Maximizing Network Lifetime using Reliable Energy Efficient Routing Protocol Based on Non Cooperative Game Theory for Wireless Sensor Networks

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Maximizing Network Lifetime using Reliable Energy Efficient Routing Protocol Based on Non Cooperative Game Theory for Wireless Sensor Networks Powered By Docstoc
					    International Journal of Emerging Trends & Technology in Computer Science (IJETTCS)
       Web Site: www.ijettcs.org Email: editor@ijettcs.org, editorijettcs@gmail.com
Volume 1, Issue 2, July – August 2012                                          ISSN 2278-6856




    Maximizing Network Lifetime using Reliable
    Energy Efficient Routing Protocol Based on
    Non Cooperative Game Theory for Wireless
                 Sensor Networks
                                      Chitra.S.M1, Vinoba.V2 and Padmavathy.T.V3
                                              1
                                              Research Scholar, Bharathidasan University,
                                                         TamilNadu, India,
                                                     2
                                                      K.N.Government Arts College,,
                                                         TamilNadu, India
                                          3
                                           R.M.K. college of Engineering and Technology,
                                                       TamilNadu,, Chennai

                                                                   as military, agricultural, industrial, and biomedical
Abstract: Wireless sensor networks create numerous                 applications [1]. Furthermore, they could easily be used in
fundamental coordination problems. For example, in a               different environments such as unreachable or dangerous
number of application domains including homeland security,         regions. Since there is no need to use a large amount of
environmental monitoring and surveillance for military             wire and complicated configuration and installation for
operations, a network’s ability to efficiently manage power        these sensors in the network, we could use them with
consumption is extremely critical as direct user intervention      lower cost in comparison with traditional networks.
after initial deployment is severely limited. In these settings,
                                                                   Recently, some research efforts have focused on
limited battery life gives rise to the basic coordination
problem of maintaining coverage while maximizing the
                                                                   establishing efficient routing paths for transmitting
network’s lifetime. In this paper we proposed game theory.         packets from a sensor node to a destination in wireless
Game theory (GT) is a mathematical method that describes           sensor networks [2]. Routing means finding the best
the phenomenon of conflict and cooperation between                 possible way for data transmission from source node to
intelligent rational decision-makers. In particular, the theory    the destination node in the network by considering
has been proven very useful in the design of wireless sensor       networks parameters (e.g. stability, consumed and
networks (WSNs).In this paper; we propose the game theory
                                                                   remained power, data transmission speed, and etc).
in the analysis of resource management in wireless sensor
networks. The game theoretic scheme is proposed to study           Network Lifetime is one of the important factors.
power control in a multi-source transmitting to multiple           Shortening the route length can help reduce the
clusters in wireless sensor network. A game where each             transmission overhead and delay time, as well as increase
sensor chooses its transmitting power independently to             the packet delivery ratio. Therefore, these networks must
achieve a target signal it is shown that the game has Nash         be designed and used in a way to optimize the power
equilibrium and it is unique under certain constraints.            consumption and life time of the network. In this paper,
Numerical results are provided to show the effectiveness of
                                                                   by using Game Theory approach for WSN, optimal route
the proposed game considering distance-dependent
attenuation with various path loss exponents.                      in WSN is found. In this approach, routing and sensor
Keywords: Wireless Sensor Networks, Game Theory,                   nodes are assumed to be the game and players
Routing, Lifetime.                                                 respectively. All players want to increase their benefit.
                                                                   So we use a mixed strategy model as well as profit and
1. INTRODUCTION                                                    loss calculation for each player. In this model, the
                                                                   destination node pays a recognition to the source node for
Wireless Sensor Networks is a new technology which is
used in a huge majority of applications. This network is a         each data packet successfully reception. Moreover, the
graph which consists of a large number of sense nodes.             source node pays a portion of this credit to each
These nodes are able to gather the information and                 intermediate node or relay node that participates in data
process it and send it to the relevant destinations. The           packet transaction. Furthermore, each node sustains a
sensors have some individual characteristics such as               cost for each data packet transaction to other node. This
small dimension and low power consumption. Because of              cost is called Transmission Cost and related to different
these characteristics, they could be used in different fields      parameters. Also each node transmits the received data
such                                                               packet to the next hope with the probability, calculated by
                                                                   the reliability of the node. This parameter is depending on

