A STUDY ON COOPERATIVE AND NON-COOPERATIVE GAME THEORY OF POWER

MANAGEMENT IN WIRELESS SENSORS NETWORKS

1Sridevi.S, 2V.Vinoba, 3S.M.Chithra

1Research scholar of Mathematics,

Kunthavai Naachiyaar Govt. Arts College for women, Thanjavur, 2Assistant professor of Mathematics,

Kunthavai Naachiyaar Govt. Arts College for women, Thanjavur, 3Assistant professor of Mathematics,

RMK College of Engineering and Technology, Chennai.

Abstract: Wireless Sensors are regarded as important components of electronic devices. In the majority applications

of wireless sensor networks (WSNs), significant and critical information be required to be delivered to the sink in a

multi-hop and energy-efficient manner. In as much as the energy of sensor nodes is limited, prolonging network

lifetime in WSNs is considered to be a critical issue. In categorize to lengthen the network lifetime, researchers

should think about energy utilization in direction-finding protocols of WSNs. A wide spectrum of issues can be

professionally addressed in current efforts in applying Game theory in wireless sensor communications and

networking. It is envision that game theory will be a primary procedure in the field of wireless sensor network

communications and networks. Cooperative and Non-cooperative Game theory was originally invented to explain

complicated economic performance. With its effectiveness in studying complex dynamics among players, game

theory has been widely applied in politics, philosophy, military, Sociology, telecommunications, and logistics. The

game theoretic model is able to address efficiently resource allocation, congestion control, attack, routing, energy

management, packet forwarding, and medium access control (MAC). This paper systematically introduces and

explains the applications of game theory in wireless communications and networking. It provides an all-inclusive

technological guide covering introductory concept, elementary techniques, recent advances, and open issues.

Keywords: Game theory, Non-Cooperative Game theory, Cooperative Game theory, Wireless communications,

Wireless Networks.

1. Introduction

In this chapter, we propose a Cooperative and Non-Cooperative and Game Theory in the analysis of resource

management in Wireless Sensor Networks. Here the game theoretic scheme is proposed to study power control in a

multi-source transmission in multiple clusters in Wireless Sensor Network. A game where each sensor chooses its

transmitting power independently to achieve a target signal, it is shown that the game has Nash equilibrium and it is

unique under certain constraints. Numerical results are provided to show the effectiveness of the proposed game

considering distance-dependent attenuation with various path loss exponents.

1.1 Cooperative Games

Games of cooperation are games where agreements are enforceable (Dixit, Skeath and Reiley 2004: 26). This means

that the players’ decisions are made in a group and that all members of the group will act according to the decision

or a game where all players act according to the agreements that can be forced collectively or directly. By doing so,

the players cooperate to maximize their payoffs. Working together they can, for example, form coalitions that aim to

increase the payoff of the coalition and thus increase the payoff to each member. The applications of cooperative

games vary quite a lot. For example in politics, where game theory can be used to help form coalitions and to

calculate how to divide payoffs amongst the different players and parties.

1.2 Non-Cooperative Game Theory

International Journal of Pure and Applied MathematicsVolume 118 No. 10 2018, 415-427ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version)url: http://www.ijpam.eudoi: 10.12732/ijpam.v118i10.42Special Issue ijpam.eu

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If the players communicate, binding agreements may not be formed. The main concept, replacing values and optimal

strategy in the notion of a strategic equilibrium, also called Nash equilibrium. This Nash equilibrium is a building

block of game theory since it both inspires new solution concepts and corresponds to the solution of many

interactive situations.

2. Existence of Nash Equilibrium for Cooperative and Non-Cooperative Game Theory

In this section, we describe the Nash Existence Theorem and apply this theorem we show the Nash Equilibrium

(NE) for our modeled by cooperative and non-cooperative game theory power game.

2.1 Nash Existence Theorem for Cooperative and Non-Cooperative Game Theory

A strategic game G = {N, A, R} has at least one NE if ∀i∈N the following condition holds.

The setA�of actions is anon-empty, compact and convex subset of a Euclidean space. The terms from set theory used

in this theorem are concisely defined by given below.

