Tree in Sensor Network

Tree in Sensor Network

Patrick Y.H. Cheung, and Nicholas F. Maxemchuk, Fellow, IEEE

3rd New York Metro Area Networking Workshop (NYMAN 2003)

Columbia University 2

NYMAN 03• xxxxx• xxx•...

Overview

Routing Problem in Sensor Network

The Tree Algorithm

Performance Evaluation

Work in Progress

1. Routing Problem in Sensor Network 1. Routing Problem in Sensor Network



Introduction

DataProcessing

Center

Sensor

Sink

Network Infrastructure

Data Flow



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



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.



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.



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



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

2. The 2. The Tree Algorithm Tree Algorithm


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



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



How affects the “shape” of a tree.

Effects of

MDT ( = 1) MST ( = 0) Tree



A Routing Example

MDT ( = 1)

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A Routing Example

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MDT ( = 1) MST ( = 0) Tree ( = 0.5)


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A Routing Example

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A Routing Example

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A Routing Example

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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

3. Performance Evaluation 3. Performance Evaluation


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


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



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



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




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




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




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.




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



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



Tree Topology with = 0.8 and path loss exponent = 4

Simulation Results

4. Work in Progress 4. Work in Progress


Work in Progress

Apply information theory to defining a generic data aggregation model, taking into consideration possible temporal and spatial correlations.


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


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.


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.


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.

Documents

Tree in Sensor Network