Modeling the correlation between the energy consumption and the end-to-end traffic of services in large telecommunication networks

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Modeling the correlation between the energy

consumption and the end-to-end traﬀic of services in

large telecommunication networks

Wilfried Yoro

To cite this version:

Wilfried Yoro. Modeling the correlation between the energy consumption and the end-to-end traﬀic of

services in large telecommunication networks. Networking and Internet Architecture [cs.NI]. Institut

National des Télécommunications, 2018. English. �NNT : 2018TELE0005�. �tel-01762147�

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ListofFigures 61 Listof Tables 63 Appendices 64 A Closed-formexpressionforShapleyvalueofaplayerinthecase without mandatoryplayers 64 B Case witha mandatoryplayer 66 B.1 Closed-formexpressionforShapleyvalueofthe mandatoryplayer 66 B.2 Closed-formexpressionforShapleyvalueofanon mandatory playerinthecasewitha mandatoryplayer ... 67

C Closed-formexpressionforShapleyvalueofaplayerinthecase

withonly mandatoryplayers 69

D Energyconsumptionofnetworkequipment 70

E Network’straﬃc 74

Bibliography 77

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Educationisthe mostpowerful weaponwhichyoucanuseto changetheworld.

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Acknow

ledgment

IwouldliketoexpressmydeepgratitudetoDoctor MamdouhElTabach,Doctor

TaouﬁkEn-Najjary, Doctor Azeddine Gati,andProfessorTijaniChahed, my

researchsupervisors,fortheirpatientguidance,constantencouragementand

usefulcriticsofthisresearch work. I wouldalsoliketothank Ms Olfa Ben

Haddada, manageroftheteam whereIconducted my PhDstudies,forher

valuablesupportinprovidingmewiththeresourcesindealingwithmyproject.

Finally,specialthanksshouldbegivento myfamilyandfriendsforthe

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Abstract

Internettraﬃcisgrowingexponentially. AccordingtoCisco,mobiledatatraﬃc

willincreasesevenfoldbetween2016and2021,grow

ingatacompoundan-nualgrowthrate(CAGR)of47%.Inordertoimproveorkeepupwithusers

qualityofexperience(QoE), mobilecarriersupgradethenetwork withadd

i-tionalequipment. Asaconsequence,thenetworkcarbonfootprintincreases

overtime,alongsidewithitsenergyconsumption.Inaddition, mobilecarriers

marginsaredecreasing. Globaltelecommunicationrevenuesdecl

inedby4%be-tween2014and2015basedontheinternationaltelecommunicationunion(ITU)

ﬁgures. Theseconcernsfosteredagreatinterestintheresearchcommunityfor

reducingnetworksenergyconsumption.Inthisregard, manyworksinthel

it-eratureinvestigatetheenergyconsumedbyservicesonnetworkequipmentfor

optimizationpurposesnotably,focusingonthevariablecomponentofenergy

consumption. Energyconsumptionofanetworkequipmentiscomposedofa

variableandaﬁxedcomponents. Thevariablecomponentisconsumedtoserve

traffic. Thefixedcomponentisconsumedirrespectiveoftraffic.Inth

isthe-sis,ourobjectiveistosharetheresponsibilityofservicecategoriesintheﬁxed

energyconsumption. Todoso,weusetheShapleyvalue.

First, weconsideraradioaccessnetworkandsharetheresponsibilityof

theservicecategoriesitdeliversintheﬁxedenergyconsumption. Theservices

areclassiﬁedintoﬁvecategories,namely,Streaming, Web, Download, Voice

andotherdataservices.Inaddition,weconsiderthecasewhensomeservice

categoriesare mandatorytobeprovided,suchasVoiceduetolegalconstraints

forinstance. BecausetheShapleyvaluehasahugecomputationalcomplexity,

weintroduceclosed-formexpressionsinordertosigniﬁcantlyreduceit.