2.2 Ne for Cooperative and Non-Cooperative Power Game

The cooperative and non-cooperative power game described in the previous section has at least one Nash

Equilibrium (NE). In order to prove this, we apply Nash Existence Theorem to the cooperative and non-cooperative

power game.

2.3 Proof

The action setsp�are non-empty and convex, by definition. Each p�is closed since it includes the boundary

levels(P�,� )and(P�, �). All power levels in p�lie within the boundary, thus it is bounded. Therefore thep�’s are

compact. Thus the cooperative and non-cooperative power game must have Nash Equilibrium point.

2.4 Nash Equilibrium Solution Method For Cooperative And Non-Cooperative Power Game

The intention of this cooperation and non-cooperation of power game for each node can be stated as for each node

i∈N, given the action tuples of the remaining players, i.e. (p�) jεN\i, find an action p�that maximize the utility

functionu�. This motivates adistributed solution approach which proceeds as an iterative optimization problem of a

scalar objective function. The iterative step is defined as follows:

� Step: For each node i∈N, given ((p�) jεN\i) ε, find the maximum utility from equation (2.4). P�,�� =max��[u�(p�,p��)], ∀i∈N… … … …………… (2.4)

This iterative procedure continues until all nodes in the network find that their utilities do not change between

iterations and the change in their power levels is less than a pre-defined bound or an upper limit on the number of

iterations is reached.

3. Energy Consumption without Losing Accuracy

Wireless Sensor nodes can use up their partial quantity of energy performance working out and transmitting data in

wireless sensor surroundings. As such, energy keeping methods of communication and working out are essential.

Wireless Sensor node generation shows a heavy-duty dependency on the battery generation. In a multi-hop WSN, a

set of teaching node plays a double role as information sender and information router. The not working of some

wireless sensor nodes in arrears to power miscarriage can cause significant topological ups and downs and might

require switching of packets and restructuring of the network.

3.1 Mathematical Model

In the distributed sensor network the game equation has to be found, with the game theoretical formulation of

transmission power and .power game model of networks. It is assumed that all the nodes in the sensor network are

the same and that all nodes are in the interference range. The activity of all the nodes is at the same level and it

increases with the increase of power level transmission. In the Cooperative and Non-Cooperative Game Theory, it is

assumed that nodes are transmitting high power, because of a high interference. Thus, the Nash equilibrium game

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has been applied for control of Cooperative and non-cooperative behavior. Powers stages of the nodes are the

minimum convey power and the maximum conveys power.

3.2 Definition.1.1.

3.2.1 Cooperative and Non-Cooperative game theory analysis of spectrum sensing scheduling power ratex

Consider a Cognitive Radio Network (CRN) with SU�, i∈N for each time slot’s’ max��,�(�) ∑ ∑ μ�,!(t) !∈ !� �∈ # × (Q�,!% (t)−V(p% + p(� +p)�(I�! − 1))) +(min {∑ μ�,!(t)�∈,� w�,�! (t),M�, ! �}) Q�,!/ (t) ………………… (2.5)

Such that ∑ μ�,!(t) !∈ !� ≤ K, ∀i∈N.

3.3 Definition 1.2.

3.3.1 Cooperative and Non-Cooperative game theory Solution under Bounded Contribution of power

organization

The general algorithm of (2.5) uses a cap on the utmost amount of in sequence that can be obtained in an analysis of

power control organization, which is represented asM�, ! �. While this magnitude has practical consequence by not

allowing subjective levels of accurateness to “accumulate” within an analysis of power organization, it also

complicates the algorithm execution. This constraint can be indifferent from thoughtfulness when correlation

weights are appropriately upper-bounded such that the bounded contribution of Cooperative and Non-Cooperative

power organization assumption holds: ∑ 01,2(3)1456 71,82 (t) ≤ 98, 2:;<∀i∈N, ∀c∈=8,∀t ………………. (2.6)

Since 01,2(3) and 71,82 (t) are upper-bounded, this assumption can be easily satisfied if 98, 2:;<is sufficiently large.

