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Wireless Sensor Placement for Reliable and Efficient Data Collection Edo Biagioni and Galen Sasaki University of Hawaii at Manoa

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Overview Wireless Sensor Networks Case study: an ecological wireless sensor network Design Considerations Regular Deployments Linear and other arrangements

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Sensor Networks are Useful Ecological study: under what conditions does the endangered species thrive? Ecological study: under what conditions does the endangered species thrive? Knowing the environment aids in setting goals or controlling processes Knowing the environment aids in setting goals or controlling processes Many applications, including ecological, industrial, and military Many applications, including ecological, industrial, and military

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Ad-hoc Wireless Networks Low-power operation Low-power operation Range-limited radios Range-limited radios Ad-hoc networking: each node forwards data for other nodes Ad-hoc networking: each node forwards data for other nodes Data may be combined en route Data may be combined en route

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Wireless Sensor Network Design How densely must we sample the environment? How densely must we sample the environment? What is the radio communications range? What is the radio communications range? How much reliability do we have, and how does it improve if we add more units? How much reliability do we have, and how does it improve if we add more units? How many units can we afford? How many units can we afford?

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The PODS project at the University of Hawaii Ecological sensing of Rare Plant environment Ecological sensing of Rare Plant environment Temperature, sunlight, rainfall, humidity Temperature, sunlight, rainfall, humidity High-resolution images High-resolution images Kim Bridges, Brian Chee Kim Bridges, Brian Chee

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Pod placement Intensive deployment where the plant does grow Intensive deployment where the plant does grow Interested also in where the plant does not grow Interested also in where the plant does not grow Connection to the internet is also a line of sensors Connection to the internet is also a line of sensors Sub-region

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Practical Constraints Higher radios have more range Higher radios have more range Camouflage Camouflage Plant densities may vary Plant densities may vary Different units may have different sensors Different units may have different sensors Ignored in this talk Ignored in this talk

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Design Goals for Deployment We are given a 2-dimensional square region with total area A Minimize the maximum distance between any point in A and the nearest sensor Minimize the maximum distance between any point in A and the nearest sensor Keep the distance between adjacent sensors less than r Keep the distance between adjacent sensors less than r Measure point values, compute gradients and significant thresholds Measure point values, compute gradients and significant thresholds

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Design Considerations Financial and other constraints often limit the total number of nodes, N Financial and other constraints often limit the total number of nodes, N Failure of individual nodes should not disable the entire network Failure of individual nodes should not disable the entire network Reducing the transmission range improves the energy efficiency Reducing the transmission range improves the energy efficiency

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Regular Deployments Square, triangular, or hexagonal tiles Square, triangular, or hexagonal tiles Nodes must be within range r of their neighbors Nodes must be within range r of their neighbors Sampling distance δ Sampling distance δ Degree 4, 6, or 3 provides redundancy Degree 4, 6, or 3 provides redundancy Which is best? Which is best? a (a) Square tiles (b) Triangle tile (c) Hexagon tile

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Computing with N, r, δ Standard formulas for tile area (α) and for distance to the center of the tile Standard formulas for tile area (α) and for distance to the center of the tile Distance to center < δ Distance to center < δ Distance between nodes < r Distance between nodes < r Each node is part of c = (6, 4, or 3) tiles Each node is part of c = (6, 4, or 3) tiles N = (A/α)/c, where A/α is the number of tiles N = (A/α)/c, where A/α is the number of tiles

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Main Results for Regular Grids N is proportional to the surface area of A N is proportional to the surface area of A if r < δ, hexagonal deployment minimizes N, and N is inversely proportional to r 2 if r < δ, hexagonal deployment minimizes N, and N is inversely proportional to r 2 If δ < r, triangular deployment minimizes N, and N is inversely proportional to δ 2 If δ < r, triangular deployment minimizes N, and N is inversely proportional to δ 2 Triangular, square, or hexagonal are within a factor of two of each other Triangular, square, or hexagonal are within a factor of two of each other

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Sparse Grids If r < δ, we can reduce the number of nodes by going to sparse grids (sparse meshes) If r < δ, we can reduce the number of nodes by going to sparse grids (sparse meshes) Communication distance remains small Communication distance remains small the number of nodes may drop substantially the number of nodes may drop substantially 3 nodes per side, s=3 3 nodes per side, s=3 S=3

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Main Results for Sparse Grids Communication radius r, tile side a = r * s Communication radius r, tile side a = r * s N is inversely proportional to a and to r N is inversely proportional to a and to r The degree of most nodes is two, so reliability is reduced – the same as for linear deployments The degree of most nodes is two, so reliability is reduced – the same as for linear deployments

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1-Dimensional Deployment Many common applications: along streams, roads, ridges Many common applications: along streams, roads, ridges Requires relatively few nodes Requires relatively few nodes With the least number of nodes for a given r, network fails if a single node fails With the least number of nodes for a given r, network fails if a single node fails How well can we do if we double the number of nodes? How well can we do if we double the number of nodes?

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Protection against node failures Paired Paired Inline Inline r r

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Paired and Inline Performance For inline, two successive node failures disconnect the network For inline, two successive node failures disconnect the network For paired, failure of the two nodes of a pair disconnects the network For paired, failure of the two nodes of a pair disconnects the network The former is about twice as likely The former is about twice as likely

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Sampling a Gradient If we know the gradient, a linear deployment is sufficient If we know the gradient, a linear deployment is sufficient A gradient can be computed from three samples in a triangle A gradient can be computed from three samples in a triangle Variable gradients need more and longer baselines, as do threshold determinations Variable gradients need more and longer baselines, as do threshold determinations Grids and sparse grids measure gradients well Grids and sparse grids measure gradients well

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Quantifying a gradient The differences between pairs of samples help determine the gradient

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Minimizing the number of nodes The ultimate sparse grid: a circle The ultimate sparse grid: a circle Tolerates single node failures Tolerates single node failures Even sampling in all directions Even sampling in all directions Lines outward from the center: a star Lines outward from the center: a star Center is well covered Center is well covered Star-3, Star-4, Star-5, Star-m Star-3, Star-4, Star-5, Star-m

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Summary Many regular deployments Generally, N and r are given, sampling distance is allowed to vary Tradeoff between N and redundancy: sparse grids allow large sampling distance Lines, circles, stars are optimal when N is small, can provide information about gradients

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Acknowledgements Kim Bridges Brian Chee and many students on the Pods project, including Michael Lurvey and Shu Chen DARPA (Pods funding) Hawaii Volcanoes National Park

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