09年数学建模手机与能源.docx

09年数学建模手机与能源.docx

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09年数学建模手机与能源

ModelingTelephoneEnergyConsumption

Abstract:

Wediscusstherelationshipbetweenthequantityofmobileandfixedphoneandtheelectricityconsumption.Wegetthebestallocationproportionbetweenmobileandfixedphoneaimat‘pseudoUS’.Then,wethinkaboutthewasteofelectricitycausedbyinappropriatehabitsofelectricityusage,furthermore,weconsidertheelectricitywasteofallthehouseholdappliances.Last,wepredicttheelectricityconsumptionofthe‘pseudoUS’infiftyyears.

Contraposingquestion1.Wesetupthepopulationcompetitionmodelconsideringthetendencyofmobileandfixedphone.Then,wefitthechangingcurveaccordingthedataweget.Last,wegetthephoneelectricityconsumptionmodelthroughthepopulationtrendsandtheestimationofmobileandfixedphone.

Contraposingquestion2.Sincethereareallkindsofstrengthsandweaknessesaboutmobileandfixedphone,theelectricityconsumption,flexibility,economicbenefitandpracticabilityarethemainaspects.Wegetthebestallocationproportionbetweenmobileandfixedphonethatis8:

2applyingtheAHP.

Contraposingquestion3.Themainwastingwayaretheusageofchargerwithoutmobileandmobilechargingexcessively.Wegettheelectricitywastingmodelthroughtheestimationofmobilewasting.

Contraposingquestion4.Weseektheinformationaboutstandbypowerandaveragestand-bytimeofprimaryhouseholdappliances.ThenweestimatethecrudethatbewastedatpresentinAmericais93034barrelseveryyear,makinguseofabove-mentionedpopulationmodel.

Contraposingquestion5.Wemakeuseofelectricityconsumptionmodelandpopulationmodelinthefirstquestion.Thenweestimatetheenergyconsumptionofthe‘pseudoUS’innearlyfiftyyears.Thenwecangivesomeadvicetostrengthenthe“pseudoUS”onthebasisoftheoutcomeofthequestionabove.

Keywords：

Two-speciesCompetitionModelAHPEnergywaste

Contents:

1.Introduction………………………………………………………………………2

2.GeneralAssumptionsandParameters……………………………………………2

3.ModelA--Two-speciesCompetitionModel……………………………………...3

3.1ModelAnalysis………………………………………………………………4

3.2ModelRequirements…………………………………………………………5

3.3ModelSolutions……………………………………………………………….7

3.3.1EnergyConsumptionofFixed-line………………………………………7

3.3.2EnergyConsumptionofMobilePhone………………………………….8

4.ModelB--AnalyticHierarchyProcess……………………………………………10

4.1ModelAnalysis…………………………………………………………………10

4.2ModelSolutions………………………………………………………………10

5.Discussion…………………………………………………………………………13

5.1TheWastedEnergybyMobilePhoneChargers……………………………….13

5.2TheWastedEnergybyHouseholdAppliances………………………………..15

5.3TheWastedEnergyintheNext50Years……………………………………..16

6.Advices……………………………………………………………………………17

7.Modelevaluation…………………………………………………………………..17

8.References…………………………………………………………………………18

Introduction:

Withthecontinuousdevelopmentoftechnology,themobilephonebecauseofitsconvenience,quickness,andgraduallyreplacefixedtelephonyhasbecomethefirstchoiceofpeopletocommunicate.Intheprocessofcellphones,cellphonebatteryneedstobecharged，sotheneedforenergyhasincreasedcomparedwiththefixed-linetelephone,ourgoalistobuildthismodeltoexploreimpactofdemandanduseofenergybecauseofasignificantincreaseinthenumberofmobilephone.WeattempttodeterminetheimpactofthischangeonAmericaenergyconsumption.

Generalassumptions:

（1）Donotconsiderapersonhasmorethanonephone

（2）Governmentinstitutionsarenotincludedintheaccountoffixed-line,onlycalculatethefamily'sfixedtelephonenumber

（3）Annualpowerconsumptionoffixed-lineandmobilephonesareunchanged

Parameters:

：

year

：

theoriginalpopularrateofmobilephone

：

theoriginalpopularrateoffixed-line

：

thegrowthrateofmobilephone’spopularrate

：

thegrowthrateoffixed-line’spopularrate

：

retardativeeffectcoefficientthatmobilephonegivestofixed-line

：

retardativeeffectcoefficientthatfixed-linegivestomobilephone

：

thenumberofmobilephone

：

annualpowerconsumptionofonemobilephone

：

annualpowerconsumptionofonefixed-line

：

thepopularrateofmobilephone

：

thepopularrateoffixed-line

:

thetotalpopulationoft

3.Two-speciesCompetitionModel

3.1Modelanalysis:

Questiononeasksforthatduringtheprogressofmobilephonegraduallyreplacethefixed-line,modelsofconsumingelectricityfromtransitiontoastablestage.Firstofallweneedtoknowthenumberofmobilephoneandfixedtelephoneateachstage.Weneedtoconductmarketsurveysandstatisticspenetration.Mobilephoneandfixedtelephonecanbeconsideredastwobiologicalsystemsspecies,twopopulationscompeteforafoodsourcelikeacompetitionforusers,themostcommonoutcomeisweakcompetitivenesswillbecomeextinct,andcompetitivewillreachthemaximumcapacityoftheenvironmentallowed.Wecaneasilyjudge,withtheprogressanddevelopmentoftechnology,fixed-linecomparedtomobilephonesisrelativelylesscompetitive,andfixed-linewillgraduallylosetheuseofthecrowd,andfinallywascompletelyreplacedbymobilephones,andoutofthemarket,thenthegrowthofmobilephonesdoesnotmatterwithfixed-line.Whencalculatingthepowerconsumptionofthemobilephone,morefactorsneedtobeconsidered.Mobilephonesrequirefrequentchargingthebattery,butthelifeofmobilephonesarenotaslongadfixedtelephone,andwillencounterlostanddamaged,accordingtotheseconditionswewillanalyzechangesinthenumberoffixed-linephoneandchangeforconsumptionanalysisofpowerchange.

3.2Modelrequirements:

Dependingonthenumberofpopulationgrowthmodelshowsthat,whentherearetwospecies,andtheylivealoneinanaturalenvironment,theevolutionnumbersofeachspeciefollowslogisticlaw.Thus,forthespecieAhastheequation:

reflectstheblockingeffectonresourceconsumptionduetoAitsowngrowth,whileotherspecieconsuminglimitedresourcesalsoaffectA’sgrowth.

Inthisquestion,mobilephoneandfixedtelephoneareregardedastwospecies,usingmobilephoneandfixed-linetelephone'spopularrateindicatesthenumberevolutionoftwospecies,N1,N2isthebiggestshareinthemarket.Knownquestionisseekingfromthetransitiontoastablestage,theinitialstageofeveryfamilyhasonetelephone,astablestageisthateveryonehasacellphone,soN1,N2areequaltoone.Sowecangetphoneandfixed-linepopularrateofevolutionequations:

Table1:

1986-2010popularrateofmobilephoneandfixed-line

Byfittingcurvecanbedeterminedintheaboveequationcoefficients,getphoneandfixed-linepopularrateofchangeovertimeasafunctionofthefollowing:

WeuseExceltohandlethedataofmobilephonesandfixed-line'spopularrate.First,selectingthe1984-2010yearsofmobilephonepopularrateandtimedata,makingascatterplotwithExcel.

Figure2:

popularrateofmobilephone

Then,weuseMatlabtomakecurvefittingfollowingLogisticlaw:

Everyhundredpeoplemobilepopularratefunction:

Determinationcoefficient

whichindicatessimulationeffectisgood.

Ascanbeseenfromthechart,mobilephonepopularratein1984alsois0,indicatingthatthattimemobilephonehasnotyetenteredthemarket,tobeused.Butsince1985,mobilephonepopularrateisincreasingeveryyear.During1985to1994,thelinegentlycurve,thephonehasjustenteredthemarket,thepopularrateisrelativelyslowgrowth.Andsince1995,theupwardtrendevidentcurve,thecurvesteeper,mobilephonepopularrateofcontinuous,rapidgrowth,until2010,themarketpopularofmobilephoneshasbeencloseto100%,almosteveryonehasacellphone.

Likewise,useofExcelsoftware,wecangetafixedtelephonescatter,anduseMatlabforcuringpopularratefollowingGaussianlaw.

Figure3:

popularrateoffixed-line

Everyhundredpeoplefixed-linepopularratefunction:

Determinationcoefficient

whichindicatessimulationeffectisgood.

Thefigureshowsthattheoverallfixedtelephonepopularrateincreasesfirstandthendecreasing.In1968,thefixedtelephonypopularratehasmorethanaquarterin1995whenthefixed-linetelephonepenetrationratereachedamaximumof64%.Insubsequentyears,thefixedtelephonypopularratedecreasing.

Tocalculatethetotalpowerconsumption,wefoundfromtheUSCensusBureau'sWebsitetheUnitedStatesnationalpopulationandthetotalnumberofhouseholdsfrom1984to2010,thedatatableisbelow:

Table4:

theusnationalpopulation

3.3Modelsolutions:

3.3.1Energyconsumptionoffixed-line:

Throughanalyzethedevelopmentoffixedtelephone,thepowerthatfixedtelephoneworkuseisnotmuchdifferenceandchangeeveryyear,soweassumethattheannualconsumptionoffixedtelephoneisafixedvalue,andfixed-linetelephonecanuseforalongtime,withoutregardingtofixeddamageandreplacementphones.Surveydatashowsthattheannualpowerconsumptionoffixedtelephone4.38kw•h

USfixed-linetotalelectricityconsumptionperyearequaltoonefixed-lineelectricityconsumptionperyearmultiplynumberoffixed-line.Thatisonefixed-lineelectricityconsumptionperyearmultiplynumberofpopulation

popularrateoffixed-line

3.3.2Energyconsumptionofmobilephone

（1）Chargingpower:

powercellphonechargeristhemostimportantpartofusingenergy.Withthecontinuousdevelopmentofthemobilephone,mobilephoneconsumptionincreasedsignificantly,butachargeofpowerhasnotchangedmuch.Nowmostofthephonechargeseveryday,aswellasseveraltimesadaywithelectriccharge,butthepastisnotsoquickphonepowerconsuming.Surveydatashows