This assumption especially holds in low SNR environments and when the temporal correlation levels of analysis of

power organization, information are high (i.e.,98, 2:;< is sufficiently large). Under this assumption, the optimization

(2.2) can be simplified as follows: >?@A6,B(C) ∑ ∑ 08,2(3) 2∈ 26 8∈ D × (E8,2F (t)-V(GF + GH< +GI<(J82 − 1))) +∑ 71,82 (3)1∈56 E8,2K (t) …………………..(2.7)

Subject to the constraints of Cooperative and Non-Cooperative power organization.

Theorem. 1.1.

Given ∈>0, the algorithm can accomplish a moment in time- averaged collection of cost: LM>H→∞ OPG QH ∑ R{T8 (3)}H�QCVW ≤∑ X8 ∈∗8∈D +

Z[ ………………… (2.8)

With all the fundamental queues surrounded by

LM>H→∞ OPG QH ∑ ∑ ∑ {E8,2K 2∈ 26 (3) + E8,2F (3)}8∈DH�QCVW ≤ \ ∑ ]6 ∈∗ ^Z

∈8∈D ………………… (2.9)

Where B = Q_ (`a_+`K_ +9:;<Q +1)∑ b8_8∈D

3.4 Proof of Theorem

We present a lemma to assist the proof of Theorem as follows:

Lemma: Given∈>0 such that ( X8 ∈∗ ) ∈ G, there exist a motionless randomized sensing development algorithm

(denoted by STAT) with sensing schedules (08,2aH cH(3)) self-determining ofvirtual queue backlogs, such that the

sensing schedules satisfy:

E{(T8,aH cH(3)} = X8 ∈∗ ,∀t, ∀i∈N,

E{(T8,aH cH(3)} ≥`F+∈, and E{(98,2aH cH(3)} ≥`K+∈,…………………(2.10) ∀t, ∀i ∈ N, ∀c ∈b8. Analogous formulations of STAT and their proofs have been given in [2.7], so we omit

the proof of Lemma for brevity.

To prove Theorem 1, we may introduce a queue vector Q(t)≜ {eE8,2K (3)f , eE8,2F (3)f} and define Lyapunov

the function L(Q(t)) as follows

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L (Q (t))≜ Q_ ∑ ∑ {E8,2K 2∈ 26 (3)_ + E8,2F (3)_}8∈D ……………..(2.11)

We define the coresponding Lyapunov drift by ∆(t)≜E{L (Q (t+1)) -L (Q (t)}.

By squaring the virtual queue dynamics (2.10) and (2.11), we can derive the following inequality of the Lyapunov

drift is given by E8,2F (3 + 1) =[E8,2F (3) + `F − 08,2(3)]^………………………..(2.12)

Where [?]^ ≜pass with flying colors {a, 0}. A “packet” arrival to the local sensing queue represents an

increase in need for local sensing, which is satisfied when the packet is “served” and departs from the queue, i.e.,

node performs local sensing. The evolution of the total sensing deficiency queue follows, ∀i ∈ N, c ∈=8, E8,2K (3 + 1) = [E8,2K (3) + `K − 98,2(3)]^…………………..(2.13)

When a sensing setting up algorithm stabilizes the virtual queues E8,2F (3) andE8,2K (3)then this means that their

one-to-one arrival rates are smaller than or equal to their average service charges ∆(t)+ V∑ i{ (T8(3) E(3)⁄ }84D ≤ B+ V∑ i{ (T8(3) E(3)⁄ }84D

+∑ ∑ i{ (`K − 98,2 (3) E(3)⁄ } 2∈ 26 E8,2K (3)}8∈D

+∑ ∑ i{ (`F − 08,2 (3) E(3)⁄ } 2∈ 26 E8,2F (3)}8∈D ………………………..(2.14)

We find an equation of ( 2.117) by rearranging terms as follows: ∆(t)+ V∑ i{ (T8(3) E(3)⁄ }84D

≤ B+ V∑ ∑ `F(E8,2F (3))) + (`K(E8,2K (3)))242684D

-∑ ∑ (08,2(E8,2F (3))) − \(GF + GH< +GI<(J82 − 1)))242684D

+98,2(3), E8,2K (3) E(3)k }…………………………….(2.15)

Where we employ the following equality by changing order of summation and noting the assumption of fair

cooperation: ∑ ∑ ∑ lIm1456 {8}n 08,2(3)24o684D = ∑ ∑ 08,2(3)24o684D lIm(J82 − 1). If the bounded contribution assumption (2.11) holds, we can further simplify (2.12) as follows: ∆(t)+ V∑ i{ (T8(3) E(3)⁄ }84D ≤ B+ ∑ ∑242684D (`F(E8,2F (3))) + (`K(E8,2K (3)))

− ∑ ∑ { 2426 i84D (08,2(3)(E8,2F (3))) +∑ (78,12 (3))(E1,2K (3)84D −\(GF + GH< +GI<(J82 − 1))) E(3)k }…………………..(2.

