on the topology of wireless sensor networks sen yang, xinbing wang, luoyi fu department of...
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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
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
Motivation
Capacity of wireless network is not scalable: in a static wireless network with nodes, the per-node capacity is
. Interference is the main reason behind.
Helping nodes are introduced to increase the network capacity
[2].
[1]1( )
logO
n n
[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
On the Topology of Wireless Sensor Networks 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 Distribution Centralized
Distribution
Multi-centralized Distribution
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]
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?
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.
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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
On the Topology of Wireless Sensor Networks 9
System Model
We consider dense networks with sensor nodes and helping nodes in a planar unit area.
All the sensor nodes are sources while only sensor nodes are randomly chosen as destinations.
The network is divided into non-overlapping cells with equal size. Nodes can communicate with each other
only when they are in the neighboring cells.
We apply a TDMA rotating scheduling scheme to bound the interference.
On the Topology of Wireless Sensor Networks 10
System Model
Obstacles
We assume there are number of obstacle nodes in the
network area, which can be arbitrarily or randomly distributed.
Cells are blocked when there are obstacle nodes in them.
Here, “blocked” has two implications:
No sensor node can be distributed in these cells;
Nodes’ communication cannot cross them directly.
On the Topology of Wireless Sensor Networks 11
System Model
Interference Model
The channel power gain is given as , where
denotes the distance of transmission, represents the path-loss
exponent.
Each cell in the network can work at a transmission rate , where
is a deterministic positive constant relevant to the cells’ scale
and is the channel bandwidth.[2]
[2] P. Li and Y. Fang, “The Capacity of heterogeneous wireless networks,” in Proc. IEEE
INFOCOM, 2010.
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 Distribution Centralized
Distribution
Multi-centralized Distribution
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
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.
1,max ,max ,max2 dij x yF N n N
1
,maxu
ij
WT
F
Maximal number of flows across a cell
Virtual destination nodes
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.
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
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
Theorem 4: For network composed of some isomorphic sub-networks, the throughput capacity of the overall
network, denoted by , and the throughput capacity of sub-network of same network scales, denoted by , have
the following relationship.
2020
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.
On the Topology of Wireless Sensor Networks 23
Impact of Topology on Capacity
Helping Nodes’ Topology
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.
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.
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
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”.
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
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.
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
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
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.
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.
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.
On the Topology of Wireless Sensor Networks 35
Complexity of the Algorithm
Complexity of the Algorithm
The algorithm complexity is when using network dividing method I and is when using method II.
On the Topology of Wireless Sensor Networks 36
Introduction
System Models
Topology of Heterogeneous WSNs Without Obstacles
Topology of Heterogeneous WSNs With Obstacles
Summary
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.
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Thank you for listening
Sen Yang, Xinbing Wang, Luoyi Fu
Email: {twood,xwang8,fly}@sjtu.edu.cn
On the Topology of Wireless Sensor Networks