Maximizing Lifetime per
Unit Cost in Wireless
Sensor Networks
Yunxia Chen
Department of Electrical and Computer
Engineering
University of California, Davis, 95616
Outline
Wireless sensor network.
 Network model.
 Lifetime per unit cost.
 Number of sensors and sensor placement.
 Numerical results.
 Conclusion.

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Wireless Sensor Networks
Sensors: low-cost, low-power, energyconstrained, limited computation and
communication capability.
 Gateways: powerful.
 Applications:

 Transportation
monitoring
 Temperature monitoring
 ……
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Gateway nodes
Sensor nodes
3
Basic Operation

Sensors:
 Monitor
certain phenomenon.
 Report to the gateway nodes.
Event-driven: triggered by the event of interest.
 Demand-driven: triggered by the request from the
gateway nodes.


Gateways:
 Collect
and process the data from sensors.
 Ensure end-user can access the data.
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Sensor Deployment

Random deployment
 Battlefield
or disaster areas.
 Generally, more sensors are used to ensure the
performance.

Deterministic deployment
 Friendly
or accessible environment.
 Optimal sensor deployment schemes which
maximize the lifetime of the network or the
coverage of the network.
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Network Model





An event-driven linear wireless sensor network.
s0
s1
s2
s3
sN 2
sN 1
0
d1
d2
d3
d N 2
d N 1
L
Each sensor monitors the region between itself and its
right neighbor.
Generates and sends a packet to its left neighbor
when an event occurs.
Packets are replayed one after another to the gateway.
The event of interest is a Poisson random process.
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Two Questions
How many sensors should we use?
 How should we place these sensors?

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Definitions
 L





: maximum coverage area of the network.
D : maximum sensing region of each sensor.
 : mean arrival rate of the event.
d k : distance to the gateway node k  0,1, N  1 .
E0 : initial energy of each sensor.
etx : energy required to transmit one packet over 1m.
 The
energy required to transmit one packet over d m

distance is etx d where  is the path loss exponent.
 es
: energy required to keep sensors alive.
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Network Lifetime

Sensor lifetime: the amount of time until the
sensor runs out of energy.
Tk 

E
Intial energy
 0
Energy consumptio n per unit time
Ek
Network lifetime: the amount of time until the
first sensor in the network runs out of energy.
T  min Tk

Given the number of sensors, what is the
maximum network lifetime?
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Motivation


Different schemes are developed to maximize the
network lifetime with N sensors.
Network lifetime can be increased by dividing the
sensors into several small groups and enabling one
group each time.
 4N
-> 4T
 2N + 2N -> 6T

# of sensors
Max. Lifetime
N
T
2N
3T
4N
4T
How many sensors should we enable each time?
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Lifetime per Unit Cost

Definition: network lifetime divided by the number
of sensors.
LC 


T
N
Characterizes the rate at which the network lifetime
increases as the number of sensors increases.
Optimal number of sensors in each group = the
number of sensors that maximizes the lifetime per
unit cost.
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Greedy Deployment Scheme




Intuitively, the network lifetime is maximized when
all the sensors run out of energy at the same time.
Greedy sensor placement scheme depends on the
number of sensors.
Maximizing network lifetime = Minimizing the
transmission energy [Cheng et. al. 2004].
Maximizing lifetime per unit cost = Minimizing total
energy consumption.
E
T
 0
N NEk
.
LC 
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Average Energy Consumption

The average energy consumption of each sensor per
unit time depends on the sensor placement of the
network.
 d
Ek  etx (d k  d k 1 ) 1  k
L

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
  es

13
Problem Formulation


Given the coverage area L , what is the number of
sensors and the corresponding deployment scheme
that maximizes the lifetime per unit cost?
A multivariate non-linear optimization problem:
Minimize : .NEk
Subject to : .E2  E3    E N 1
.0  d1  D
.0  d k  d k 1  D, k  2,, N  1
.0  L  d N 1  D
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Numerical Results






unit per packet over distance 1 m.
All the energy quantities are normalized by etx .
E0  10 units.
D  2m .
L  10m .
 2.
etx  1
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Sensor Placement
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Lifetime per Unit Cost
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Optimal Number of Sensors
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Conclusion



We observed that network lifetime can be increased
by dividing sensors into small groups and enabling
one group each time.
We proposed a new performance metric, the lifetime
per unit cost.
We studied the number of sensors and the sensor
deployment scheme that maximizes the lifetime per
unit cost.
 Enable small
number of sensors when the mean arrival rate
of the event is low or the sensing energy consumption is
small.
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Thanks!
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