Volume 1, Issue 2 July-August 2012                                                                                 Page 210
    International Journal of Emerging Trends & Technology in Computer Science (IJETTCS)
       Web Site: www.ijettcs.org Email: editor@ijettcs.org, editorijettcs@gmail.com
Volume 1, Issue 2, July – August 2012                                          ISSN 2278-6856


several items, e.g. failure probability, sleep cycling, etc.   Meanwhile, each node also receives all the location
                                                               information from all its one hop neighbors. When nodes
2. RELATED WORKS                                               acquire their neighbor location information, they compute
There are some secure routing protocols for ad hoc             the distance between themselves and the sink, and the
networks [3], [4], but because of the assumption of small      distance between every one hop neighbor and the sink.
scale networks, large memory and high power they are
not suitable for WSNs. Some security protocols for             4. MATHEMATICAL MODEL
wireless sensor networks were also proposed. The authors       In the distributed sensor network the game equation has
                                                               to be found, with application of a game strategy. It is
in [5], addressed secure communication in resource
                                                               assumed that all the nodes in the sensor network are the
constrained sensor networks by introducing two low-level
                                                               same and that all nodes are in the interference range. The
secure building blocks. The Security Protocols for Sensor      activity of all the nodes is at the same level and it
Networks (SPINS) consists of SNEP and µTESLA. SNEP             increases with the increase of power level transmission.
provides confidentiality, authentication, and freshness        In the non-cooperative game theory, it is assumed that
between nodes and the destination, and µTESLA provides         nodes are transmitting high power, because of a high
authenticated broadcast. But disadvantage of SPINS             interference. Thus, the equilibrium game strategy has
protocol is: route discovery depends on the detection of       been applied for control of non-cooperative behavior.
authenticated beacons and node to node authentication by       Powers levels of the nodes are the minimum transmit
the destination.                                               power and the maximum transmit power.
Secure Auction-based routing (SAR) was proposed in              Theorem 1: Every game with complete information
[6], based on the concept of sealed auctioning. In this        and a finite tree has atleast one equilibrium point.
case nodes of the sensor network are the players of the        Although not all finite n-person non-cooperative games
game which compete with each other, to be a member in          have pure strategy equilibria we can ask about the
the route and the amount of the bid that each bidder           situation if mixed strategies are permitted. His result,
suggests is the amount of utility it had achieved during       which generalizes the Von Neumann mini-max theorem,
                                                               is the main objective of this section and certainly provides
past plays. This idea is implemented on DSR protocol
                                                               one of the strongest arguments in favour of equilibrium
although this protocol is not well suited for WSNs, and
                                                               points as a solution concept for n person non-cooperative
the other drawback is that when a packet on a path does
                                                               games.
not get to the destination, all the nodes on that path get
                                                                The mini-max principles say, minimizes the maximum
negative reputation, regardless of being malicious or          losses ie minimizes the number of node failure due lake of
normal. Utility-based dynamic source routing (UDSR)            energy threshold level. The maximum losses with respect
was proposed in [7]. It was based on a two player, non-        to different alternatives of player B(node2), irrespective of
cooperative and non zero-sum game between attacker and         player A’s (node1) alternatives, are obtained first. The
IDS residing at base station. It has the same two              minimum of these maximum losses is known as the mini-
weaknesses of SAR protocol, although the IDS can only          max value and the corresponding alternative is called as
defend one cluster and the attacker can also attack only       Mini-Max strategy.
one cluster at a time.                                         Let index set I be the set of nodes. For an n person
The authors in [8], [9], [10] proposed Game theory             game I   ,2,3,.....n. Let xi be an arbitrary mixed
                                                                          1
which has been used         in     sensor networks, with                                  th
incentives     for forwarding nodes and punishing              strategy for the i player, and the probability of
misbehaving nodes [11]. In the autonomous sensor               distribution of set S i of that player’s pure strategies. The
network using non cooperative game technique, Nash             probability assigned by xi to some         i  S i is denoted
Equilibrium is used to get optimal solutions of energy
conservation. Optimal probability of the two states is the     by xi ( i ) . Since the game is non-cooperative, the
sleep and wakeup use in repeated games.                        mixed strategies of all players (1,2,3,.....n) , viewed as
                                                               probability distributions are jointly independent. The
3. PROPOSED RELIABLE ENERGY                                    probability x ( ) of arriving at the pure strategy n - tuple
EFFICIENT ROUTING PROTOCOL                                     is    1 ,  2 , ....., n  ,   i  S i is assumed to
Due to the resource constraints, a sensor node in our
protocol does not need to have global information about        be x( )  x1  1 x 2  2 .......x n  n  . In terms of pure
the network. The following sections explain the                strategies the payoff to player i is given by Pi ,
mathematical model to prolong the network lifetime. In
the proposed work, since the nodes are static, all nodes       where Pi : S  S1 x.....xS n  R , that is Pi is a function
know their own locations before network initialization. In                                                 
                                                               which maps each   ( 1 ,...... n )  S to a real
the initialization stage of the network, each node sends its
own location information to its one hop neighbors.
Volume 1, Issue 2 July-August 2012                                                                                   Page 211
    International Journal of Emerging Trends & Technology in Computer Science (IJETTCS)
       Web Site: www.ijettcs.org Email: editor@ijettcs.org, editorijettcs@gmail.com
Volume 1, Issue 2, July – August 2012                                          ISSN 2278-6856