Next,weconsidertheend-to-endnetworkandallitssegments,thatis,the

mobileaccess,theﬁxedaccess,thecollect,themobilecore,theregisters,theIP

coreandtheserviceplatforms.Foreachsegment,wesharetheresponsibilityof

theservicecategoriesintheﬁxedenergyconsumptionwiththeShapley-based

modelintroducedintheprecedingchapter. WeﬁndthatStreamingistheservice

thatconsumesthe mostwhateverthenetworksegment,exceptforregisters,as

itrepresentsthevast majorityofInternettraﬃc.

Eventually, wefocusontheservicecategoriesenergyeﬃciency. First, we

considerabasestationandcomputetheservicesenergyeﬃciencyforthecases

withandwithoutsleep mode. Then, weconsideraradioaccessnetworkand

computetheservicesenergyeﬃciencywithandwithouta mandatoryplayer.

Moreover,wediscusstheconditionstonotdeter

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Résumé

D’après Cisco,letraﬁc mobilededonnéesaugmenterad’unfacteur7entre

2016et2021. Pourfairefaceàl’augmentationdutraﬁc,lesopérateurs

mo-biledimensionnentleréseau,cequis’accompagned’uneaugmentationdesa

consommationd’énergieetdesonempreinteCarbonne. Enoutre,les marges

ﬁnancièresdesopérateursbaissent. Ainsi,lerevenuglobalgénéréparlesecteur

destélécommunicationsaconnuunebaissede4%entre2014et2015d’après

l’unioninternationaledestélécommunications(UIT). Cespréoccupationsont

suscitél’intérêtdelacommunautéscientiﬁquepourlaréduct

iondelaconsom-mationélectriquedesréseaux. Desétudesdanslalittératureestimentl’énergie

consomméeparlesservicessurleséquipementsréseauxensefocalisantsurla

consommationvariable.Laconsommationénergétiqued’unéquipementréseau

estcomposéed’unecomposanteﬁxeetd’unecomposantevariable. Danscette

thèse,nouspartageonslaresponsabilitédescatégoriesdeserv

icedanslacon-sommationﬁxeduréseauenutilisantlavaleurdeShapley.

Dansunpremiertemps,nousconsidéronsunréseaud’accèsmobi

leetparta-geonslaresponsabilitédescatégoriesdeservicequ’ilfourn

itdanslaconsomma-tionﬁxe. Nousdéﬁnissons5catégoriesdeservice,àsavoir,le«Streaming»,

le Web,letéléchargement,lavoixetlesautresservicesdedonnées. Enoutre,

noustraitonslecasdeﬁgureoùcertainescatégoriesdeservicesontobligatoires.

EtantdonnélacomplexitéalgorithmiquedelavaleurdeShapley

,nousenpro-posonsuneformeapprochéequipermetd’enréduireconsidérablementletemps

decalcul.

Ensuite,nousconsidéronsleréseaudebout-en-bout,c’est-à-dire,l’accès

mobile,l’accèsﬁxe,lacollecte,lecœurIP,lecœur mobile,lesregistresetles

plateformesdeservice.Pourchaquesegment,nouspartageonslaresponsabilité

descatégoriesdeservicedanslaconsommationﬁxeenappliquantnotremodèle

departagebasésurlavaleurdeShapley.L’analysedesrésultats montrequele

service«Streaming»consommeleplusd’énergiequelquesoitlesegmentde

réseauconsidéré,àl’exceptiondesregistres.

