang, “The Capacity of heterogeneous wireless networks,” in Proc. IEEE INFOCOM, 2010.

19. On the Topology of Wireless Sensor Networks 19 Capacity of WSNs w.o. Obstacles  Throughput capacity of the network  Uniform Network  Centralized Network  Multi-centralized Network

20. On the Topology of Wireless Sensor Networks Properties of “Combined Networks”  Impacts of combination:  The interference of different sub- networks  Flows passing through a cell 20

21. On the Topology of Wireless Sensor Networks Properties of “Combined Networks” 21

22. On the Topology of Wireless Sensor Networks 22 Impact of Topology on Capacity  Sensor Nodes’ Topology  Theorem 5: For the topology of sensor nodes, if the value range of nodes distribution’s PDF is bounded, the gap in achievable throughput of non-uniform networks and uniform networks is at most a constant time.  For networks without helping nodes, uniform sensor nodes’ distribution is order optimal on maximizing throughput capacity.

23. On the Topology of Wireless Sensor Networks 23 Impact of Topology on Capacity  Helping Nodes’ Topology

24. On the Topology of Wireless Sensor Networks 24 Impact of Topology on Capacity  Helping Nodes’ Topology – for uniform sensor nodes  Theorem 6: For networks with uniformly distributed sensor nodes, regularly distributed helping nodes are optimal to maximize the network throughput capacity.

25. On the Topology of Wireless Sensor Networks 25 Impact of Topology on Capacity  Helping Nodes’ Topology – for non-uniform sensor nodes  Theorem 7: For networks with non-uniformly distributed sensor nodes, though regularly distributed helping nodes are no longer optimal, any improvement on the helping nodes’ topology cannot change the scale of network throughput capacity.  Regularly distributed helping nodes are optimal on maximizing the throughput capacity in the sense of scaling law.

26. On the Topology of Wireless Sensor Networks 26 Introduction System Models Topology of Heterogeneous WSNs Without Obstacles Topology of Heterogeneous WSNs With Obstacles  Algorithm to Obtain the Optimal Network Topology  Complexity of the Algorithm Summary

27. On the Topology of Wireless Sensor Networks 27 The Optimization Algorithm  Algorithm - “Wall with Gate”:  Step 1) Transform the original problem to a simple scenario - “Wall with Gate”.

28. On the Topology of Wireless Sensor Networks 28 The Optimization Algorithm  Algorithm - “Wall with Gate”:  Step 2) Transform the problem with obstacles to a problem without obstacles. Virtual destination nodes

29. On the Topology of Wireless Sensor Networks 29 The Optimization Algorithm  Algorithm - “Wall with Gate”:  Step 2) Transform the problem with obstacles to a problem without obstacles.

30. On the Topology of Wireless Sensor Networks 30 The Optimization Algorithm  Algorithm - “Wall with Gate”:  Step 3) For the degraded sub-network, use techniques and conclusions given in previous sections to generate an optimal sub-network topology

31. On the Topology of Wireless Sensor Networks 31 The Optimization Algorithm  Algorithm - “Wall with Gate”:  Step 4) Combine all of the sub-networks’ topology to obtain the overall topology of the network

32. On the Topology of Wireless Sensor Networks 32 The Optimization Algorithm  More words about the algorithm:  This is a centralized algorithm which results in a global optimal solution  Since the gate areas here might be relatively large, nodes distribution in these areas can no longer be ignored and Step 2 – 3 must be applied to these gate areas.

33. On the Topology of Wireless Sensor Networks 33 Complexity of the Algorithm  How to divide the network?  Method I: take blocked cells in a row (either vertical or horizontal) as a wall and cells without obstacles in this row as gates.

34. On the Topology of Wireless Sensor Networks 34 Complexity of the Algorithm  How to divide the network?  Method II: Firstly construct a wall in the row with the most number of blocked cells, dividing the network area into two parts. For each part, repeat this step iteratively until all the blocked cells are crossed by at least one wall.

35. On the Topology of Wireless Sensor Networks 35 Complexity of the Algorithm

36. On the Topology of Wireless Sensor Networks 36 Introduction System Models Topology of Heterogeneous WSNs Without Obstacles Topology of Heterogeneous WSNs With Obstacles Summary

37. On the Topology of Wireless Sensor Networks 37 Summary  For networks without obstacles, we find that uniformly distributed sensor nodes and regularly distributed helping nodes have some advantages in improving the throughput capacity.  For networks without obstacles, we propose an algorithm of linear complexity to generate optimal sensor nodes’ topology for any given obstacle distribution.

38. 38 Thank you for listening Sen Yang, Xinbing Wang, Luoyi Fu Email: {twood,xwang8,fly}@sjtu.edu.cn On the Topology of Wireless Sensor Networks