number. If mixed strategies xi , i  I are used the payoff                                                tries to maximize their utility. In the game theory no
                                                                                                          player is getting benefit by changing their strategy until
will be the statistical expectation of Pi with respect to the                                             other player changes their strategy. The set of strategy
distribution x  , namely,                                                                              and the corresponding utilities is a foundation of Nash
                                                                                                          equilibrium. Every player should show their best response
Pi  x1 , x 2 ,....x n    Pi  x                                                                  of their strategy, which results in Nash Equilibrium.
                                        S
                                                                                                          Let us consider non-cooperative n person game in which
                                                                                 n
Pi  x1 ,...., x n    ......  Pi  1 ,......, n  x j  j                                        each player or each node i  I has exactly two pure
                              11             n S n                          j 1                      strategies, either  i  1 (node1) or  i  2 . The payoff
                                                          (1)                                             is,
It is convenient to introduce the following notation:                                                     Pi ( 1 ,..... n )   i  1    i ,  j , i  I         (5)
For the strategy n tuple x  ( x1 ,.....x n ) then this can be                                                                                 ji
                               '                             '
written as, x xi  ( x1 ,....xi 1 , xi , xi 1 ........x n ) . This                                      Where     is the kronecker  given by
                                                                                                                          1, if  i   j
means that the player i has in x replaced the strategy                                                      i ,  j                                    (6)
xi by xi' . Now equation (1) can be written as,                                                                           0 otherwise
                                                                                  n                       If node i uses a mixed strategy in which pure strategy 1 is
P x i    .....  ......  .......P  
 i
                 1S1       i 1Si 1
                                        i
                                                i1Si1        Snn
                                                                                x  
                                                                                j 1 j 1
                                                                                            j    j
                                                                                                          chosen with probability pi (i  I ) , then pi 
                                                                                                                                                              1
                                                                                                                                                                      ,
                                                                                                                                                                  1
                                                                                                (2)                                                       1 2   n 1
Definitions:
                                                                                                             i  I and for n  2,3 this is the only equilibrium
Anon-cooperative                        game   I, X i iI , Pi iI  ,                        in
                                                                                                          point.
which the sets of players is I , the set of strategies for                                                Proof: For node1, if            1 1, then P1 = 0 unless
player i is X i and the payoff to player i is given by
                                                                                                           2  ......   n  2, in which case P1  1. If  1  2,
Pi :  X i  R , Here the sets X i could be taken to be                                                   then P = 0 unless  2  ......   n  1, in which case
                                                                                                                   1
       iI

