Research Article Dual-Level Game-Based Energy Efficiency...

Research ArticleDual-Level Game-Based Energy Efficiency and Fairness forGreen Cellular Networks

Sungwook Kim

Department of Computer Science Sogang University 35 Baekbeom-ro (Sinsu-dong) Mapo-gu Seoul 121-742 Republic of Korea

Correspondence should be addressed to Sungwook Kim swkim01sogangackr

Received 28 January 2016 Revised 25 April 2016 Accepted 4 May 2016

Academic Editor Laurence T Yang

Copyright copy 2016 Sungwook Kim This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In the recent decades cellular networks have revolutionized the way of next generation communication networks However dueto the global climate change reducing the energy consumption of cellular infrastructures is an important and urgent problem Inthis study we propose a novel two-level cooperative game framework for improving the energy efficiency and fairness in cellularnetworks For the energy efficiency base stations (BSs) constantly monitor the current traffic load and cooperate with each otherto maximize the energy saving For the energy fairness renewable energy can be shared dynamically while ensuring the fairnessamong BSs To achieve an excellent cellular network performance the concepts of the Raiffa Bargaining Solution and Jainrsquos fairnessare extended and practically applied to our dual-level cooperative game model Through system level simulations the proposedscheme is evaluated and compared with other existing schemes The simulation results show that our two-level game approachoutperforms the existing schemes in providing a better fair-efficient system performance

1 Introduction

The current explosive popularity of smartphones and mobiledevices has ignited surging traffic demands for wirelessaccesses and has been incurring massive energy consump-tion which causes global warming due to CO

2emissions

With the increasing awareness of global warming and envi-ronmental consequences of Information and Communica-tions Technology (ICT) researchers have been seeking waysto reduce energy consumption As a significant component ofICT energy consumption cellular network system will havegreater economic and ecological impact in the coming yearsConcentrating on environmental influences a new researcharea called ldquogreen cellular networksrdquo has recently emergedThis green approach can give extra commercial benefitsmainly by reducing the operating expense related to energycost [1ndash3]

In wireless cellular networks energy consumption ismainly drawn frombase stations (BSs) they account formorethan 50 percent of the cellular networkrsquos energy consumptionIn addition the number of BSs is expected to be doubled by2012 [4] Therefore promising technology has been devel-oped to improve the energy efficiency in BSs it is crucial

to implement green cellular networks while approximatingan optimal energy saving From the perspective of cellularnetwork management the energy-efficient operation of BSsis not only amatter of social environmental responsibility butalso tightly related to cellular network control issues [4ndash7]

Motivated by the above discussion in this study ourmain focus is devoted tomaximizing the energy efficiency forBSs To address the challenge of increasing energy efficiencyand profitability in future green cellular networks we con-sider various paradigm-shiftingmethodologies [1 4] Amongall the promising energy saving approaches BS sleepingand renewable energy (RE) distribution methods are veryeffective and prominent solutions to optimize the energyutilization in green cellular networks [4ndash6] The past decadehas seen a surge of research activities in each individualmethodHowever little research has been done for the propercombination of these two methods

The intuitive idea of BS sleeping method is to switch offthe BSs when the traffic load is below a certain thresholdduring a certain time period Simply the BS sleeping problemcan be formulated as an optimization problem thatminimizesthe number of active BSs while supporting the traffic load in acellular networkThis problem is awell-known combinatorial

Hindawi Publishing CorporationMobile Information SystemsVolume 2016 Article ID 9036929 10 pageshttpdxdoiorg10115520169036929

2 Mobile Information Systems

optimization problem [4] However the BS sleeping problemhas been proven to be NP-hard Moreover solving this prob-lem generally requires a central controller as well as the globalinformation which makes the problemmore challenging [1]

Another leading approach for green cellular networks isthe use of RE [5 6] In recent years RE resources such as solarpanels and wind turbines can be considered as complemen-tary energy providers for conventional power systems such asdiesel generators or the power grid Due to the significantlyhigher cost of conventional power generation RE becomesmore and more attractive However although RE sourcesare attractive for green cellular network operations theysuffer from higher variability as compared to conventionalenergy sources [5] Therefore a key consideration for theRE management is to maximize the energy efficiency whilecompensating the variability of the RE source

Under widely dynamic cellular system conditions BSsand RE Providers (REPs) can be assumed as intelligentrational decision makers and they select a best-responsestrategy to maximize their expected payoffs This situationis well suited for the game theory Game theory is a fieldof applied mathematics that provides an effective tool tomodel interactions among independent decision makers Itcan describe the reactions of one set of decision makers toanother and analyze the situations in terms of conflict andcooperation [8] Therefore game theory is really useful inanalyzing the mutual interactions among BSs and REPs andit can be a major paradigm to retain an effective solution ingreen cellular networks

In order to feature the complex interactive relations of BSsand REPs we propose a novel energy control scheme for thegreen cellular network management To ensure fair-efficientenergy provisioning the methodology adopted in the pro-posed scheme is a two-level cooperative game model Thisapproach can improve effectively the energy efficiency andfairness in cellular networks At the efficient-control stagesome BSs are grouped together as a cluster and work togethertoward an optimal system performanceWhen the traffic loadof a specific BS is below a certain threshold this BS is switchedoff and running services are taken care of by neighboring BSsthat remain active in the cluster At the fairness-control stageREPs fairly distribute the available RE to their correspondingBSs Under dynamically changing network environmentsBSs and REPs coordinate with each other in order toensure the fair-efficient energy management Therefore theproposed dual-level game approach is suitable to get a glob-ally desirable network performance while considering thepractical implementation in real-world network operations

This paper is organized as follows The following sectiongives an overview on related studies in the literature Section 3describes how to implement our two-level game model forgreen cellular networks Afterwards the main steps of theproposed algorithm are presented In Section 4 performanceevaluation results are presented along with comparisons withthe existing schemes proposed in [1 4] Through simulationwe show the ability of proposed scheme to achieve highaccuracy and promptness in dynamic cellular network envi-ronments Finally we end up with some concluding remarksin Section 5

2 Related Work

Recently several BS energy management schemes have beenpresented for green cellular network systemsTheDistributedEnergy-Power Control (DEPC) scheme [9] provided a costand energy saving solution for cellular operators In theDEPC scheme two energy-efficient power control algorithmswere developed gradient-based distributed power controlalgorithm and energy-efficient game-based power controlalgorithm The gradient-based approach maximized energyefficiency by macro-BS or femtoaccess points operating in asemiautonomous mode with partial derivatives and systempower information exchanged periodically between neigh-boringmacro-BSs or femtoaccess pointsThe energy-efficientapproach was proposed based on game theory in whicheach BS updated its power-allocation strategy to maximizeits utility The existence and uniqueness of equilibrium of thepower control game were proved [9]

The Switching and Cell Zooming Design (SCZD) scheme[10] investigated the QoS-aware BS switching and cell zoom-ing that is BS power control problem for green wirelesscellular networks This scheme was developed as a unifiedcross-layer model that captured interaction between thephysical and network layers By partitioning each cell intocell partitions the SCZD scheme can explicitly model theintercell interference and location-dependent usersrsquo QoSsThis approach designed an efficient BS switching mechanismthat can maintain user QoS requirements while exploitingheterogeneous traffic distribution over space and time forenergy saving In addition the SCZD scheme developed apower control algorithm that can further improve the energyefficiency [10]

The Decentralized Powered Base Station Control (DPBC)scheme [11] considered a green wireless communication sys-tem inwhich base stationswere powered by renewable energysources This system consisted of a capacity-constrainedrenewable power supplier and a BS that faced a predictablerandom connection demand frommobile user equipment Inthe DPBC scheme the BS which was powered via a com-bination of a renewable power source and the conventionalelectric grid sought to specify the renewable power inventorypolicy that is the power storage level In addition MM1make-to-stock queuing model was proposed to investigatethe decentralized decisions when the two parties optimizedtheir individual costs in a noncooperativemannerThereforethe problemwas formulated as a noncooperative gamewhoseNash equilibrium strategies were characterized to identifythe causes of inefficiency in the decentralized operationMoreover the DPBC scheme provided valuable energy costsavings by allowing the BSs to smartly use a combination ofrenewable and traditional energy even when the BS had aheavy traffic of connections [11]

