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Maximizing Lifetime per Unit Cost in Wireless Sensor Networks

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Maximizing Lifetime per Unit Cost in Wireless Sensor Networks Powered By Docstoc
					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.



Mar. 18, 2005    EEC 273 Computer Networks   2
Wireless Sensor Networks
 Sensors: low-cost, low-power, energy-
  constrained, limited computation and
  communication capability.
 Gateways: powerful.
 Applications:
       Transportation monitoring
       Temperature   monitoring                    Gateway nodes
       ……                                          Sensor nodes


Mar. 18, 2005           EEC 273 Computer Networks                   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:
       Collectand process the data from sensors.
       Ensure end-user can access the data.
Mar. 18, 2005                EEC 273 Computer Networks            4
Sensor Deployment
   Random deployment
       Battlefieldor disaster areas.
       Generally, more sensors are used to ensure the
        performance.
   Deterministic deployment
       Friendlyor accessible environment.
       Optimal sensor deployment schemes which
        maximize the lifetime of the network or the
        coverage of the network.
Mar. 18, 2005          EEC 273 Computer Networks         5
Network Model
   An event-driven linear wireless sensor network.
                s0   s1   s2   s3                        sN 2     s N 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.

Mar. 18, 2005                       EEC 273 Computer Networks                   6
Two Questions
 How many sensors should we use?
 How should we place these sensors?




Mar. 18, 2005    EEC 273 Computer Networks   7
Definitions
 L     : maximum coverage area of the network.
     D : maximum sensing region of each sensor.

     : mean arrival rate of the event.

    d : distance to the gateway node k  0 ,1,  N  1 .
       k


    E : initial energy of each sensor.
        0



    e : energy required to transmit one packet over 1m.
       tx


       The      energy required to transmit one packet over d m
                              
            distance is e tx d where  is the path loss exponent.
 es        : energy required to keep sensors alive.

Mar. 18, 2005                 EEC 273 Computer Networks             8
Network Lifetime
   Sensor lifetime: the amount of time until the
    sensor runs out of energy.
                                 Intial energy                     E0
                Tk                                            
                       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 T k

   Given the number of sensors, what is the
    maximum network lifetime?
Mar. 18, 2005                   EEC 273 Computer Networks               9
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.
                                     # of sensors   Max. Lifetime
     4N -> 4T                             N             T
     2N + 2N -> 6T                       2N            3T
                                          4N            4T

   How many sensors should we enable each time?

Mar. 18, 2005          EEC 273 Computer Networks                    10
Lifetime per Unit Cost
   Definition: network lifetime divided by the number
    of sensors.
                                 T
                          LC 
                                 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.


Mar. 18, 2005          EEC 273 Computer Networks           11
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.
                             T       E0
.                     LC        
                             N       NE k


Mar. 18, 2005         EEC 273 Computer Networks        12
Average Energy Consumption
   The average energy consumption of each sensor per
    unit time depends on the sensor placement of the
    network.

                                                 d 
                E k   e tx ( d k  d k 1 )  1  k   e s
                                                   L 




Mar. 18, 2005                  EEC 273 Computer Networks        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    : . NE k
                Subject to : . E 2  E 3    E N 1
                             .0  d 1  D
                             . 0  d k  d k 1  D , k  2 ,  , N  1
                             . 0  L  d N 1  D

Mar. 18, 2005                      EEC 273 Computer Networks              14
Numerical Results
            unit per packet over distance 1 m.
      e tx  1

     All the energy quantities are normalized by e   tx   .
     E  10 units.
         0


     D  2m .

     L  10 m .

      2.




Mar. 18, 2005           EEC 273 Computer Networks              15
Sensor Placement




Mar. 18, 2005   EEC 273 Computer Networks   16
Lifetime per Unit Cost




Mar. 18, 2005   EEC 273 Computer Networks   17
Optimal Number of Sensors




Mar. 18, 2005   EEC 273 Computer Networks   18
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.

Mar. 18, 2005               EEC 273 Computer Networks              19
                Thanks!


Mar. 18, 2005   EEC 273 Computer Networks   20

				
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