sets of pure or mixed strategies. If the X i to consist of                                                 P1  2 similarly for other players also. Consider now the
mixed strategies then  is called the mixed extension of                                                  mixed strategy n -tuple x   x1 ,.....x n  , where
the original pure strategies. A mixed strategy n - tuple                                                   xi  ( pi , 1  pi ) for 1  i  n and pi is the probability
 x   x1 ,.....x n , xi  X i , is an equilibrium point of an                                           of choosing  i  1 .
n person            non-cooperative                      game             if    for            each            From the above observation we obtain,
i,1  i  n, and x  X i , Pi x x  Pi  x  .
                                   '
                                   i                       '
                                                             i
                                                                                                          Pi ( x)  p i  (1  p i )  2 (1  p j )  p j                   (7)
                                                                                                                         j 1                          j 1
Theorem 2: A mixed strategy n -tuple x   x1 ,.....x n  is
                                                                                                          Also
an equilibrium point of a finite game     if and only if for                                             Pi x  i    (1  p i ) if  i  1                             (8)
each player index i, Pi x  i   Pi  x             (3)                                                                j 1

for every pure strategy.                                                                                  Pi x  i   2  p j if  i  2                                  (9)
                                                                                                                             j 1
Theorem3:         For any mixed strategy           n -tuple
x   x1 ,.....x n  each player i,1  i  n, possesses a                                                 According to theorem 2, “A mixed strategy n tuple
                                                                                                          x   x1 ,.....x n  is an equilibrium point of a finite game
pure         strategy                    ik such           that             
                                                                          xi  ik  0 and
                                                                                                           if and only if for each player index i ,
   
Pi x        k
             i     P x  .
                         i                                                                      (4)
                                                                                                          Pi x  i   Pi  x  for every pure strategy  i  S i ”.
                                                                                                          x is an equilibrium point iff
5. LIFETIME EXTENSION FOR NASH
EQUILIBRIUM                                                                                                (1  p j )  pi  (1  p j )  2(1  pi )  p j and
                                                                                                           ji                          j i                         j i
In game theory, players are picking their own strategies
simultaneously. Any finite n person non-cooperative                                                       2 p j  pi  (1  p j )  2(1  pi )  p j for every
                                                                                                                j i             j i                         j i
game  has at least one mixed strategy equilibrium
point. By using Nash equilibrium condition every player                                                   iI .

Volume 1, Issue 2 July-August 2012                                                                                                                                      Page 212
       International Journal of Emerging Trends & Technology in Computer Science (IJETTCS)
       Web Site: www.ijettcs.org Email: editor@ijettcs.org, editorijettcs@gmail.com
Volume 1, Issue 2, July – August 2012                                          ISSN 2278-6856


                                                                                       6. LIFETIME EXTENSION ALGORITHM
Rearranging equation (1), then                                                         In this section, we propose a non-cooperative game
                                                                                       lifetime extension algorithm. In order to implement the
(1  pi ) (1  p j )  2(1  pi )  p j this can be                                   algorithm, on the one hand, the node i receives the sum
            j i                                            j i                                                                                     n

simplified as,                                                                         of interference power                               x   and
                                                                                                                                         n S n   j  1 j 1
                                                                                                                                                                j         j             on the