Pourﬁnir,noustraitonsdela modélisationdel’eﬃcacitéénergétiquedes

catégoriesdeservice. Dansunpremiertemps,nouscalculonsl’eﬃcac

itéénergé-tiquedescatégoriesdeserviceétantdonnéunestationdebaseavecetsans«

sleep mode». Ensuite,nouscalculonsl’eﬃcacitéénergétiquedescatégoriesde

serviceétantdonnéunréseaud’accès mobileetconsidérantlescasavecetsans

catégoriesdeserviceobligatoires. Aussiétudions-nouslesconditionspourne

pasdétériorerl’eﬃcacitéénergétiqueduréseauaucoursdutempsenfonction

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Chapter1

Introduct

ion

1 .1 Context

AccordingtoCiscovisualnetworkingindex(VNI)2017[1],global mobiledata

trafficgrew63%in2016,ascomparedto2015figures. Mobiledatatraffic

hasgrown18-foldoverthepast5years. Almosthalfabillion mobiledevices

andconnectionswereaddedin2016.Smartphonesaccountedfor mostofthat

growth. Mobilenetwork(cellular)connectionspeedsgrew morethan3-foldin

2016. Mobilevideotraﬃcaccountedfor60%oftotalmobiledatatraﬃcin2016.

Averagesmartphoneusagegrew38%in2016.

Global mobiledatatraﬃc willincreasesevenfoldbetween2016and2021,

growingatacompoundannualgrowthrate(CAGR)of47percent,Fig. 1.1.

Mobilenetworkconnectionspeeds willincreasethreefoldby2021, Fig. 1.2.

Mobilevideowillincrease9-foldbetween2016and2021,accountingfor78%of

total mobiledatatraﬃcbytheendof2021,Fig. 1.3. Global mobiledevices

andconnectionsCAGRwillbe8%onthesameperiod,Fig.1.4.

Figure1.1: Mobiledatatraﬃcfrom2016to2021

Accordingtotheinternationaltelecommunicationunion(ITU),information

andcommunicationtechnologies(ICTs)havebeenestimatedtocurrent

lycon-tribute2%to2.5%ontheglobalgreenhousegas(GHG)emissions. Thisshare

isexpectedtoincreaserapidlywithbusinessasusualduetotheexponentia

lin-creaseofinternettraﬃc[2,3].InternationalInternetbandwidthgrewworldwide

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Figure1.2: MobileSpeedsbyTechnology:2GVersus3GVersus4Gfrom2016 to2021

Figure1.3: Mobilevideotraﬃcfrom2016to2021

Figure1.4: Global mobiledevicesandconnectionsgrowthfrom2016to2021

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1.6. Meanwhile,globaltelecommunicationrevenuesdeclinedby4%between

2014and2015,Fig.1.7.

Figure1.5:InternationalInternetbandwidthperregionfrom2008to2016,

sourceITU

Figure1.6: Yearlypowerconsumptionforecastfrom2007to2020,sourceITU

Manyworks intheliteratureaddressedtheissueofenergyconsumptionin

networksingeneralandin mobilenetworksinparticular[4,5,6,7,8,9].It

hasbeenshownthatthemostpowerconsumingpartofthenetworkistheradio

accessincludingbasetransceiverstations. Modelshavealsobeengiventoassess

thepowerconsumptionofamobileaccessnetworkatcountrylevel. Wecanalso

ﬁnd moreﬁned-grainedpowerconsumption modelswh

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Figure1.7: Telecommunicationrevenues, worldandbylevelofdevelopment

from2007to2015,sourceITU

consumptionof microbasestationsisstudiedinthecontextofheterogeneous

networks.

Fewerworksconsideredenergyconsumptionoftheservicestransportedby

thenetwork[10,11,12,13,14].Ithasbeenshownthatitisnota

lwaysenergy-wisetousethe Cloud;performingcertaintaskslocallycanbe

moreenergy-eﬃcient. Theenergyconsumptionofinformationandcommunicationtechno

l-ogyservicesand CO2emissionatlife-cycleofequipmentisalsodiscussedin

termsofnegativeandpositiveimpacts:positiveimpactreferstopotentialgains

duetodematerialization,suchasphysicaltransportsubstitution. Negat

iveim-pactreferstoCO2emissionsnotably.