TheDistributed Cooperative Base Station Sleeping (DCBS)scheme in [1] was developed as a distributed cooperativescheme for improving the energy efficiency of green cellularnetworks To maximize the energy saving the DCBS schemetried to select the BS sleeping strategy while guaranteeingusersrsquo minimal service requirements In this approach theinter-BS cooperation was formulated following the principle

Mobile Information Systems 3

of ecological self-organization To capture the networkimpact of the BS switching operation an interaction graphwas defined and then the problem of energy saving wasformulated as a constrained graphical game where each BSacted as a game player with the constraint of traffic load [1]

The Hybrid Energy Green Utilization (HEGU) schemein [4] decomposed the energy saving problem into twosubproblems the multistage energy allocation problem andthemulti-BSs energy balancing problemThese two problemswere subsequently solved based on the characteristics ofthe green energy generation and the mobile traffic Takingadvantages of the spatial diversity of the mobile trafficthe HEGU scheme attempted to balance the green energyconsumption among BSs so as to reduce the on-grid energyconsumption of the cellular network In the HEGU schemeindividual BSs applied the multistage energy allocation algo-rithm to optimize the green energy allocation based onthe estimation of the mobile traffic and the green energygenerationWith the feedback of green energy allocation thenetwork controller tried to balances the green energy usageamong the BSs and determined the BSs cell sizes [4] Allthe earlier work has attracted much attention and introducedunique challenges However little has been done for the issueof fairness in the green cellular network management

3 Proposed Fair-Efficient EnergyControl Algorithms

In this section we consider a green cellular network poweredby the conventional and renewable energy grid First weintroduce a BS sleeping algorithm for the energy efficiencyAnd then RE distribution algorithm is presented for theenergy fairness Finally we describe the main steps of fair-efficient energy control scheme based on the two-level gamemodel

31 Two-Level Game Model for Green Cellular Networks Atpresent all BSs in cellular networks are working on theldquoalways-ONrdquo state regardless of the traffic levels associatedwith them Moreover a traditional on-state BS is designedto satisfy peak traffic requirements However in fact theaverage peak utilization rates of BSs are merely at 65sim70This situation motivates many power saving efforts thathave been done towards underutilized BSs Nowadays BSsleeping strategy is an effective mechanism to reduce energyconsumption of cellular networks Generally a sleeping BSreduces its energy consumption by 12sim23 compared with itsactive mode Therefore it is reasonable to let a subset of BSsgo to sleep when the traffic load is below a certain threshold[12 13]

During cellular system operations BSs and REPs shouldmake decisions individually In this situation amain issue foreach agent is how to performwell by considering the mutual-interactive relationship In this study the dynamic interac-tions of BSs and REPs are formulated as a two-level gameAt the first level BSs play an efficient-control game the BSsdynamically create an ad hoc cluster and a low traffic load BSis switched off At thismoment the traffic load in the sleeping

BS is effectively shared through a cooperative manner Atthe second level BSs and REP play a fairness-control gamesome BSs are grouped as permanent clusters with one REPand each REP provides the available RE to its correspondingBSs through a cooperative manner For the implementationpracticality our proposed scheme is designed in an entirelydistributed and self-organizing interactive fashion

Mathematically the efficient-control level game (GEC)can be defined as GEC

= NC119894119894isinNL S119895119895isinN 119880119895119895isinN 119879 at

each time period 119905 of gameplay

(i) N = 1 119899 is the finite set of all BSs they are gameplayers in GEC

(ii) C119894is the ad hoc cluster for the sleeping BS 119894 that is

119894 isin N Multiple ad hoc clusters can exist based on thecurrent traffic condition

(iii) L is the set of BSs traffic loads in theC If119898 BSs existinC L can be defined as L = 119897

1 119897

2 119897

119898

(iv) S119895is the set of strategies of the BS 119895 isin C S

119895represents

the amount of taken traffic load from the sleeping BSinC

(v) 119880

119895is the payoff received by the BS 119895 It is the profit

obtained from the BS sleeping algorithm Usuallyit corresponds to the received benefit minus theincurred cost

(vi) The 119879 is a time period The GEC is repeated 119905 isin 119879 lt

infin time periods with imperfect information

To distribute the RE to BSs BSs in green cellular networksare also clustered Compared to the cluster C in GEC theseclusters are formed permanently One REP has its own per-manent cluster and each REP is responsible for distributingits RE to the BSs in its corresponding cluster To formulateinteractions betweenBSs andREPs the fairness-control game(GFC) can be defined asGFC

= K M119894119894isinK A119894119894isinK U119894119895

119894isinK

119895isinM119894

119879 at each time period 119905 of gameplay

(i) K = K1 K

119911 is the finite set of REPs in the

green cellular network where 119911 is the total numberof REPs andK

1198941le119894le119911is the permanent cluster 119894

(ii) M119894 = B1198941 B119894

119908 is the finite set of BSs in the

permanent cluster 119894 where 119908 is the number of BSs inM119894

(iii) In our fairness-control game (GFC)K and M119894119894isinK aregame players

(iv) A119894 = (A1198941A1198942 A119894

119908) is the set of strategies forM119894

A119894 represents the amount of allocated RE and it isdecided by the REPK

119894isin K

(v) U119894119895is the payoff received by BS 119895 isin M119894 It is BS 119895rsquos

profit obtained from the REPK119894

(vi) 119879 is a time period The GFC is repeated 119905 isin 119879 lt infin

time periods with imperfect information


A simple example of GEC can be demonstrated like this ifBS 119894 has a threshold-below traffic load an ad hoc cluster (C)can be formed BSs in this cluster take over the traffic loadfrom BS 119894 while getting the payoff based on the cooperativegame model And then BS 119894 is switched off When the trafficload increases in BS 119894 area BS 119894 is switched on A simpleexample ofGFC can be demonstrated like this if 30 BSs and 5REPs exist in the cellular system each REP can cover 6 BSs ina permanent cluster (M) In each cluster RE is distributedto ensure the fairness among BSs it is also implementedin a cooperative manner The notations for our game-basedalgorithms are given as follows

N the finite set of all BSs

C the ad hoc cluster in the efficient-control levelgame

L the set of BSs traffic loads inC

S the set of strategies of the BS in the efficient-controllevel game

119880 the payoff received by the BS

119879 a time period for game play

K the finite set of REPs

M the finite set of BSs in the permanent cluster

A the set of strategies in the fairness-control levelgame

FB119895 the fixed power consumption for BS 119895

DB119895 the dynamic power consumption for BS 119895

SB BS switching cost including the traffic transfer-ring overhead

119871

minus119894 the transferring traffic load vector from the

sleeping BS 119894

Ψ

B119895 the power consumption in BS 119895

Γ

119871 Γ119867 the lower and upper thresholds

P the incentive-payment vector for BSs

F119890 V the economic fairness index

F119900 119897 the overload fairness index

119872 F119895

M a multiobjective fairness function forM119895

120573 control parameter to different fairness indexes

32 Efficient-Control Game at the First Stage In this studya cellular network deployed in an urban area is consideredand each cell may experience various traffic densities overspace and time Each cell is typically shaped as a hexagonalarea and it is serviced by a BS with a rational operatorFor adaptive power control decisions each BS exchangeslocal information periodically with the adjacent neighboringBSs To save the consuming energy we can switch off theBS with light traffic load while transferring the runningservices to its neighboring BSs [12] In general the powerconsumption in BS 119895 (ΨB

119895) is composed of two types of

power consumptions fixed power consumption (FB119895) and

dynamic power consumption (DB119895) [1 13] FB

119895denotes the

power consumed statically even though a BS is idle In activeBS mode it includes power cost by power amplifier feedertransmit antennas and air conditioningDB

119895mainly denotes

the power used for actual data transmission it is relatedto the current traffic load in BS 119895 [1 13] In addition BSswitching cost (SB) occurs for the case of BS sleeping it is theextra power consumption when the status of BS transformsbetween active and sleepmodesDepending on the associatedtraffic load SB can be estimated by including the traffictransferring overhead