 (1  p
 ji
              j    )  2 p j
                                  j i
                                                                             (10)
                                                                                       other hand, the lifetime of sensor node increased by twice
                                                                                       according to the equation (9).When a node want to send
Similarly rearranging the (2) gives                                                    data message, it will search its information table and
(2  2  2 p i ) p j  pi  (1  p j )                                                compute its transmitting power according equation (2),
                           j i               j i                                     then send the power value to sink node, iterate this
2 p j   (1  p j )                                                        (11)      process until reach Nash Equilibrium.
   j i             j i
From equation (3) and (4) it follows that x is an                                      7.  SIMULATION                                              RESULTS                                  AND
equilibrium point if and only if,                                                      DISCUSSION
                                                                                       The proposed algorithm has been simulated and validated
 (1  p
 ji
              j    )  2 p j for every i  I
                              j i
                                                                             (12)
                                                                                       through simulation. The sensor nodes are deployed
                                                                                       randomly in a 100x100 meters square and sink node
                                                                                       deploy at the point of (50, 50), the maximum transmitting
For n  2 or 3 the system of equation (5) has no solution                              radius of each node is 80m, other simulation parameters
with any pi  0 or 1 , but for n  4 these are several such                            are displayed in Table 1. In this section, we first discuss
                                                                                       utility factor and pricing factor’s influences on
solutions, for example                      p1  p 4  1, p 2  p3  0. If             transmitting power, then evaluate the algorithm of NGLE
n  5 , we can find the                                             solutions   with   algorithm and compare it with other existing algorithm.
p1  p 4  1, p 2  p3  0 , and                                   the     remaining
                                                                                                    Table1: Simulation Parameters
n  4 pi arbitrary. To complete the analysis suppose                                            Parameters                    Value
0  p i  1 for every i  I .                                                              Transmission Range                 250 m
Considering the equation (12) for i  k , i  l , where                                        Network Area                 100 x 100
                                                                                            Number of Sensors                 50-100
k  l , then
                                                                                                Packet rate                 5 pkt/sec
 (1  p j )  2  p j and  (1  p j )  2  p j
 ji                              j i               j l                   j l
                                                                                                Packet size                   50bytes
                                                                                             Radio Bandwidth                  76kbps
Let A      (1  p               j   ) and B   p j ,since                               Transmitting Power             75mW ( 270J)
                                                                                             Receiving Power             36mW (129.6J)
0  p i  1 for all i
                                                                                       Power Consumption in Sleep        100µ W (0.36 J)
Then the expression can be written as                                                              mode
    A      2B       A      2B                                                          Sending and Receiving Slot            50msec
               ,        
 1  pk     p k 1  pl pl                                                                      Type of mote                   Mica2
Since A  0 and B  0 , then p k  p l , but k and                                     Inital energy of sensor node            2KJ
                                                                                          Energy Threshold E   thd           0.001mJ
 l where arbitrary, so that every player or every node use                                                                              Network Lifetime

the same mixed strategy in x . Equation (12) can be                                                          100
                                                                                                                                                                                    LEACH
                                                                                                             90                                                                     LEACH-M
rewritten as ,                                                                                                                                                                      HEED
                                                                                                             80                                                                     REER
(1  p ) n1  2 p n 1 , by solving p can be calculated as,                                                 70
                                                                                         N b of N es Alive




                     1                                                                                       60
                                                                                                 od




                    n 1
(1  p )  2                p                                                                                50
                                                                                          um er




                                                                                                             40
                    1
                                                                                                             30
                   n 1
1  p (1  2 )                                                                                               20

          1                                                                                                  10
p          1
                                                                          (13)                                0
                                                                                                                   0   50   100   150   200   250    300            350       400     450     500
                 n 1                                                                                                                   Number of Rounds
          1 2
                                                                                                              Figure 1: Network Lifetime of Sensor Networks
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Volume 1, Issue 2, July – August 2012                                          ISSN 2278-6856