In[15,16,17,18,19,20],theauthorsassesstheenergyconsumptionof

serviceson mobiledevices. Theyprovide modelsusefultodevelopersandhelp

themtounderstandapplicationenergyconsumptionbehavior.Itisshowedthat

3Gand GSMinterfacesconsume moreenergythan WiFi,whichadvocatesfor

thedeploymentof WiFiinHeterogeneousnetworks.Inaddition,itresultsfrom

theseinvestigationsthatfreeapplicationsconsumesign

iﬁcantenergyconsump-tionduenotablytothird-partyadvertisement modules. Moreover,itisshowed

thatenergyconsumedforsignalingtraﬃccanrepresentalargepartinthe

energyconsumption,notablyforalways-onapplicationswhichsendkeep-alive

signalsonacontinuousbasis.

1 .2 Mot

ivat

ionand methodo

logy

Basedonﬁeld measurements,thepowerconsumptionofanetworkequipment

canbe modeledasalinearfunctionoftheloadasillustratedin Fig. 1.8.

Itconsistsoftwocomponents: avariablecomponent whichisconsumedto

servetraffic,andafixedcomponentconsumedirrespectiveoftraffic. Asa

networkequipmentisacommonresourcetypicallysharedbyseveralservices,it

isworthtodeterminethepartofeachserviceintheoverallequipmentenergy

consumptionforoptimizationoreco-designpurposesforexample. Mostauthors

assigntoeachserviceashareinthevariableenergyconsumptionequaltoits

traﬃcproportionasthisenergycomponentisload-dependent[10,11]. Theﬁxed

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traﬃc.

Fixed power consumption Fixed power consumption Fixed power consumption Fixed power consumption Fixed power consumption Fixed power consumption Fixed power consumption Fixed power consumption Fixed power consumption Fixed power consumption Fixed power consumption

Variable power consumption Variable power consumption Variable power consumption Variable power consumption Variable power consumption Variable power consumption Variable power consumption Variable power consumption Variable power consumption Variable power consumption Variable power consumption

0 400 800 1200 0% 25% 50% 75% 100% Trafficload e No de B po we r co ns u mp ti on ( Wa tt)

Figure1.8:Exampleofpowerconsumptionofa4Gbasestation.

Inthisthesis,ourobjectiveistosharetheresponsibilityofservicecategories

intheﬁxedenergyconsumption,knowingthatitcanrepresentupto80%of

thetotalenergyconsumption.It mayseemintuitivetoassigntheﬁxedenergy

consumptionequallytotheservicecategoriesasitisconsumedirrespectiveof

traﬃc. However,thisenergycomponentincreases withtraﬃcovertimedue

tonetworkupgradeoperationsasdepictedinFig.1.9,andso,itissomehow

relatedtoservices.Becauseofthis,weproposetoassigntoeachservicecategory

ashareoftheﬁxedenergyconsumptionbasedonitsimpactonthisincrease.

Weconsiderthattheservicecategoriescooperatetousethenetworkasthe

ﬁxedenergyconsumptiongetsamortized withtraﬃc. Cooperationbehaviors

amongdiﬀerentplayers,inourcaseservicecategories,arestudiedunderthe

frameworkofcooperativegametheory.Incooperativegames,asolutionconcept

isafunctionthatallowstoshareacommoncostorrevenueamongdiﬀerent

players. Theshareofaplayeriscalleditspayoﬀ,andthevectorofpayoﬀsis

anallocation. Somesolutionconceptsfocusonallocationswhichstabilizethe

grandcoalition,thatis,thecoalitionofalltheplayers,andaresuchthatno

subsetofplayerscanimproveitspayoﬀbyleavingthegrandcoalition. Some

othersolutionconceptsdealwithallocationshavingsome"fairness"properties.

Weassumeinourcasethattheservicecategoriescannotformcoalitionsinthe

network,andso,onlythegrandcoalitioncanbeformed. Therefore,thereisno

needforstudyingthestabilityofthegrandcoalition. Weproposeinsteadtouse

theShapleyvaluebecauseofits"fairness"propertyaxiomaticallydeﬁnedbyL.

