Tree in Sensor Network

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? 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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Overview

• Routing Problem in Sensor Network
• The ? Tree Algorithm
• Performance Evaluation
• Work in Progress

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Routing Problem in Sensor Network
Introduction
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Routing Problem in Sensor Network
Introduction

• Sensor Network vs. 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
Our Approach

• 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.

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Routing Problem in Sensor Network
Our Approach

• 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.

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The ? Tree Algorithm
Basic Concepts

• It is the same as the Dijkstras Algorithm,
  except that we label the next closest node with
• ? ? (distance to the destination)
• The parameter ? (0lt?lt1) is adjusted according to
  the data aggregation performance, in order to
  find topologies which minimize total energy
  costs.

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The ? Tree Algorithm
Effects of ?

• 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.

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The ? Tree Algorithm
Effects of ?

• How ? affects the shape of a tree.

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The ? Tree Algorithm
A Routing Example
MDT (? 1)
MST (? 0)
? Tree (? 0.5)
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The ? Tree Algorithm
A Routing Example
MDT (? 1)
MST (? 0)
? Tree (? 0.5)
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The ? Tree Algorithm
A Routing Example
MDT (? 1)
MST (? 0)
? Tree (? 0.5)
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The ? Tree Algorithm
A Routing Example
MDT (? 1)
MST (? 0)
? Tree (? 0.5)
2.5
5?.5
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The ? Tree Algorithm
A Routing Example
MDT (? 1)
MST (? 0)
? Tree (? 0.5)
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The ? Tree Algorithm
Impacts

• 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.

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Performance Evaluation
Introduction

• 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.

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Performance Analysis
Introduction

• In the fixed-ratio model, data is always
  compressed by the same ratio c at each forwarding
  node.

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Performance Analysis
Optimality of ? Tree for Fixed-Ratio Model

• ? 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

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Performance Analysis
Optimality of ? Tree for Fixed-Ratio Model

• Proof

Let wi (distance between nodes i and i-1)n ?
transmission power on the link
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Performance Analysis
Optimality of ? Tree for Fixed-Ratio Model

• 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)

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Performance Analysis
Optimality of ? Tree for Fixed-Ratio Model
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)
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Performance Analysis
Optimality of ? Tree for Fixed-Ratio Model

• 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.

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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

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Performance Analysis
Simulation Results

• The total energy costs are summarized as follows

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Performance Analysis
Simulation Results

• ? Tree Topology with ? 0.8 and path loss
  exponent 4

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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

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.