16)

With the employment of the following equality:

q q q(78,12 (3))(E8,2K (3))1456

01,2(3)24o684D

= ∑ ∑ 01,2(3)24o684D (∑ (78,12 (3)), (E8,2K (3))1456 )…………………….(2.17)

Where we have changed the order of summations. Note that the third term of the Right-Hand Side (RHS) of

(2.13) (and of (2.14)) is minimized by the algorithm projected over the set of all reasonable algorithms together with

STAT introduce in Lemma. Therefore, we can replacement into the RHS of (2.12) a stationary randomized

algorithm STAT with the price tag rate vector ( X8,∈∗ ), and obtain: ∆(t)+V∑ i{ (T8(3) E(3)⁄ }84D ≤B+\ ∑ ∑ [ 242684D (E8,2F (3))E8,2K (3))]………….(2.18)

We take the probability with respect to the giving out of Q (t) on both sides of (2.18) and take the time

average on t =0, · · · , T − 1, which leads to

QH E{L (Q (t))} +

[H ∑ ∑ i{T8(3)84DH�QCVW }

≤ B+ \ ∑ (X8,∈∗84D )-4H ∑ ∑ ∑ i{eE8,2F (3)f + eE8,2K (3)f}242684DH�QCVW ……………(2.19)

By taking limit suprimum of T on both sides of (2.19). We can prove (2.8) and (2.9) respectively.

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3.5 Definition 1.3.

3.5.1 Non-cooperative Game Power Control (NGPC)

NGPC is defined as G=[N, {G8},{08}],where N={1, 2,...,n} is the node set of the equivalent frequency interfering in

the same sub channel, G8 = [0, G:;<]is the approach space of each node, 08is the effectiveness function of node i . In

a sensor network, each node selects a approach according to usefulness function to maximize its income, that is

Max (08{G8,G�8}), i= 1, 2... n.

3.6 Definition 1.4.

If for all ∀i ∈ N and l8′'∈G8 , (08{G8,G�8}) ≥ (08{l8′, G�8}) then power vector P is the Nash Equilibrium of Cooperative

and Non-cooperative Game Power Control (CANGPC).

Theorem. 1.2.

Nash equilibrium exists in Non-cooperative Game Power Control (CANGPC).

Proof;

Since approach space of each sensor node is defined in [0, G:;<] approach space G8is a non-empty curved and

compacted subset of Euclidean space 08(G) is nonstop on p.

Since

tu6(v6,vw6)tv6 =

Axy6z{|m z6n5}~��∑ y�v��{|m�6 ^t~����,��6 �^xy6v6 �{|m ��k �

–�ℎ8R:;< R8n ……….. (2.20)

On the other hand, it shows that

t~u6(v6,vw6)tv6~ =

A(xy6)~(�{|m�6 )~

5}~��∑ y�v��{|m�6 ^t~����,��6 �^xy6v6 �{|m ��k �~ ……………………. (2.21)

We havet~u6(v6,vw6)

tv6~ < 0. So P8(G8 , G�8) is concave on G8. Nash equilibrium exists in Cooperative and Non-cooperative Game Power Control (CANGPC).

The most favorable answer of NGPC is arg>?@v6∈�6 P8(G8 , G�8). According to maximum assessment theory. We can

get from (18) that

G8 = A�5}~ y6

R8 R:;<n -z6��∑ y�v��{|m�6 ^t~����,��6 ��

xy6z{|m ………………….(2.22)

In pratical appliance G8≥0. So the charge range of � is that

�≤ A(x)5}~��∑ �����{|m�6 ��~����,��6 ��

……………….(2.23)

Theorem.1.3. The Nash Equilibrium of NGPC is unique.