Shapleyasonethatsatisﬁesthefollowingproperties[21,22,23]:i.Symmetry:

onlytheroleofaplayerinthegameshould matter,nothisspeciﬁcnamesor

label;ii. Carrier:onlyplayerscontributingtothecostshouldbeallocateda

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Inthissense,thefairnesspropertyoftheShapleyvalueisnotafairness

measuresuchas theonesbelongingtoα-fairness[24,25,26,27]oryetthe

Jain’sfairnessindex[28,29].

ItisagoodoutcomethatourmodelsatisﬁestheaxiomsoftheShapleyvalue

astheseaxiomsconveyrationalfairnessproperties.

Fixed energy consumption ofthe network

Traffic evolution ofthe network

0 1 2 3 4 5

Upgrade epochs

Figure1.9:Evolutionoftheloadandnetworkinfrastructure.

AnappreciableoutcomeofourShapley-based modelisthatitisatrade-oﬀ

betweenanequalsharing(uniformsharing)andasharingassigningtoeach

servicecategoryashareequaltoitstraﬃcproportion(proportionalsharing).

Auniformsharingfavorsservicecategorieshavingalargetraﬃc

,andapropor-tionalsharingfavorsthosehavingasmalltraﬃc.

Then,wederivetheenergyeﬃciencyofservicecategor

iesbasedontheout-putofourShapley-based model.

Theproposed modelsarevalidatedwithrea

ldatasetstakenfromanoper-ationalEuropeannetwork.

1 .3 Contr

ibut

ionsand manuscr

iptorgan

izat

ion

Inchapter2,wesharetheresponsibilityofservicecategoriesintheﬁxedenergy

consumptionofaradioaccessnetwork withtheShapleyvalue. Weconsider

thecasewhensomeservicecategoriesare mandatorytobeprovided. Taking

intoaccountthe mandatorynatureofaservicecategoryintheShapley-based

modelincreasesitsshareascomparedtothecasewhenitisnotconsideredtobe

mandatory. BecausetheShapleyvalueisofhugecomputationalcomplexity,we

introduceclosed-formexpressionswhichsigniﬁcantlyreducethecomputational

complexitywhilebeingspeciﬁctotheproposed model. Moreover,westudythe

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Then,inchapter3,weconsidertheend-to-endnetworkandallitssegments,

thatis,the mobileaccess,theﬁxedaccess,thecollect,the mobilecore,the

registers,theIPcoreandtheserviceplatforms. Foreachsegment, weshare

theresponsibilityoftheservicecategoriesintheﬁxedenergyconsumptionwith

theShapley-based modelintroducedintheprecedingchapter. Weapplyour

Shapley-based modeltotraﬃc,toso-calledusefuloutputs(accordingtoETSI

[30],theusefuloutputofanequipmentisdeﬁnedasitsmaximumcapacity,and

isexpressedasthenumberofErlangs,packets/s,subscribers,orsimultaneously

attachedusers)andtobothofthem.Thelasttwocasesimpactonlythesharesin

the mobilecoreenergyconsumptioncomparedwiththeﬁrstcase. Weﬁndthat

Streamingistheservicethatconsumesthemostwhateverthenetworksegment,

exceptforregisters,asitrepresentsthevast majorityofInternettraﬃc.

Next,inchapter4,wederivetheenergyeﬃciencyoftheservicecategories.

Accordingtothe Europeantelecommunicationsstandardsinstitute’s(ETSI)