In the proposed scheme each BS reports its own trafficload (119897) periodically to the Mobile Switching Center (MSC)which works as a network gateway and is responsible forthe intercell management of BSs When the traffic load ofBS 119894 is less than the threshold (Γ) BS 119894 and its neighboringBSs dynamically form an ad hoc cluster (C

119894) And then BS 119894

attempts to transfer its traffic load to the neighboring activeBSs in C

119894 In C

119894 the transferring traffic load (119897) from the

sleeping BS 119894 is denoted by

119871

minus119894= [

119897

119894

1

119897

119894

2

119897

119894

119894minus1

119897

119894

119894+1

119897

119894

119898]

119871

minus119894is decided geographically If BS 119894 is switched off the

active BSs inC119894will get paid according to

119871

minus119894 Therefore the

BS sleeping problem can be formulated to an optimizationproblem as follows the goal of this problem is to minimizethe total power consumption ofC

119894

minS119895

sum

119895isinC119894

Ψ

B119895

st if BS 119894 is not switched off ΨB119895

= FB119895

+DB119895 where all 119895 isin C

119894

if BS 119894 is switched off

Ψ

B119895

= FB

119895+DB119895

+T (

119897

119895) where 119895 isin C

119894minus 119894

Ψ

B119894

= SB119894 where 119894 = 119895

DB119895

= 120578 times 119897

119895 S

B119894

= 120576 times 119897

119894 T (

119897

119895) = (120576 times

119897

119895) + (120578 times

119897

119895)

(1)


where 120578 and 120576 are the energy parameters for the trafficload (119897) execution and transferring respectively Even thoughthe BS sleeping strategy is essential to the energy efficiencyin green cellular networks frequent BS onoff switchingmay cause the degradation to the Quality-of-Service (QoS)while increasing the network operational cost To avoid thefrequentmode transitions we develop a dual-threshold basedsleep mechanism When the traffic load of BS is less thanthe lower threshold (Γ

119871) the BS will switch off When the

traffic load of BS reaches the upper threshold (Γ119867) the BS

will switch on Our dual-threshold approach can effectivelyprevent shuttling of BS status between on and off states Basedon the state transition cost and current power consumptionwe adaptively adjust two threshold values while minimizingthe energy consumption In this study Γ

119871and Γ

119867of BS 119894 are

defined as follows

Γ

119894

119871= S

B119894

Γ

119894

119867=

1

1003816

1003816

1003816

1003816

C119894

1003816

1003816

1003816

1003816

times sum

119895isinC119894

119897

119895

(2)

If the active BS 119894rsquos Ψ

B119894

is less than Γ

119894

119871 BS 119894 is switched off If

the traffic load in the sleeping BS 119894rsquos area reaches Γ

119894

119867 the BS

119894 will switch on In this study the MSC and neighboring BSsare assumed to have the ability of detecting the traffic load inthe sleeping BSrsquos area

To design the BS sleeping algorithm we should con-sider how self-interested BSs would agree to serve thetransferred traffic load from the sleeping BS In this studywe use an incentive-payment technique because it canmake a self-organizing system effectively functional Forneighboring BSs the incentive-payment vector P =

[P1(sdot) P

119894minus1(sdot)P119894+1

(sdot) P119898(sdot)] is provided to induce

selfish BSs to participate in the BS sleeping mechanism To

ensure the socially efficient outcome incentive compatibilitybudget balance and participation constraints P should bedynamically decided Based on P the neighboring BS 119895rsquosutility function (119880

119895(sdot)) is defined by

119880

119895(

119897

119894

119895

Ψ

B119895) = minus [(Δ

119890times (120578 times

119897

119894

119895)) + (Δ


119897

119894

119895))]

+P119895(

119871

minus119894

Ψ

B119895)

st

119871

minus119894= [

119897

119894

1

119897

119894

2

119897

119894

119894minus1

119897

119894

119894+1

119897

119894

119898]

119894 = 119895 119894 119895 isin C119894

(3)

where

119897

119894

119895is the transferring traffic load from the sleeping BS

119894 to BS 119895 and

Ψ

B119895

is the extra power consumption for

119897

119894

119895

Δ

119890 Δ119905are the cost fee parameters for using electricity and

transferring overhead for the traffic load (119897119894119895) respectively

P119895(

119871

minus119894

Ψ

B119895) is decided by the MSC based on the traf-

fic distribution information

119871

minus119894 According to the rational

participation constraint P119895(sdot) is dynamically decided to

guarantee 119880

119895(sdot) ge 0 This condition can translate the selfish

motives of BSs into desirable actions for traffic sharingIn this study we develop a cooperative game mechanism

to decidePThemain design goal is to effectively redistributethe saving energy while meeting the rational constraints Tosatisfy this goal our proposed scheme adopts the concept ofRaiffa Bargaining Solution (RBS) this solution can ensure thePareto Optimality Independence of Linear TransformationsSymmetry andMonotonicity [12] To implement the RBS BS119895rsquos preference function V

119895(

119871

minus119894

Ψ

B119895) is defined with the mini-

mum utility119880

min119895

(

119897

119894

119895

Ψ

B119895) and maximum utility119880

max119895

(

119897

119894

119895

Ψ

B119895)

V119895(

119871

minus119894

Ψ

B119895) =

[

[

(119880

119895(

119897

119894

119895

Ψ

B119895) minus 119880

min119895

(

119897

119894

119895

Ψ

B119895)) +

1

1003816

1003816

1003816

1003816

C119894

1003816

1003816

1003816

1003816

minus 2

times ( sum

119896isinC119894 119896 =119894119895

119880

max119896

(

119897

119894

119896

Ψ

B119895) minus 119880

119895(

119897

119894

119895

Ψ

B119895))

]

]

120572119895

st sum

119895isinC119894 119895 =119894

120572

119895= 1

(4)

where 119880

min119895

(

119897

119894

119895

Ψ

B119895) is expected to be the result if BSs cannot

reach an agreement It is at least guaranteed for the BS 119895 inthe cooperative game that is zero in our system 120572

119895is the

normalized bargaining power In the proposed scheme 120572119895is

obtained as sum

119896isinC119894 119896 =119894(

119897

119894

119895

119897

119894

119896) Given this preference function

we can write the RBS optimization problem as follows

Plowast= [Plowast

1(

119871

minus119894

Ψ

B1) P

lowast

119894minus1(

119871

minus119894

Ψ

B119894minus1

) Plowast

119894+1(

119871

minus119894

Ψ

B119894+1

) Plowast

119898(

119871

minus119894

Ψ

B119898)] = argmax

Pprod

119895isinC119894 119895 =119894

V119895(

119871

minus119894

Ψ

B119895)

st sum

119895isinC119894 119895 =119894

Plowast

119895(

119871

minus119894

Ψ

B119895) le (Δ

119890times (120578 times 119897

119894))

(5)


33 Fairness-Control Game at the Second Stage RE is gen-erally defined as energy that comes from resources such assunlight wind tides waves and geothermal heat To decreasethe global greenhouse gas emissions there are many benefitsof using RE sources For green cellular networks RE sourcescan replace conventional energy grid in powering cellularBSs It is useful not only in the environmental but also inthe economic sense while opening opportunities for newbusiness models Nowadays it is of great importance to studythe REmanagement in order to determine the potential gainsand applicability scenarios [14 15]

Adopting RE in cellular systems affects the planningmethodology and architecture of cellular platformThe greencellular network architecture consists of conventional grid-poweredBSs which are also connected byREPs Tomaximizethe energy efficiency the joint design and cooperative com-bination of conventional grid and REPs are critical In thisstudy we assume that multiple RE sources exist uniformlyand a BS is connected by only one RE source Thereforeeach BS is connected by dedicated power lines from theconventional power system and one REP Usually most ofthe energy of BS is provided by the conventional grid whilereceiving subsidized aids from REPs It is a quite general andreal-world applicable architecture [4ndash6]

