On the Topology of Wireless Sensor Networks Sen

On the Topology of Wireless Sensor Networks Sen Yang, Xinbing Wang, Luoyi Fu Department of Electronic Engineering, Shanghai Jiao Tong University, China Email: {twood, xwang 8, fly}@sjtu. edu. cn

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

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

Motivation q Network Topology Ø We investigate throughput capacity of networks with the following topologies and then generalize the results to get some useful conclusions. Uniform Distribution Centralized Distribution Multi-centralized Distribution On the Topology of Wireless Sensor Networks 4

Motivation q In practice, sensor nodes may not be placed uniformly, which could have a huge impact on network performance, including the capacity [3]. Wireless Networks with Inhomogeneous Node Density. [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

Motivation q In practice, sensor nodes may not be placed uniformly, which could have a huge impact on network properties, including the capacity [3]. q 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. What are the best network topologies for given network regions, especially for networks with obstacles? [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

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

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

System Model On the Topology of Wireless Sensor Networks 9

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

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

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

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

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

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

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

Properties of “Combined Networks” q Impacts of combination: Ø The interference of different subnetworks Ø Flows passing through a cell On the Topology of Wireless Sensor Networks 20

Impact of Topology on Capacity q Sensor Nodes’ Topology Ø 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. Ø For networks without helping nodes, uniform sensor nodes’ distribution is order optimal on maximizing throughput capacity. On the Topology of Wireless Sensor Networks 22

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

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

Impact of Topology on Capacity q Helping Nodes’ Topology – for non-uniform sensor nodes Ø 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. Ø Regularly distributed helping nodes are optimal on maximizing the throughput capacity in the sense of scaling law. On the Topology of Wireless Sensor Networks 25

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

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

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

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

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

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

The Optimization Algorithm q More words about the algorithm: Ø This is a centralized algorithm which results in a global optimal solution Ø 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. On the Topology of Wireless Sensor Networks 32

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

Complexity of the Algorithm q How to divide the network? Ø 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. On the Topology of Wireless Sensor Networks 34

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

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

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

Thank you for listening Sen Yang, Xinbing Wang, Luoyi Fu Email: {twood, xwang 8, fly}@sjtu. edu. cn On the Topology of Wireless Sensor Networks 38