Proof:

Let � (G8) = A�5}~ y6

R8 R:;<n -z6��∑ y�v��{|m�6 ^t~����,��6 ��

xy6z{|m ………………….(2.22)

NGPC has been proved in [2.18] that if � (G8) is a normal function (i.e. the function have the properties of

positivity, monotonicity, and extendibility), then the fixed point of it is unique. On the other hand, it is easy to know

that Nash Equilibrium position of NGPC be required to is a fixed point of it. Therefore, it is sufficient to

demonstrate that (� (G8) ) is a normal function.

� Positivity ;

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�≤ A(x)5}~��∑ �����{|m�6 ��~����,��6 ��

……………….(2.23)

Then �(G8) ≥0. Obiviously � (G8) is positivity.

� Monotonicity ; ∀i ∈WhenG, ≥ G, �(G)′ − �(G) =

�∑ y�(v�w��′����,��6 �

xy6 ≤ 0.………………………(2.24)

So � (G8) monotonicaly decrease.

� Extendibility ; ∀∝> 1,

∝ �(G) − �(∝ G) = (∝ −1) R8R: �h� [ μλIn_ − ∂_G ]

(2`21) follows that λ≤ µ( ),~��∑ ¡¢£¢¤¥¦§¤� �¨~©¢��,¢�� ��

≤ µ( )ª~,~ ………………………..(2.25)

From further calculation, it is not easier said than done to attain that ∝ f(p) − f(∝ p)≥ 0 for that reason f (p�)is a normal function and there exist an only one of its kind fixed point. Hence, the Nash Equilibrium of the

NGPC is unique.

4. Simulation and performance analysis of cooperative and non-cooperative game theory

In this subdivision, we initial talk about utility factor and pricing factor’s influence on transmit cooperative and non-

cooperative power under the different average remaining liveliness of the sensor nodes, then estimate the algorithm

of CANCPC and measure up to it with other obtainable algorithms. For simulation make straightforward, assume

ten nodes are randomly distributed in a 100×100 meter square, sink node deploy at the point of (50,50), the

maximum transmitting radius of each node is 80m, average residual energy E is 30J and 40J respectively. Other

simulation parameters are displayed as Table 1:

Parameter Description Value

W channel bandwidth 1 MHZ

R data rate 10Kbps

G spreading gain 100 δ_ background noise 5Ce�Q®W h� path gain 7.75V10�Q° d�°.²k

E � maximum energy 50J

4.1 Power Control

In the cooperative and non-cooperative power control problem, each user’s utility is ever-increasing in his signal-to-

inference-and-noise ratio and decreasing in his power altitude. If all other user’s power level were fixed, then

increasing one’s power would increase one’s SINR. However, when a user raises her transmission sensor power

control, this action increases the interference seen by other users, driving their SINRs down, inducing them to

increase their own power levels.

Figure1.1. and Figure1.2.Shows average transmit power cooperative and non-cooperative game theory

against an average reserve of going underneath the surface node in assessment with far removed from average

residual energy and utility factor when λ is fixed. The above two curves be a symbol of the equilibrium transmitting

sensor power control when λ is fixed (λ=1.5), utility factor µ=15, and run of the mill residual energy of ten nodes is

30J and 40J respectively. The below two curves represent the equilibrium transmitting sensor power when λ is fixed

(λ=1.5), utility factor µ= 1.5, and average residual energy of ten sensor nodes is 30J and 40J respectively.

Figure.2.6.and figure.2.7.reflects the humanizing trend of average transmitting sensor power varies with the average

distance increasing of go under the surface node. As shown in Figure.2.6.high utility factor implies nodes will use

high power to transmitting data, the larger utility factor is, the higher transmit power will nodes has. Under the

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circumstance of the same utility factor, if nodes have smaller residual energy, it will use smaller power to

transmitting data, which can save node energy efficiency and prolong network lifetime.