Each REP has a set of supporting BSs called permanentcluster (M) In a M each BS has its own traffic load whileconsuming energy differently Due to the intermittent supplythe main goal of REmanagement is to fairly distribute the REinM Therefore fairness is a new concern in the RE sharingapproach In computer science the concept of fairness isrelated to the amount of delay in servicing a request thatcan be experienced in a shared resource environment [16]In green cellular network engineering fairness is measuredwhether BSs receive a fair share of RE provisioning Ingeneral RE is relatively cheaper compared to electricity fromtraditional power grid Therefore BSs would always preferusing the RE [14] From the economic viewpoint each BSshould get the same money saving from the RE From theviewpoint of traffic load balancing the BS with a heavy trafficload should get themore RE To characterize the proportionalfairness of RE sharing we follow Jainrsquos fairness index (F) ithas been frequently used to measure the fairness of networkoperations [17] According to the fundamental idea of Fthe economic fairness index (F

119890 V) and the overload fairnessindex (F

119900 119897) in theM119895 are given by

F119895

119890 V =

(sum

119908

119894=1120574

119894(A119895))

2

119908 times sum

119908

119894=1(120574

119894(A119895))

2

F119895

119900 119897=

(sum

119908

119894=1120583

119894(A119895))

2

119908 times sum

119908

119894=1(120583

119894(A119895))

2

(6)

where 119908 and A119895 = (A119895

1A119895

2 A119895

119908) are the number of

BSs and the RE distribution vector for each BSs in M119895respectively 120574

119894(A119895) is BS 119894rsquos obtained money saving from the

RE and 120583

119894(A119895) is the traffic load supported by the traditional

power grid To get the proper combination ofF119895119890 V andF

119895

119900 119897

they should be transformed into a single objective functionTo provide the best compromise in the presence of differentfairness indexes a multiobjective fairness function (119872 F

119895

M)

for M119895 is developed based on the weighted sum methodBy using dynamic joint operations the developed 119872 F

119895

Mis

formulated as follows

119872 F119895

M= [120573

119895timesF119895

119890 V] + [(1 minus 120573

119895) timesF

119895

119900 119897] (7)

where 120573

119895 controls the relative weights given to different fair-ness indexes Under diverse network environments we treat120573

119895 value decision problem as an online decision problemWhen the traffic is uniformly distributed over the BSs inM119895 we can put more emphasis on the economic fairnessthat is on F119895

119890 V In this case a higher value of 120573

119895 is moresuitable But if traffic distributions are relatively nonuniformdue to temporal and spatial traffic fluctuations we shouldstrongly consider the overload fairness that is on F

119895

119900 119897 In

this case a lower value of 120573119895 is more suitable Therefore byconsidering the current traffic profiles of M119895 we decide 120573

119895

value as follows

120573

119895=

min B119895

119897isin M119895 | 120601

119895

119897

max B119895

119896isin M119895 | 120601

119895

119896

(8)

whereB119895119896and 120601

119895

119896are the BS 119896 and the current traffic load of

BS 119896 inM119895Therefore in our fair-control algorithm the valueof 120573 in each M is dynamically adjusted to make the systemmore responsive to current traffic conditions

34 The Main Steps of Proposed Algorithm In this study weinvestigate the BS sleeping and RE distribution algorithmsto maximize the performance of green cellular networksBased on BSsrsquo rationality these algorithms are formulated asa two-level cooperative game model Therefore we assumethat BSs would like to join voluntarily the BS sleeping andRE distribution algorithms only when they can get a profitFor the energy efficiency BSs are grouped dynamically asad hoc clusters and a low traffic load BS is switched offto save the energy Based on the concept of RBS the savedenergy is distributed by active BSs in each cluster For theenergy fairness we intensively use the RE for BSs To geta multiobjective fairness each REP adaptively distributesthe RE to its corresponding permanent cluster The maincontribution of our proposed approach is a sophisticatedcombination of the reciprocal relationship between energyefficiency and fairness it can provide much more suitableenergy sharing scheme Based on the real-time interactiveprocess each BS and each REP act strategically to achievea better profit In this work we do not focus on trying toget an optimal solution based on the traditional approachbut instead an adaptive interactive model is proposedThis approach can dramatically reduce the computationalcomplexity and overheads Usually the traditional optimalsolutions need exponential time complexity However theproposed solution concept only needs polynomial time com-plexityThe proposed algorithm is described by the followingmajor steps


Table 1 Application and system parameters used in the simulation experiment

Application type Maximum service requirement Minimum service requirement Service durationaveragesec

I 128 Kbps 064Kbps 1200 sec (20min)II 256 Kbps 128 Kbps 1800 sec (30min)III 384Kbps 192 Kbps 600 sec (10min)IV 512 Kbps 256Kbps 900 sec (15min)V 640Kbps 320Kbps 1800 sec (30min)VI 724Kbps 362 Kbps 3000 sec (50min)Parameter Value Descriptionn 70 The number of all BSs in green cellular network119911 10 The number of all REPs in green cellular network119898 119908 7 7 The number of BSs inC andM respectivelyFB 1 kW The fixed power consumption for each BS120578 1 The energy parameters for the traffic load execution120576 06 The energy parameters for the traffic transferringΔ

1198901 The cost fee parameters for using electricity

Δ

11990512 The cost fee parameters for transferring traffic load

Step 1 At the starting time all control parameters that is 119899119911119898 119908FB 120578 120576 Δ

119890 and Δ

119905 are chosen from Table 1

Step 2 Based on the distributed online manner each BS ismonitoring individually its own traffic load and periodicallyreports this information to the MSC

Step 3 When a BSrsquos current traffic load is less than Γ

119871or a

traffic load in the sleeping BS area is higher than Γ

119867 this BS

and its neighboring BSs are grouped as a C In each C thevalues of Γ

119871and Γ

119867are dynamically decided according to (2)

Step 4 The MSC makes a BS switching decision whilesatisfying the power minimization problem of (1)

Step 5 If the BS is switched off to save energy the savedenergy is dynamically redistributed through RBS in thecorresponding C The preference function V of each neigh-boring BS in C is estimated according to (4) and the RBSoptimization problem in (5) is solved to get the incentive-paymentP

Step 6 In each M supported by a REP the RE is adaptivelydistributed by considering F

119890 V and F119900 119897 simultaneously

To get a proper multiobjective fairness 120573 and 119872 FM areobtained using (8) and (7) respectively

Step 7 To reduce the computation complexity the amountof energy distribution is specified in terms of basic energyunits (BEUs) where one BEU is the minimum amount of theenergy readjustment for optimal solution

Step 8 Individual BS and REP constantly self-monitor thecurrent traffic situation in a distributed online manner thenext iteration resumes at Step 2

4 Performance Evaluation

In this section we compare the performance of the proposedscheme with other existing schemes [1 4] and confirm theperformance superiority of the proposed approach usinga simulation model We have used the simulation toolMATLAB to develop our simulation model MATLAB isone of the most widely used tools in a number of scientificsimulation fields MATLABrsquos high-level syntax and dynamictypes are ideal for model prototyping In order to ensure thatour simulation model is sufficiently generic to be valid inthe real-world the assumptions used in our simulation areas follows

(i) Our simulation model was a representation of greencellular network system that included traditionalpower grid and REPs

(ii) The simulated system consisted of 70 BSs and 10 REPsfor the green cellular platform

(iii) In each C or M cluster 7 BSs existed and they wereconnected simultaneously by the conventional andrenewable energy grid

(iv) In the traffic load service 1 Kbps service needed 10Welectrical power

(v) In wireless cellular networks traffic services wereelastic applications Application service request wasPoisson with rate 120588 (servicess) and the range of theoffered service load was varied from 0 to 30

(vi) Energy distribution is sequentially negotiated by thesize of one BEU where one BEU is the minimumenergy amount (eg 10W in our system) for theenergy readjustment process

(vii) The RE in each REP was generated randomly from aGaussian distribution


(viii) The service durations of applications were exponen-tially distributed with different means for differentapplication types

(ix) Network performance measures obtained based on100 simulation runs were plotted as a function of theoffered traffic load

(x) The performance criteria obtained through simu-lation were energy saving ratio normalized powerconsumption and system fairness

Table 1 shows the system parameters used in the simulationIn order to emulate a real green cellular network system andperform a fair comparison we used the system parametersfor a realistic simulation model

In this paper we compare the performance of the pro-posed scheme with existing schemes the DCBS scheme[1] and the HEGU scheme [4] These existing schemeswere recently developed as effective green cellular net-work management algorithms However they are success-ful only in certain circumstances and cannot adaptivelyestimate the current cellular system conditions In addi-tion these schemes operate the cellular network system bysome fixed system parameters Compared to these existingschemes we can confirm the superiority of our dual-levelgame approach

