Minimizing Energy Consumption with Probabilistic Distance Models in

Wireless Sensor Networks

Yanyan Zhuang, Jianping Pan, Lin Cai

University of Victoria, Canada

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Background & Related Work

Clustering Schemes Cluster Head (CH) + cluster nodes

two-tier hierarchical structure: simple node coordination

Multi-hop: avoid long-range transmissions

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Background & Related Work (cont.)

Grid-Based Clustering Partition: equal-sized squares

Facilitate data dissemination: sensors can transmit data without route setup in advance

Manhattan Walk Diagonal-First Routing

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Background & Related Work (cont.)

Variable-size Clustering traffic volume highly skewed → bottleneck

consume their energy much faster than other nodes → earlier breakdown of the network

Existing Work time synchronization/frequent message exchanges

linear network, or quasi-two-dimensional

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Distance Distribution Model

Wireless Transmitter

: data transmission rate

: a constant related to the environment

: path loss exponent [2,6]

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Distance Distribution Model

Energy consumption → node distance → average distance (?) → Average Distance Model

Grid structure & geometric property →

probabilistic distance distribution → Distance Distribution Model

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Coordinate Distributions

Two nodes in same grid (AB): U[0,1]

Two nodes in diagonal grids (PQ)

X1, Y1 ~ U[0,1] and X2, Y2 ~ U[-1,0]

Two nodes in parallel grids (RS)

X1, Y1, Y2 ~ U[0,1] and X2 ~ U[-1,0]

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Distance Distributions

Node distance:

Goal:

Four step derivation

Difference --> Square --> Sum --> Square Root

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Distance Distributions

Node distance:

Goal:

Four step derivation

Difference --> Square --> Sum --> Square Root

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(1) Difference distribution

Example: P and Q

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(2) Square distribution

Example: P and Q

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(3) Sum distribution

(4) Square-root distribution

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Example: P and Q

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PDF within a Unit Grid & Polyfit

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PDF between Parallel/Diagonal Grids

Parallel Diagonal

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Probabilistic Energy Optimization Simulation Setup: Friis Free Space & Two-Ray Ground

cross-over distance

: system loss factor

: rx/tx antenna height

: wavelength of the carrier signal

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Distance Verification

CDF vs. Simulation One-hop Energy Consumption

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Total Energy Consumption: Distance Distribution vs. Average Model

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Improvement: Variable Size Griding

P and Q

X1, Y1 ~ U[0,1-q]

X2, Y2 ~ U[-q(1-q),0]

R

X1 ~ U[-q,0], Y1 ~ U[0,1-q]

S

X2 ~ [-q, -q(1-q)], Y2 ~ U[-q(1-q),0]

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Distance Verification

CDF vs. Simulation One-hop Energy Consumption

CDF with q=0.4 and 0.7 One-Hop Energy Consumption with q=0.5

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Per-Grid/Total Energy Consumption vs. Size Ratio

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Conclusions

Energy consumption model based on distance distributions

Nonuniform grid-based clustering: both data traffic and energy consumption balanced

The importance of grid-based clustering and the optimal grid size ratio that can balance the overall energy consumption

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Thanks!

Q&A

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Coordinate Distributions

Two nodes in same grid (AB): U[0,1]

Two nodes in diagonal grids (PQ)

X1, Y1: U[0,1] and X2, Y2: U[-1,0]

Two nodes in parallel grids (RS)

X1, Y1, Y2: U[0,1] and X2: U[-1,0]

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X1, Y1 ~ U[0,1]

X2, Y2 ~ U[-1,0]

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Improvement: Variable Size Griding

PQ: X1, X2 ~ U[0,1-q] and Y1, Y2 ~ U[-q(1-q),0]

R: X1 ~ U[-q,0], Y1 ~ U[0,1-q]

S: X2 ~ [-q, -q(1-q)], Y2 ~ U[-q(1-q),0]

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Wireless Channel Model

: the data transmission rate

: a constant related to the environment

: path loss exponent [2,6]

: distance distribution function (poly fit appx)