Figure.1.1. Nodes equilibrium

Figure.1.2. Nodes equilibrium transmitting power

Figure1.3. and Figure1.4.Shows

involvement of sink sensor node in evaluation

when µ is fixed. The higher than two curves

(µ=1), price feature λ=1.5, and average residual energy of ten nodes is 30J and 40J respectively. The below two

curves represent the stability transmitting

residual energy of ten nodes is 30J and 40J respectively. Figure.2.8 also reflects the improving trend of average

transmitting power varies with the average distance

the ground pricing factor imply sensor nodes will use low powe

is, the lower transmitting power will nodes has. Under the condition

less significant residual energy, it will use

and-go efficiency and prolong network lifetime.

of the same utility factor, if nodes have smaller residual energy, it will use smaller power to

save node energy efficiency and prolong network lifetime.

Nodes equilibrium transmitting power (µ=1)

Nodes equilibrium transmitting power (λ=1.5)

common transmit sensor power in opposition to

evaluation with poles apart run of the mill left behind energy and pricing

two curves correspond to the equilibrium transmitting sensor power when

=1.5, and average residual energy of ten nodes is 30J and 40J respectively. The below two

transmitting sensor power when µ is fixed (µ=1), pricing factor

and 40J respectively. Figure.2.8 also reflects the improving trend of average

transmitting power varies with the average distance ever-increasing of sink node. As shown in figure.2.9.

nodes will use low power to transmitting sensor data, the larger pricing factor

is, the lower transmitting power will nodes has. Under the condition of the same pricing factor, if sensor

residual energy, it will use less significant power to transmitting data, which can save node

efficiency and prolong network lifetime.

of the same utility factor, if nodes have smaller residual energy, it will use smaller power to

in opposition to an average lack of

energy and pricing feature

power when µ is fixed

=1.5, and average residual energy of ten nodes is 30J and 40J respectively. The below two

=1), pricing factor λ=6 and average

and 40J respectively. Figure.2.8 also reflects the improving trend of average

of sink node. As shown in figure.2.9. far above

data, the larger pricing factor

of the same pricing factor, if sensor nodes have

ing data, which can save node get-up-

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Figure.1.3. Performance comparison of

Figure.1.4. Performance comparison of transmitting power between NGPC and NPGP

In order to analysis the performance of the new algorithm, we compare the new algorithm NGPC

algorithm NPGP which introduced the power control strategy of NPGP is defined

P� rµ

λ&

Q

 ´��∑ h�p� '#

�VQ,�µ� δ_)……………………. .(2.20)

It is clear from Fig.4 and Fig.5 that NGPC outperforms NPGP in transmitting power and

function, this is for the reason that we think through the reason of sensor nodes residual energy on the design of the

utility function, and consider the aspects of sensor node residual energy, path gain, transmitting power on the

evaluating function, thus the performance of NGPC meaningfully improved and can reduce the

power efficiency.

Performance comparison of pricing function between NGPC and NPGP

Performance comparison of transmitting power between NGPC and NPGP

In order to analysis the performance of the new algorithm, we compare the new algorithm NGPC

algorithm NPGP which introduced the power control strategy of NPGP is defined as follows:

)……………………. .(2.20)

It is clear from Fig.4 and Fig.5 that NGPC outperforms NPGP in transmitting power and

, this is for the reason that we think through the reason of sensor nodes residual energy on the design of the

ts of sensor node residual energy, path gain, transmitting power on the

evaluating function, thus the performance of NGPC meaningfully improved and can reduce the

pricing function between NGPC and NPGP

Performance comparison of transmitting power between NGPC and NPGP

In order to analysis the performance of the new algorithm, we compare the new algorithm NGPC with the

It is clear from Fig.4 and Fig.5 that NGPC outperforms NPGP in transmitting power and evaluating

, this is for the reason that we think through the reason of sensor nodes residual energy on the design of the

ts of sensor node residual energy, path gain, transmitting power on the plan of

evaluating function, thus the performance of NGPC meaningfully improved and can reduce the total transmitting

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Figure 1.5.(a). Optimal energy consumption vs.

Figure 1.5.(b). Optimal energy number of

correlation weights

Optimal energy consumption vs. sensor nodes for different sensing nodes quality rates

Optimal energy number of consumption vs. number of sensor for

correlation weights among neighbors

nodes quality rates

for different

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Figure .1.6. Energy consumption vs

Figure .1.6.(a) Energy consumption vs.