Figure 1 presents the performance comparison of eachscheme in terms of energy saving ratio in the green cellularnetwork systems In this study the energy saving ratio is usedfor the performance metric which is defined as [1 minus (theratio between energy consumptions when a number of BSsare turned off and when all BSs are turned on)] Traditionallymonitoring how the power energy is saved is one of the mostcritical aspects of green cellular network management Ourproposed scheme adaptively distributes the energy resourceto BSs according to the game-based approach However theDCBS and HEGU schemes cannot adaptively estimate thecurrent cellular system conditions while causing the extracontrol overhead Therefore we can get a higher energysaving ratio than the other schemes from low to heavy trafficload intensities

Figure 2 shows the normalized power consumption underdifferent traffic loads It is clear that the power consumptionincreases proportional to the number of active BSs this isbecause the power consumptionmainly comes from the fixedpower consumption in each BS From the simulation resultsobtained it is observed that the proposed scheme can adaptto the current traffic condition and effectively reduce thetotal power consumption However other existing schemescan cause potential erroneous decisions under dynamicnetwork environments In general lower power consumptionis a highly desirable property for real-world green cellularsystem operations Under different traffic loads the proposedscheme can provide a lower power consumption than theother schemes

The curves in Figure 3 illustrate the system fairnessfor all the schemes For fair comparison we estimate thesystem fairness of each scheme while considering the eco-nomic and overload fairness equally (120573 = 05) Accord-ing to the intelligent fairness policy the proposed scheme

05 1 15 2 25 30

01

02

03

04

05

Offered traffic loads

Ener

gy sa

ving

ratio

Proposed schemeThe DCBS schemeThe HEGU scheme

Figure 1 Energy saving ratio

05 1 15 2 25 30

01

02

03

04

05

06

07

08

09

1


Nor

mal

ized

pow

er co

nsum

ptio

n


Figure 2 Normalized power consumption

makes the network system adaptable in order to achievea balanced energy distribution while ensuring reciprocalfairness Therefore the proposed scheme can maintain theexcellent system fairness under various traffic load intensi-ties

The simulation results presented in Figures 1ndash3 show thatthe proposed scheme generally exhibits attractive networkperformance compared with the other existing schemes [1 4]under widely different traffic load intensities Due to ouradaptive dual-level game approach we rely on the practi-cal assumptions for real-world cellular system operationsTherefore the proposed algorithm can get an appropriateperformance balance between energy efficiency and fairness


5 10 15 20 25 30

055

06

065

07

075

08

085

09

095

1


Syste

m fa

irnes

s


Figure 3 System fairness

while theDCBS scheme [1] and theHEGU scheme [4] cannotoffer such an attractive network performance

5 Summary and Conclusions

Research on green cellular networks is quite broad anda number of research issues and challenges lie ahead Inparticular energy efficiency is a growing concern for cellularsystem operators to maintain profitability while reducing theoverall environment effects In this study we have looked intothe feasibility of green cellular networks with RE sourcesEmploying RE not only is environment friendly but also hasother benefits with one of the notable points being the shiftfrom energy efficiency to energy fairness To design a novelenergy control scheme we start from a BS sleeping algorithmto maximize the energy efficiency while ensuring the fairnessamong BSs Using two-level game approach self-regardingBSs are induced to actively participate in the fair-efficientenergy control mechanism By analyzing the simulationresults it can be concluded that the proposed scheme caneffectively deal with the energy distribution problem ingreen cellular networks compared to other existing schemesFor future research we need to investigate the design ofenergy aware heterogeneous networks where the high-powermacrocell BSs and low-power femtocell BSs coexist Inaddition to further reduce the energy consumption we arealso looking on the optimal cell size decisions and femtocellBS locations taking into consideration the energy spent forthe system backhaul and signaling overhead

Competing Interests

The author declares that there are no competing interestsregarding the publication of this paper

Authorsrsquo Contributions

Sungwook Kim is a sole author of this work and ES (ieparticipated in the design of mathematical equations theimplementation of proposed algorithm and compared theperformance of the proposed scheme with other existingschemes)

Acknowledgments

This research was supported by the MSIP (Ministry ofScience ICT and Future Planning) Korea under the ITRC(Information Technology Research Center) support pro-gram (IITP-2016-H8501-16-1018) supervised by the IITP(Institute for Information amp Communications TechnologyPromotion) and was supported by Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Education (NRF-2015R1D1A1A01060835)

References

[1] J Zheng Y Cai X Chen R Li and H Zhang ldquoOptimal basestation sleeping in green cellular networks a distributed coop-erative framework based on game theoryrdquo IEEE Transactions onWireless Communications vol 14 no 8 pp 4391ndash4406 2015

[2] J Wu Y Zhang M Zukerman and E K-N Yung ldquoEnergy-efficient base-stations sleep-mode techniques in green cellularnetworks a surveyrdquo IEEE Communications Surveys amp Tutorialsvol 17 no 2 pp 803ndash826 2015

[3] B-H Park Y Kim B-D Kim T Hong S Kim and J K LeeldquoHigh performance computing infrastructure application andoperationrdquo Journal of Computing Science and Engineering vol6 no 4 pp 280ndash286 2012

[4] T Han and N Ansari ldquoOn optimizing green energy utilizationfor cellular networks with hybrid energy suppliesrdquo IEEE Trans-actions on Wireless Communications vol 12 no 8 pp 3872ndash3882 2013

[5] Y-K Chia S Sun and R Zhang ldquoEnergy cooperation incellular networks with renewable powered base stationsrdquo IEEETransactions on Wireless Communications vol 13 no 12 pp6996ndash7010 2014

[6] N Reyhanian V Shah-Mansouri B Maham and C YuenldquoRenewable energy distribution in cooperative cellular net-workswith energy harvestingrdquo inProceedings of the 26thAnnualInternational Symposium on Personal Indoor and Mobile RadioCommunications (PIMRC rsquo15) pp 1617ndash1621 Hong KongSeptember 2015

[7] J Xiao and R Boutaba ldquoThe design and implementation of anenergy-smart home inKoreardquo Journal of Computing Science andEngineering vol 7 no 3 pp 204ndash210 2013

[8] S Kim Game Theory Applications in Network Design IGIGlobal Pennsylvania Pa USA 2014

[9] T Mao G Feng L Liang S Qin and B Wu ldquoDistributedenergy-efficient power control for macro-femto networksrdquoIEEE Transactions on Vehicular Technology vol 65 no 2 pp718ndash731 2016

[10] L B Le ldquoQoS-aware BS switching and cell zooming designfor OFDMA green cellular networksrdquo in Proceedings of theIEEEGlobal Communications Conference (GLOBECOM rsquo12) pp1544ndash1549 IEEE Anaheim Calif USA December 2012


[11] D Li W Saad I Guvenc A Mehbodniya and F AdachildquoDecentralized energy allocation for wireless networks withrenewable energy powered base stationsrdquo IEEE Transactions onCommunications vol 63 no 6 pp 2126ndash2142 2015

[12] Y Bao J Wu S Zhou and Z Niu ldquoBayesian mechanismbased inter-operator base station sharing for energy savingrdquo inProceedings of the IEEE International Conference on Communi-cations (ICC rsquo15) pp 49ndash54 London UK 2015

[13] H Zhang J Cai andX Li ldquoEnergy-efficient base station controlwith dynamic clustering in cellular networkrdquo in Proceedings ofthe 8th IEEE International ICST Conference on Communicationsand Networking in China (CHINACOM rsquo13) pp 384ndash388Guilin China August 2013

[14] C Zhang W Wu H Huang and H Yu ldquoFair energy resourceallocation by minority game algorithm for smart buildingsrdquo inProceedings of the 15th Design Automation and Test in EuropeConference and Exhibition (DATE rsquo12) pp 63ndash68 March 2012

[15] H Al Haj Hassan L Nuaymi and A Pelov ldquoRenewable energyin cellular networks a surveyrdquo in Proceedings of the IEEE OnlineConference on Green Communications (GreenCom rsquo13) pp 1ndash7IEEE Piscataway NJ USA October 2013

