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Xin LiuComputer Science DepartmentUniversity of California, Davis

Joint work with P. Mohapatra

On the Deployment of Wireless Sensor Networks

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Network Deployment

Many-to-one communication Data from all nodes directed to a sink

node/fusion center Unbalanced traffic load Uneven power consumption

Limitations on network lifetime if uniformly distributed “Important” nodes in the route die quickly

Capacity bottleneck and Power bottleneck Desire for long-lived sensor networks

Linear and planar networks

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Many-to-One Communication

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Precise deployment With access Expensive nodes Higher layer of a hierarchical structure

Random deployment No access Cheap nodes Lower layer of the hierarchy Coverage and connectivity issues

Precise vs. Random Deployment

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Maximize coverage area Given the desired lifetime and # of node

available Maximize the lifetime of the network

Given the number of nodes and coverage area Minimize the number of nodes required

Given the coverage area and the desired lifetime

Consider large networks with long lifetime requirements

Objectives

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Why linear networks? Applications: Traffic monitoring, border line control,

train rail monitoring, etc. Model narrow-and-long networks

Great Duck Island deployment Tractability, insights for general cases

Highly asymmetric traffic load & location-dependent power consumption

Focus on communications What options do we have?

Linear Networks

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Possible Approaches

More energy for nodes with heavier load

More nodes in the area closer to the sink

Nodes closer to each other

Load balancingDeployment involves

topology control, routing, power allocation

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System Model

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Total energy constraint: Energy can be arbitrarily allocated among

nodes The network dies when no energy left

Thus,

i

Total Energy Constraint

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Problem Formulation

Numerical results as benchmark

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Arbitrary energy allocation is impractical

Performance benchmark More realistic: homogenous individual

energy constraint Network lifetime: first node dies Complexity: routing and associated

power allocation options

Individual power constraint

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Homogenous initial energy allocation Observation: longer hops consume

more energy “jump” may not be a good idea

Observation: we do not want residual energy when the network dies. Power consumption per unit time should

be the same for all nodes Consider large T (desired lifetime)

A Greedy Algorithm

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A Greedy Algorithm Cont’d

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Benchmark vs. Greedy

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Cont’d

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Numerical Result

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Individual vs. greedy

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Good news: the effect of arbitrary energy allocation is negligible

Greedy performs very well Conjecture: greedy is optimal in the case

of individual energy constraints

Observations

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Closed-form for Greedy

Lifetime, nodes, and coverage

=4, 19% more node to double lifetime

=4, 138% more node to double coverage

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Assume the same communication model Consider receiving power, idling power,

etc. Assume negligible sensing/sleep power Assume perfect synchronization These power consumptions will decrease

dramatically (hopefully)

Transmit at maximum power/rate Keep awaking time as short as possible

Other Power Consumption

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The other power consumption is well modeled by a power efficiency factor.

Pmax: maximum transmission power by the antenna

Pa: power consumed by the transmitter other than the power emitted by the antenna

Pr: receiving power Transmit at maximum rate, short duration,

less energy consumption

Other Power Consumption

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Decrease in transmission distance does not decrease per-bit energy consumption Nodes very close Limit on modulation and coding

A bound on the distance

Power Attenuation Model

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Performance Evaluation

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Non-uniform Data Density

Density varies over locations Greedy scheme adapts well

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Non-uniform Density Cont’d

Greedy scheme performs well in the presence of estimation errors <2% lifetime degradation <1% additional nodes

Uniform deployment Lifetime: 35% and 47%

Random deployment <1% lifetime

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Data within 2-D area is aggregated to a sink node

Much more complicated Coverage Potential triangular routes Large search space

Heuristic solution based on insights from the linear network Star mode Linear approximation

Planar Networks

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Conclusions

Data back-hauling in a many-to-one network Traffic load vs. communication energy

consumption Optimal vs. greedy Lifetime, # of nodes, and network coverage Various issues:

Miscellaneous power consumption Minimum distance constraint Non-uniform data density

Future work: Planar networks Data compression and aggregation