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Transcript of Tree in Sensor Network Patrick Y.H. Cheung, and Nicholas F. Maxemchuk, Fellow, IEEE 3 rd New York...
![Page 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)](https://reader034.fdocuments.net/reader034/viewer/2022051418/5697bff01a28abf838cbad69/html5/thumbnails/1.jpg)
Tree in Sensor Network
Patrick Y.H. Cheung, and Nicholas F. Maxemchuk, Fellow, IEEE
3rd New York Metro Area Networking Workshop (NYMAN 2003)
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NYMAN 03• xxxxx• xxx•...
Overview
Routing Problem in Sensor Network
The Tree Algorithm
Performance Evaluation
Work in Progress
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1. Routing Problem in Sensor Network 1. Routing Problem in Sensor Network
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Routing Problem in Sensor Network
Introduction
DataProcessing
Center
Sensor
Sink
Network Infrastructure
Data Flow
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Routing Problem in Sensor Network
Introduction
Sensor Network vs. Conventional Network
Perform data collection Point-to-point communications
Compress data on the way Data is transparent
Impulse arrival process triggered by an event
Poisson arrival process
Sensor Network Conventional Network
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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.
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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.
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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
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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
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2. The 2. The Tree Algorithm Tree Algorithm
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The The Tree Algorithm 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
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The The Tree Algorithm 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
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The The Tree Algorithm Tree Algorithm
How affects the “shape” of a tree.
Effects of
MDT ( = 1) MST ( = 0) Tree
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The The Tree Algorithm Tree Algorithm
A Routing Example
MDT ( = 1)
4
2
1
2
3 43
4
5.5
[0]
[2]
[5.5]
MST ( = 0) Tree ( = 0.5)
1
2
3 43
4 4
2
5.5
[0]
[2]
[5.5]
1
2
3 43
4 4
2
5.5
[0]
[2]
[5.5]
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The The Tree Algorithm Tree Algorithm
A Routing Example
4
[0]1
2
3 43
4
2
5.5
[0]
[5.5] [5]
1
2
3 43
4 4
2
5.5
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[2.5]
[5.5]
[1]
1
2
3 43
4 4
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[0]
[2]
[5.5][6] [4] [4] [5]
MDT ( = 1) MST ( = 0) Tree ( = 0.5)
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[5.5]
The The Tree Algorithm Tree Algorithm
A Routing Example
[2.5]3
[0]1
2
3 4
4 4
2
5.5
[5]
[1]
1
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3 43
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[5.5][6] [4]
4
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1
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3 43
4
5.5
[0]
[0]
[0] [3]
MDT ( = 1) MST ( = 0) Tree ( = 0.5)
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[5.5]
The The Tree Algorithm Tree Algorithm
A Routing Example
3[2.5]
[0]
[2.5]
1
2
3 4
4 4
2
5.5
[1]
1
2
3 43
4 4
2
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[2]
[5.5][6]3
1
2
3 4
4 4
2
5.5
[0]
[0]
[0] [0]
MDT ( = 1) MST ( = 0) Tree ( = 0.5)
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The The Tree Algorithm Tree Algorithm
A Routing Example
1
2
3 4
4 4
2
1
2
3 4
4
2
5.5
3
1
2
3 4
4
2
MDT ( = 1) MST ( = 0) Tree ( = 0.5)
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The The Tree Algorithm 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
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3. Performance Evaluation 3. Performance Evaluation
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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
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Performance Analysis
In the fixed-ratio model, data is always compressed by the same ratio c at each forwarding node.
Introduction
L cL c2L ciL
…0 1 i2
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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
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Performance Analysis
Proof:
wK wK-1 wK-2 w1…K K-1 1K-2 0
Let wi = (distance between nodes i and i-1)n
transmission power on the link
Optimality of Tree for Fixed-Ratio Model
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Performance Analysis
By the definition of the tree algorithm, the distance from node K to node 0
DK = wK + DK-1
= wK + (wK-1 + DK-2)
…
= wK + wK-1 + 2 wK-2 + … + K-1 w1 ………… (1)
wK wK-1 wK-2 w1…K K-1 1K-2 0
Optimality of Tree for Fixed-Ratio Model
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Performance Analysis
With a fixed compression ratio c, the total energy for sending a unit of data from node K to node 0
EK = Energy consumed on each link
[wK + cwK-1 + c2 wK-2 + … + cK-1 w1] ………… (2)
1 c c2 cK-1
wK wK-1 wK-2 w1
…K K-1 1K-2 0
Optimality of Tree for Fixed-Ratio Model
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Performance Analysis
DK = wK + wK-1 + 2 wK-2 + … + K-1 w1 ………… (1)
EK [wK + cwK-1 + c2 wK-2 + … + cK-1 w1] ………… (2)
By comparing Eqns. (1) and (2), we find that DK EK 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
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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 messageEnergy Cost =
all links
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Performance Analysis
The total energy costs are summarized as follows:
Simulation Results
Path Loss Exp. (n) = 0MST
= 1MDT
= 0.8
2 2302 (8.7%) 2763 (30.5%) 2118
3 4360 (6.3%) 5512 (34.3%) 4103
4 8892 (3.7%) 10033 (17%) 8574
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Performance Analysis
Tree Topology with = 0.8 and path loss exponent = 4
Simulation Results
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4. Work in Progress 4. Work in Progress
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Work in Progress
Apply information theory to defining a generic data aggregation model, taking into consideration possible temporal and spatial correlations.
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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
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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.
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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.
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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.