[16] M Etinski and A Schulke ldquoFair sharing of RES amongmultipleusersrdquo in Proceedings of the IEEE Power and Energy SocietyInnovative Smart Grid Technologies Conference (ISGT rsquo14) pp1ndash5 Washington DC USA February 2014

[17] M Dianati X Shen and S Naik ldquoA new fairness index forradio resource allocation inwireless networksrdquo inProceedings ofthe IEEE Wireless Communications and Networking Conference(WCNC rsquo05) vol 2 pp 712ndash715 March 2005

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Distributed Sensor Networks


Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014


ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014


Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications


Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia


Biomedical Imaging


ArtificialNeural Systems

Advances in


RoboticsJournal of



Computational Intelligence and Neuroscience

Industrial EngineeringJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in



optimization problem [4] However the BS sleeping problemhas been proven to be NP-hard Moreover solving this prob-lem generally requires a central controller as well as the globalinformation which makes the problemmore challenging [1]

Another leading approach for green cellular networks isthe use of RE [5 6] In recent years RE resources such as solarpanels and wind turbines can be considered as complemen-tary energy providers for conventional power systems such asdiesel generators or the power grid Due to the significantlyhigher cost of conventional power generation RE becomesmore and more attractive However although RE sourcesare attractive for green cellular network operations theysuffer from higher variability as compared to conventionalenergy sources [5] Therefore a key consideration for theRE management is to maximize the energy efficiency whilecompensating the variability of the RE source

Under widely dynamic cellular system conditions BSsand RE Providers (REPs) can be assumed as intelligentrational decision makers and they select a best-responsestrategy to maximize their expected payoffs This situationis well suited for the game theory Game theory is a fieldof applied mathematics that provides an effective tool tomodel interactions among independent decision makers Itcan describe the reactions of one set of decision makers toanother and analyze the situations in terms of conflict andcooperation [8] Therefore game theory is really useful inanalyzing the mutual interactions among BSs and REPs andit can be a major paradigm to retain an effective solution ingreen cellular networks

In order to feature the complex interactive relations of BSsand REPs we propose a novel energy control scheme for thegreen cellular network management To ensure fair-efficientenergy provisioning the methodology adopted in the pro-posed scheme is a two-level cooperative game model Thisapproach can improve effectively the energy efficiency andfairness in cellular networks At the efficient-control stagesome BSs are grouped together as a cluster and work togethertoward an optimal system performanceWhen the traffic loadof a specific BS is below a certain threshold this BS is switchedoff and running services are taken care of by neighboring BSsthat remain active in the cluster At the fairness-control stageREPs fairly distribute the available RE to their correspondingBSs Under dynamically changing network environmentsBSs and REPs coordinate with each other in order toensure the fair-efficient energy management Therefore theproposed dual-level game approach is suitable to get a glob-ally desirable network performance while considering thepractical implementation in real-world network operations

This paper is organized as follows The following sectiongives an overview on related studies in the literature Section 3describes how to implement our two-level game model forgreen cellular networks Afterwards the main steps of theproposed algorithm are presented In Section 4 performanceevaluation results are presented along with comparisons withthe existing schemes proposed in [1 4] Through simulationwe show the ability of proposed scheme to achieve highaccuracy and promptness in dynamic cellular network envi-ronments Finally we end up with some concluding remarksin Section 5

2 Related Work

Recently several BS energy management schemes have beenpresented for green cellular network systemsTheDistributedEnergy-Power Control (DEPC) scheme [9] provided a costand energy saving solution for cellular operators In theDEPC scheme two energy-efficient power control algorithmswere developed gradient-based distributed power controlalgorithm and energy-efficient game-based power controlalgorithm The gradient-based approach maximized energyefficiency by macro-BS or femtoaccess points operating in asemiautonomous mode with partial derivatives and systempower information exchanged periodically between neigh-boringmacro-BSs or femtoaccess pointsThe energy-efficientapproach was proposed based on game theory in whicheach BS updated its power-allocation strategy to maximizeits utility The existence and uniqueness of equilibrium of thepower control game were proved [9]

The Switching and Cell Zooming Design (SCZD) scheme[10] investigated the QoS-aware BS switching and cell zoom-ing that is BS power control problem for green wirelesscellular networks This scheme was developed as a unifiedcross-layer model that captured interaction between thephysical and network layers By partitioning each cell intocell partitions the SCZD scheme can explicitly model theintercell interference and location-dependent usersrsquo QoSsThis approach designed an efficient BS switching mechanismthat can maintain user QoS requirements while exploitingheterogeneous traffic distribution over space and time forenergy saving In addition the SCZD scheme developed apower control algorithm that can further improve the energyefficiency [10]

The Decentralized Powered Base Station Control (DPBC)scheme [11] considered a green wireless communication sys-tem inwhich base stationswere powered by renewable energysources This system consisted of a capacity-constrainedrenewable power supplier and a BS that faced a predictablerandom connection demand frommobile user equipment Inthe DPBC scheme the BS which was powered via a com-bination of a renewable power source and the conventionalelectric grid sought to specify the renewable power inventorypolicy that is the power storage level In addition MM1make-to-stock queuing model was proposed to investigatethe decentralized decisions when the two parties optimizedtheir individual costs in a noncooperativemannerThereforethe problemwas formulated as a noncooperative gamewhoseNash equilibrium strategies were characterized to identifythe causes of inefficiency in the decentralized operationMoreover the DPBC scheme provided valuable energy costsavings by allowing the BSs to smartly use a combination ofrenewable and traditional energy even when the BS had aheavy traffic of connections [11]

TheDistributed Cooperative Base Station Sleeping (DCBS)scheme in [1] was developed as a distributed cooperativescheme for improving the energy efficiency of green cellularnetworks To maximize the energy saving the DCBS schemetried to select the BS sleeping strategy while guaranteeingusersrsquo minimal service requirements In this approach theinter-BS cooperation was formulated following the principle
















1 119897

2 119897

119898


119895represents


(v) 119880






= K M119894119894isinK A119894119894isinK U119894119895

119894isinK

119895isinM119894


(i) K = K1 K




(ii) M119894 = B1198941 B119894




(iv) A119894 = (A1198941A1198942 A119894



119894isin K



















119871


sleeping BS 119894

Ψ


Γ





119872 F119895







119895denotes the





119894) And then BS 119894


119894 In C



119871

minus119894= [

119897

119894

1

119897

119894

2

119897

119894

119894minus1

119897

119894

119894+1

119897

119894

119898]

119871



119871



119894

minS119895

sum

119895isinC119894

Ψ

B119895


= FB119895


119894


Ψ

B119895

= FB

119895+DB119895

+T (

119897

119895) where 119895 isin C

119894minus 119894

Ψ

B119894

= SB119894 where 119894 = 119895

DB119895

= 120578 times 119897

119895 S

B119894

= 120576 times 119897

119894 T (

119897

119895) = (120576 times

119897

119895) + (120578 times

119897

119895)

(1)






119871and Γ

119867of BS 119894 are

defined as follows

Γ

119894

119871= S

B119894

Γ

119894

119867=

1

1003816

1003816

1003816

1003816

C119894

1003816

1003816

1003816

1003816

times sum

119895isinC119894

119897

119895

(2)


B119894

is less than Γ

119894



119894

119867 the BS



[P1(sdot) P

119894minus1(sdot)P119894+1





119880

119895(

119897

119894

119895

Ψ

B119895) = minus [(Δ


119897

119894

119895)) + (Δ


119897

119894

119895))]

+P119895(

119871

minus119894

Ψ

B119895)

st

119871

minus119894= [

119897

119894

1

119897

119894

2

119897

119894

119894minus1

119897

119894

119894+1

119897

119894

119898]

119894 = 119895 119894 119895 isin C119894

(3)

where

119897

119894


119894 to BS 119895 and

Ψ

B119895


119897

119894

119895

Δ



P119895(

119871

minus119894

Ψ



119871



guarantee 119880




119895(

119871

minus119894

Ψ


mum utility119880

min119895

(

119897

119894

119895

Ψ


max119895

(

119897

119894

119895

Ψ

B119895)