The network lifetime for each simulation is showed in                                                               source and destination, it has the high probability to be
Figure 1. These curves are showing that lifetime of                                                                 the forwarding node. Thus, the proposed REER protocol
network for various routing protocols after 500 rounds,                                                             consumes less node energy for transmitting data between
about 27% of nodes in the network are alive in the                                                                  the nodes.
proposed REER routing protocol, but 1%,5% and 7% of
nodes are alive in existing protocols LEACH, LEACH-M                                                                                                                                                     Energy Consumption              REER
and HEED respectively. So the network lifetime is                                                                                                                         4500                                                           HEED




                                                                                                                                                Energy Consumption (mJ)
increasing about 73% with using of our model and                                                                                                                          4000
                                                                                                                                                                                                                                         LEACH-M
                                                                                                                                                                          3500
algorithm.                                                                                                                                                                3000                                                           LEACH
                                                                Average Delivery Delay                                                                                    2500
                                      160                                                                                                                                 2000
                                                                                                    LEACH                                                                 1500
                                                                                                    LEACH-M
                                      140                                                                                                                                 1000
                                                                                                    HEED
                                                                                                                                                                           500
                                                                                                    REER
                                                                                                                                                                             0
    A vearge Deliv ery Delay(m sec)




                                      120
                                                                                                                                                                                      20            40             60       80    100
                                                                                                                                                                                            Transmission Rate (packets/Second)
                                      100


                                       80                                                                                                                                  Figure 3: Energy Consumption with various
                                                                                                                                                                                       Transmission Rate
                                       60


                                                                                                                                                                                                         Packet Delivery ratio            REER
                                       40
                                                                                                                                                                                                                                          HEED
                                                                                                                                                              100
                                                                                                                                                                                                                                          LEACH-M
                                       20                                                                                                                      90
                                                                                                                     Packet Delivery ratio(%)




                                            0   10   20      30    40     50     60     70     80     90      100                                              80                                                                         LEACH
                                                          Transmission Rate (Packets/Second)                                                                   70
                                                                                                                                                               60
                                      Figure 2: Average Delivery Rate with various                                                                             50
                                                  Transmission Rate                                                                                            40
                                                                                                                                                               30
                                                                                                                                                               20
Figure 2 shows the average delivery delay with increasing                                                                                                      10
                                                                                                                                                                0
transmission rate. The average delivery delay means the                                                                                                                          20            40             60          80     100
average time delay between the instant the source sends a                                                                                                                                  Transmission Rate (packets/Second)
packet and moment the destination receives this packet.
When the transmission rate is 1 packet per second, we
                                                                                                                                                                           Figure 4: Packet Delivery Ratio with various
can see that the average delivery delay of LEACH,
                                                                                                                                                                                       Transmission Rate
LEACH-M is lower than the proposed REER protocol
and HEED. This is because LEACH is always tries to
                                                                                                                    Figure 4 shows the packet delivery ratio of proposed
discover a high speed path for forwarding packets. Since
                                                                                                                    protocol is compared with existing protocols. The plot
the transmission rate increases, the average delivery delay                                                         infers that the proposed REER protocol has better
of LEACH increases significantly. This is because                                                                   performance than LEACH, LEACH-M and HEED. With
congestions occur at the intermediate nodes in LEACH.                                                               the increase of transmission rate, LEACH, LEACH-M
In the proposed protocol, when the packets reaches at                                                               and HEED always forward packets along the relay nodes
destination, the relay or intermediate nodes have a lower                                                           by perimeter approach. This leads to a high probability of
forwarding probability than normal nodes by using                                                                   packet congestion around the relay node. In REER
multiple strategy. In the forwarding node selection game,                                                           protocol, since the process of forwarding node selection is
the probability that a great amount of packets are                                                                  a game process, the source has lower probability to make
forwarded by the same node is relatively low. Thus, the                                                             the same candidate gain too much benefit from the game
average delivery delay of our protocol does not                                                                     process. This is the reason the packet delivery ratio of our
significantly increase with an increase in transmission                                                             protocol does not significantly decrease with the increase
rate.                                                                                                               of transmission rate.
Figure 3 shows the energy consumption of the four
protocols. For LEACH, LEACH-M and HEED protocols,                                                                   8. CONCLUSION
the source always selects the node closest to the                                                                   In this paper, we introduce a game theory for extending
destination in the neighbor set. However, normally the                                                              sensor network lifetime. In the process of network
closest node is the local superior decision, not the global                                                         initialization, we use the connectivity property of nodes to
optimal decision. This has been proven by lemma 2. For                                                              determine the connectivity of nodes that can be forward
our protocol, in the forwarding node selection game, if                                                             any packets to its neighbour nodes. This approach
some node has a lesser angle with the line formed by                                                                improves the transmission success rate and decreases the