Energy consumption vs. (a) PT�and (b) number of sensor nodes N. R/= 0.

Energy consumption vs. PT�=PR�, N = 9, Rs= 0.55

.9,W��(t) = 0.6.

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Figure .1.6.(b) Energy consumption vs.

In Figure.1.4, Figure .1.5, Figure .1.6

of cooperative and non-cooperative game theory transmitting

effectiveness factor, pricing factor, and left over

factor is 7.13, left over energy is 14.0, the transmitting

underneath the circumstance of a convinced

factor and assessing factor can optimize transmitting

introduce RD = 0.9, the (per node per time slot) energy

spatial-correlation-based algorithm, and the cooperative and non

(CORN) indeed leave behind the spatial-correlation

similar numeral of SU nodes. We also detect that when the numeral of nodes is minor (e.g.,

three-dimensional messages alone cannot pay off for the additional cooperative and non

cost, compared to the cooperative and non-

Cooperative and Non-cooperative Power control is a

in WSNs, how to formulate full use of sensor

Multi-Services demand in WSNs. In this paper, we propose a cooperative and non

model based on the WSNs model of CDMA, the

proved for the projected cooperative and non

the factor of sensor node residual energy on

power control algorithm proposed in the paper can reduces

energy and prolongs sensor network lifetime efficiently.

optimization can provide some useful guidelines for the

[1] T. Melly, A. Porret, C.C. Enz, E.A. Vittoz, A 1.2 V, 430 MHz, 4dBm power amplifier and a 250 lW

Frontend, using a standard digital CMOS process, IEEE International Symposium on Low Power Electronics and

Design Conference, San Diego, August 1999,

[2] R. Min, T. Furrer, A. Chandrakasan, Dynamic voltage scaling techniques for distributed microsensor

networks, Proceedings of ACM MobiCom’95, August 1995.

[3] F.R. Mireles, R.A. Scholtz, Performance of equicorrelated ultra

in the indoor wireless impulse radio channel, IEEE Conference on Communications, Computers and Signal

Processing, Vol. 2, 1997, pp. 640–644.

Energy consumption vs. N, PT�= PR�= 0.1125 mJ, R%= 0.

Figure .1.6, Figure .1.6(a) and Figure .1.6(b), we reproduce

cooperative game theory transmitting sensor power under different combinations of

left over energy. For example, when effectiveness factor is 6.65, pricing

energy is 14.0, the transmitting sensor power will be 13.3.reproduction

convinced left over energy, pick out appropriate combinations of the

factor and assessing factor can optimize transmitting sensor power effectively. With the identical

9, the (per node per time slot) energy utilization is shown in Figure 3 under (CORN), the

based algorithm, and the cooperative and non-cooperative algorithm. It can be

correlation-based set of rules and the non-cooperative set of rules under the

so detect that when the numeral of nodes is minor (e.g.,

alone cannot pay off for the additional cooperative and non-cooperative communiqué

-cooperative pickup algorithm.

5. Conclusion

cooperative Power control is a well-organized way to saving imperfect energy of

sensor node energy is an important object on the design of

WSNs. In this paper, we propose a cooperative and non-cooperative game power control

model of CDMA, the continuation and exceptionality of the Nash Equilibrium are also

tive and non-cooperative game model. recreation results show, because

node residual energy on the design of the model, the cooperative and non

power control algorithm proposed in the paper can reduces sensor node transmitting power, saves

network lifetime efficiently. It is believed that introduce game theory into the power

optimization can provide some useful guidelines for the performance optimization of WSNs.

References

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.4

reproduce the change processes

power under different combinations of

factor is 6.65, pricing

reproduction results show,

combinations of the effectiveness

identical simulation setup as

is shown in Figure 3 under (CORN), the

cooperative algorithm. It can be investigational that

cooperative set of rules under the

so detect that when the numeral of nodes is minor (e.g., N=2), the gain from

cooperative communiqué

energy of sensor nodes

node energy is an important object on the design of WSNs. To meet

cooperative game power control

of the Nash Equilibrium are also

results show, because think about

the design of the model, the cooperative and non-cooperative game

transmitting power, saves sensor node

introduce game theory into the power

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