V119895(

119871

minus119894

Ψ

B119895) =

[

[

(119880

119895(

119897

119894

119895

Ψ

B119895) minus 119880

min119895

(

119897

119894

119895

Ψ

B119895)) +

1

1003816

1003816

1003816

1003816

C119894

1003816

1003816

1003816

1003816

minus 2

times ( sum

119896isinC119894 119896 =119894119895

119880

max119896

(

119897

119894

119896

Ψ

B119895) minus 119880

119895(

119897

119894

119895

Ψ

B119895))

]

]

120572119895

st sum

119895isinC119894 119895 =119894

120572

119895= 1

(4)

where 119880

min119895

(

119897

119894

119895

Ψ



119895is the


obtained as sum

119896isinC119894 119896 =119894(

119897

119894

119895

119897

119894



Plowast= [Plowast

1(

119871

minus119894

Ψ

B1) P

lowast

119894minus1(

119871

minus119894

Ψ

B119894minus1

) Plowast

119894+1(

119871

minus119894

Ψ

B119894+1

) Plowast

119898(

119871

minus119894

Ψ

B119898)] = argmax

Pprod

119895isinC119894 119895 =119894

V119895(

119871

minus119894

Ψ

B119895)

st sum

119895isinC119894 119895 =119894

Plowast

119895(

119871

minus119894

Ψ

B119895) le (Δ

119890times (120578 times 119897

119894))

(5)







F119895

119890 V =

(sum

119908

119894=1120574

119894(A119895))

2

119908 times sum

119908

119894=1(120574

119894(A119895))

2

F119895

119900 119897=

(sum

119908

119894=1120583

119894(A119895))

2

119908 times sum

119908

119894=1(120583

119894(A119895))

2

(6)

where 119908 and A119895 = (A119895

1A119895

2 A119895




RE and 120583



119895

119900 119897


119895

M)


119895

Mis


119872 F119895

M= [120573

119895timesF119895

119890 V] + [(1 minus 120573

119895) timesF

119895

119900 119897] (7)

where 120573





119895

119900 119897 In


119895

value as follows

120573

119895=

min B119895

119897isin M119895 | 120601

119895

119897

max B119895

119896isin M119895 | 120601

119895

119896

(8)

whereB119895119896and 120601

119895









Δ



119890 and Δ




119871or a


119867 this BS


119871and Γ



























05 1 15 2 25 30

01

02

03

04

05


Ener

gy sa

ving

ratio



05 1 15 2 25 30

01

02

03

04

05

06

07

08

09

1


Nor

mal

ized

pow

er co

nsum

ptio

n






5 10 15 20 25 30

055

06

065

07

075

08

085

09

095

1


Syste

m fa

irnes

s






Competing Interests




Acknowledgments


References


























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in


















1 119897

2 119897

119898


119895represents


(v) 119880






= K M119894119894isinK A119894119894isinK U119894119895

119894isinK

119895isinM119894


(i) K = K1 K




(ii) M119894 = B1198941 B119894




(iv) A119894 = (A1198941A1198942 A119894



119894isin K



















119871


sleeping BS 119894

Ψ


Γ





119872 F119895







119895denotes the





119894) And then BS 119894


119894 In C



119871

minus119894= [

119897

119894

1

119897

119894

2

119897

119894

119894minus1

119897

119894

119894+1

119897

119894

119898]

119871



119871



119894

minS119895

sum

119895isinC119894

Ψ

B119895


= FB119895


119894


Ψ

B119895

= FB

119895+DB119895

+T (

119897

119895) where 119895 isin C

119894minus 119894

Ψ

B119894

= SB119894 where 119894 = 119895

DB119895

= 120578 times 119897

119895 S

B119894

= 120576 times 119897

119894 T (

119897

119895) = (120576 times

119897

119895) + (120578 times

119897

119895)

(1)






119871and Γ

119867of BS 119894 are

defined as follows

Γ

119894

119871= S

B119894

Γ

119894

119867=

1

1003816

1003816

1003816

1003816

C119894

1003816

1003816

1003816

1003816

times sum

119895isinC119894

119897

119895

(2)


B119894

is less than Γ

119894



119894

119867 the BS



[P1(sdot) P

119894minus1(sdot)P119894+1





119880

119895(

119897

119894

119895

Ψ

B119895) = minus [(Δ


119897

119894

119895)) + (Δ


119897

119894

119895))]

+P119895(

119871

minus119894

Ψ

B119895)

st

119871

minus119894= [

119897

119894

1

119897

119894

2

119897

119894

119894minus1

119897

119894

119894+1

119897

119894

119898]

119894 = 119895 119894 119895 isin C119894

(3)

where

119897

119894


119894 to BS 119895 and

Ψ

B119895


119897

119894

119895

Δ



P119895(

119871

minus119894

Ψ



119871



guarantee 119880




119895(

119871

minus119894

Ψ


mum utility119880

min119895

(

119897

119894

119895

Ψ


max119895

(

119897

119894

119895

Ψ

B119895)

V119895(

119871

minus119894

Ψ

B119895) =

[

[

(119880

119895(

119897

119894

119895

Ψ

B119895) minus 119880

min119895

(

119897

119894

119895

Ψ

B119895)) +

1

1003816

1003816

1003816

1003816

C119894

1003816

1003816

1003816

1003816

minus 2

times ( sum

119896isinC119894 119896 =119894119895

119880

max119896

(

119897

119894

119896

Ψ

B119895) minus 119880

119895(

119897

119894

119895

Ψ

B119895))

]

]

120572119895

st sum

119895isinC119894 119895 =119894

120572

119895= 1

(4)

where 119880

min119895

(

119897

119894

119895

Ψ



119895is the


obtained as sum

119896isinC119894 119896 =119894(

119897

119894

119895

119897

119894



Plowast= [Plowast

1(

119871

minus119894

Ψ

B1) P

lowast

119894minus1(

119871

minus119894

Ψ

B119894minus1

) Plowast

119894+1(

119871

minus119894

Ψ

B119894+1

) Plowast

119898(

119871

minus119894

Ψ

B119898)] = argmax

Pprod

119895isinC119894 119895 =119894

V119895(

119871

minus119894

Ψ

B119895)

st sum

119895isinC119894 119895 =119894

Plowast

119895(

119871

minus119894

Ψ

B119895) le (Δ

119890times (120578 times 119897

119894))

(5)







F119895

119890 V =

(sum

119908

119894=1120574

119894(A119895))

2

119908 times sum

119908

119894=1(120574

119894(A119895))

2

F119895

119900 119897=

(sum

119908

119894=1120583

119894(A119895))

2

119908 times sum

119908

119894=1(120583

119894(A119895))

2

(6)

where 119908 and A119895 = (A119895

1A119895

2 A119895




RE and 120583



119895

119900 119897


119895

M)


119895

Mis


119872 F119895

M= [120573

119895timesF119895

119890 V] + [(1 minus 120573

119895) timesF

119895

119900 119897] (7)

where 120573





119895

119900 119897 In


119895

value as follows

120573

119895=

min B119895

119897isin M119895 | 120601

119895

119897

max B119895

119896isin M119895 | 120601

119895

119896

(8)

whereB119895119896and 120601

119895









Δ



119890 and Δ




119871or a


119867 this BS


119871and Γ



























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Acknowledgments


References


























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in

















119871


sleeping BS 119894

Ψ


Γ





119872 F119895







119895denotes the





119894) And then BS 119894


119894 In C



119871

minus119894= [

119897

119894

1

119897

119894

2

119897

119894

119894minus1

119897

119894

119894+1

119897

119894

119898]

119871



119871



119894

minS119895

sum

119895isinC119894

Ψ

B119895


= FB119895


119894


Ψ

B119895

= FB

119895+DB119895

+T (

119897

119895) where 119895 isin C

119894minus 119894

Ψ

B119894

= SB119894 where 119894 = 119895

DB119895

= 120578 times 119897

119895 S

B119894

= 120576 times 119897

119894 T (

119897

119895) = (120576 times

119897

119895) + (120578 times

119897

119895)

(1)






119871and Γ

119867of BS 119894 are

defined as follows

Γ

119894

119871= S

B119894

Γ

119894

119867=

1

1003816

1003816

1003816

1003816

C119894

1003816

1003816

1003816

1003816

times sum

119895isinC119894

119897

119895

(2)