Volume 1, Issue 2 July-August 2012                                                                                                                                                                                                      Page 214
   International Journal of Emerging Trends & Technology in Computer Science (IJETTCS)
       Web Site: www.ijettcs.org Email: editor@ijettcs.org, editorijettcs@gmail.com
Volume 1, Issue 2, July – August 2012                                          ISSN 2278-6856


transmission delays of packets. In the aspect of setting up    [9] L. Buttyan and J.P. Hubaux, “Nuglets: A
the routing path, we consider the residual energy. We               Virtual Currency to Stimulate Cooperation in
conclude the forwarding probability and payoff function             Self        organized     Mobile          Ad-Hoc
of forwarding participants. Finally, the Nash Equilibrium           Networks,”Technical     Report DSC/2001/001,
exists when it is assume for minimum and maximum                    Swiss Fed. Inst. Of Technology, Jan. 2001.
threshold for channel condition and power level. By            [10] W. Wang, M. Chatterjee,        and    K. Kwiat,
using Non cooperative game theory the network lifetime              “Enforcing Cooperation in Ad Hoc Networks
is extended, that is after 500 rounds 27% of node are alive         with Unreliable Channel,” Proc. Fifth IEEE Int’
where as 1%,5% and 7% of nodes are alive in existing                Conf. Mobile      Ad-Hoc and Sensor Systems
protocols LEACH, LEACH-M and HEED respectively.                     (MASS), pp. 456-462, 2008.
So the network lifetime is increasing about 73% with           [11] V. Srinivasan, P. Nuggehalli, C. Chiasserini, and
using of our model and algorithm.                                   R. Rao,“Cooperation      in Wireless Ad Hoc
In our future, we plan to implement our algorithm in s              Networks,” Proc. IEEEINFOCOM, vol. 2, pp. 808-
real application scenario to verify the effectiveness in the        817, Apr. 2003.
real world. Also, in this paper, we assume that all nodes
are stationary. There are some application scenarios
where we need the nodes to be able to move. In such a
case, we will need to consider the nodes’ mobility in our
future work.

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Volume 1, Issue 2 July-August 2012                                                                        Page 215

				
DOCUMENT INFO
Description: International Journal of Emerging Trends & Technology in Computer Science (IJETTCS) is an online Journal in English published bimonthly for scientists, Engineers and Research Scholars involved in computer science, Information Technology and its applications to publish high quality and refereed papers. Papers reporting original research and innovative applications from all parts of the world are welcome. Papers for publication in the IJETTCS are selected through rigid peer review to ensure originality, timeliness, relevance and readability. The aim of IJETTCS is to publish peer reviewed research and review articles in rapidly developing field of computer science engineering and technology. This journal is an online journal having full access to the research and review paper. The journal also seeks clearly written survey and review articles from experts in the field, to promote intuitive understanding of the state-of-the-art and application trends. The journal aims to cover the latest outstanding developments in the field of Computer Science and engineering Technology.