B119894

is less than Γ

119894



119894

119867 the BS



[P1(sdot) P

119894minus1(sdot)P119894+1





119880

119895(

119897

119894

119895

Ψ

B119895) = minus [(Δ


119897

119894

119895)) + (Δ


119897

119894

119895))]

+P119895(

119871

minus119894

Ψ

B119895)

st

119871

minus119894= [

119897

119894

1

119897

119894

2

119897

119894

119894minus1

119897

119894

119894+1

119897

119894

119898]

119894 = 119895 119894 119895 isin C119894

(3)

where

119897

119894


119894 to BS 119895 and

Ψ

B119895


119897

119894

119895

Δ



P119895(

119871

minus119894

Ψ



119871



guarantee 119880




119895(

119871

minus119894

Ψ


mum utility119880

min119895

(

119897

119894

119895

Ψ


max119895

(

119897

119894

119895

Ψ

B119895)

V119895(

119871

minus119894

Ψ

B119895) =

[

[

(119880

119895(

119897

119894

119895

Ψ

B119895) minus 119880

min119895

(

119897

119894

119895

Ψ

B119895)) +

1

1003816

1003816

1003816

1003816

C119894

1003816

1003816

1003816

1003816

minus 2

times ( sum

119896isinC119894 119896 =119894119895

119880

max119896

(

119897

119894

119896

Ψ

B119895) minus 119880

119895(

119897

119894

119895

Ψ

B119895))

]

]

120572119895

st sum

119895isinC119894 119895 =119894

120572

119895= 1

(4)

where 119880

min119895

(

119897

119894

119895

Ψ



119895is the


obtained as sum

119896isinC119894 119896 =119894(

119897

119894

119895

119897

119894



Plowast= [Plowast

1(

119871

minus119894

Ψ

B1) P

lowast

119894minus1(

119871

minus119894

Ψ

B119894minus1

) Plowast

119894+1(

119871

minus119894

Ψ

B119894+1

) Plowast

119898(

119871

minus119894

Ψ

B119898)] = argmax

Pprod

119895isinC119894 119895 =119894

V119895(

119871

minus119894

Ψ

B119895)

st sum

119895isinC119894 119895 =119894

Plowast

119895(

119871

minus119894

Ψ

B119895) le (Δ

119890times (120578 times 119897

119894))

(5)







F119895

119890 V =

(sum

119908

119894=1120574

119894(A119895))

2

119908 times sum

119908

119894=1(120574

119894(A119895))

2

F119895

119900 119897=

(sum

119908

119894=1120583

119894(A119895))

2

119908 times sum

119908

119894=1(120583

119894(A119895))

2

(6)

where 119908 and A119895 = (A119895

1A119895

2 A119895




RE and 120583



119895

119900 119897


119895

M)


119895

Mis


119872 F119895

M= [120573

119895timesF119895

119890 V] + [(1 minus 120573

119895) timesF

119895

119900 119897] (7)

where 120573





119895

119900 119897 In


119895

value as follows

120573

119895=

min B119895

119897isin M119895 | 120601

119895

119897

max B119895

119896isin M119895 | 120601

119895

119896

(8)

whereB119895119896and 120601

119895









Δ



119890 and Δ




119871or a


119867 this BS


119871and Γ



























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Acknowledgments


References


























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in








119871and Γ

119867of BS 119894 are

defined as follows

Γ

119894

119871= S

B119894

Γ

119894

119867=

1

1003816

1003816

1003816

1003816

C119894

1003816

1003816

1003816

1003816

times sum

119895isinC119894

119897

119895

(2)


B119894

is less than Γ

119894



119894

119867 the BS



[P1(sdot) P

119894minus1(sdot)P119894+1





119880

119895(

119897

119894

119895

Ψ

B119895) = minus [(Δ


119897

119894

119895)) + (Δ


119897

119894

119895))]

+P119895(

119871

minus119894

Ψ

B119895)

st

119871

minus119894= [

119897

119894

1

119897

119894

2

119897

119894

119894minus1

119897

119894

119894+1

119897

119894

119898]

119894 = 119895 119894 119895 isin C119894

(3)

where

119897

119894


119894 to BS 119895 and

Ψ

B119895


119897

119894

119895

Δ



P119895(

119871

minus119894

Ψ



119871



guarantee 119880




119895(

119871

minus119894

Ψ


mum utility119880

min119895

(

119897

119894

119895

Ψ


max119895

(

119897

119894

119895

Ψ

B119895)

V119895(

119871

minus119894

Ψ

B119895) =

[

[

(119880

119895(

119897

119894

119895

Ψ

B119895) minus 119880

min119895

(

119897

119894

119895

Ψ

B119895)) +

1

1003816

1003816

1003816

1003816

C119894

1003816

1003816

1003816

1003816

minus 2

times ( sum

119896isinC119894 119896 =119894119895

119880

max119896

(

119897

119894

119896

Ψ

B119895) minus 119880

119895(

119897

119894

119895

Ψ

B119895))

]

]

120572119895

st sum

119895isinC119894 119895 =119894

120572

119895= 1

(4)

where 119880

min119895

(

119897

119894

119895

Ψ



119895is the


obtained as sum

119896isinC119894 119896 =119894(

119897

119894

119895

119897

119894



Plowast= [Plowast

1(

119871

minus119894

Ψ

B1) P

lowast

119894minus1(

119871

minus119894

Ψ

B119894minus1

) Plowast

119894+1(

119871

minus119894

Ψ

B119894+1

) Plowast

119898(

119871

minus119894

Ψ

B119898)] = argmax

Pprod

119895isinC119894 119895 =119894

V119895(

119871

minus119894

Ψ

B119895)

st sum

119895isinC119894 119895 =119894

Plowast

119895(

119871

minus119894

Ψ

B119895) le (Δ

119890times (120578 times 119897

119894))

(5)







F119895

119890 V =

(sum

119908

119894=1120574

119894(A119895))

2

119908 times sum

119908

119894=1(120574

119894(A119895))

2

F119895

119900 119897=

(sum

119908

119894=1120583

119894(A119895))

2

119908 times sum

119908

119894=1(120583

119894(A119895))

2

(6)

where 119908 and A119895 = (A119895

1A119895

2 A119895




RE and 120583



119895

119900 119897


119895

M)


119895

Mis


119872 F119895

M= [120573

119895timesF119895

119890 V] + [(1 minus 120573

119895) timesF

119895

119900 119897] (7)

where 120573





119895

119900 119897 In


119895

value as follows

120573

119895=

min B119895

119897isin M119895 | 120601

119895

119897

max B119895

119896isin M119895 | 120601

119895

119896

(8)

whereB119895119896and 120601

119895









Δ



119890 and Δ




119871or a


119867 this BS


119871and Γ



























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Competing Interests




Acknowledgments


References


























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in









F119895

119890 V =

(sum

119908

119894=1120574

119894(A119895))

2

119908 times sum

119908

119894=1(120574

119894(A119895))

2

F119895

119900 119897=

(sum

119908

119894=1120583

119894(A119895))

2

119908 times sum

119908

119894=1(120583

119894(A119895))

2

(6)

where 119908 and A119895 = (A119895

1A119895

2 A119895




RE and 120583



119895

119900 119897


119895

M)


119895

Mis


119872 F119895

M= [120573

119895timesF119895

119890 V] + [(1 minus 120573

119895) timesF

119895

119900 119897] (7)

where 120573





119895

119900 119897 In


119895

value as follows

120573

119895=

min B119895

119897isin M119895 | 120601

119895

119897

max B119895

119896isin M119895 | 120601

119895

119896

(8)

whereB119895119896and 120601

119895









Δ



119890 and Δ




119871or a


119867 this BS


119871and Γ



























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Competing Interests




Acknowledgments


References


























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in








Δ



119890 and Δ




119871or a


119867 this BS


119871and Γ



























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m fa

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Competing Interests




Acknowledgments


References


























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in












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Competing Interests




Acknowledgments


References


























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




5 10 15 20 25 30

055

06

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Competing Interests




Acknowledgments


References


























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in


















Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



Research Article Dual-Level Game-Based Energy Efficiency...

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Transcript of Research Article Dual-Level Game-Based Energy Efficiency...