[31],theenergyeﬃciencyofamobileaccessequipmentisdeﬁnedtobetheratio

ofitstraﬃcvolumetoitsenergyconsumption. Weextendthisdeﬁnitionand

definetheenergyefficiencyofaservicecategorytobetheratioofitstrafficvo

l-umetoitsenergyconsumption. Weconsiderﬁrstabasestation. Considering

the meantraﬃcthroughputand meanpowerconsumption, weexpressedthe

energyeﬃciencyofaservicecategoryastheratioofitstraﬃcthroughputto

itspowerconsumption. Wesharetheresponsibilityoftheservicecategoriesin

theequipmentﬁxedpowerconsumptionusingourShapley-based model. A

fter-ward, westudythecasewhenthebasestationisputintosleep modeduring

idleperiods. Weintroducetheanalyticalexpressionoftheequipmentpower

consumptioninthisscenarioandassignittotheservicecategoriesusinganew

Shapley-basedmodelconsistentwiththisexpression.Inaddition,weconsidera

radioaccessnetworkandcomputetheenergyeﬃciencyoftheservicecategories

itdelivers. Weconsiderthecasewhennoservicecategoryis mandatory,and

thecasewhensomeservicecategoriesare mandatory. Moreover,wediscussthe

conditionstonotdeteriorateanetworkenergyeﬃciencyovertime. Weconsider

thecasewhenthenetworkisupgradedwiththesameradiotechnology,andthe

case whenitisupgraded withanewradiotechnology,typically moreenergy

andspectraleﬃcient.

Eventually,chapter5concludesthe manuscriptandgivessomehintson

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Chapter2

Shar

ingthe Respons

ib

i

l

ity

ofServ

ice Categor

iesinthe

F

ixedEnergy Consumpt

ion

ofa Rad

io Access Network

2 .1 Contextandprob

lemstatement

Inthischapter,weconsideraradioaccessnetworkandsharetheresponsibi

l-ityoftheservicecategoriesitdeliversintheﬁxedenergyconsumption. We

classifytheservicesintocategoriesbasedoncriteriasuchastraﬃc,originating

serviceprovidersand/ordevices. Basedontraﬃc,wesegmenttheservicesinto

5categories,namely,Streaming, Web,Download,otherdataservicesandVoice.

Weconsidertwosettings:theﬁrstonewithaconstantnetworkinfrastructure

andtheotheronewithanevolvinginfrastructure,overalargertimescale,in

termsofadditionaland/orchangingequipmentsoastokeepup withtraﬃc

loadincrease.

Westudytwovariantsofthesharingmodel:onewherenoservicecategoryis

mandatoryandanotheronewithmandatoryplayer(s)whichreﬂectstherealistic

casewhensomeoperatorsmaybelegallymandatedbythestatetooﬀeracertain

service,suchasVoice.

Theremainderofthischapterisorganizedasfollows.Insection2.2, we

reviewsomeliteraturerelatedtocostsharing. Insection2.3, weintroduce

our methodologyforassigningashareoftheﬁxedenergyconsumptiontoeach

servicecategory.Insection2.4, wegivesome materialontheShapleyvalue

concept.Insection2.5,weproposea modelforassigningashareoftheﬁxed

energyconsumptiontoeachservicecategorywiththeShapleyvalue,considering

diﬀerentscenarios. WediscusssomeimplementationissuesoftheShapley-based

modelandhow wetackletheseissuesinsection2.6. Insection2.7, werun

numericalapplicationsbasedonourShapley-basedproposal,onarealdata

settakenfromanoperationalEuropeannetworktransportingthree maindata

services:Streaming, Weband Download,inadditionto Voiceandotherdata

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2 .2 Re

lated work

In[32,33,34,35,36,37,38],theauthorsdiscusscostsharinginajobscheduling

problemusingtheShapleyvalue. Theyhoweverdonotdistinguishbetweenthe

variableandﬁxedcostcomponents,asopposedtoourworkwherewefocuson

theﬁxedenergycomponent. Forinstance, Mishraetal.[32]considerasetof

jobsthatneedtobeservedbyasingleserverwhichcanserveonlyonejobata

time.Jobshaveprocessingtimesandincurwaitingcosts. Thejobssharetheir

coststhroughcompensationusingmonetarytransfers. Theauthorscharacterize

theShapleyvalueruleforthis modelusingfairnessaxioms. Theydeﬁnethe

worthofacoalitionasthecostincurredbyjobsinthecoalitionifthesearethe

onlyjobsservedinthequeue. Theyprecisethatthereare manyotherwaysto

deﬁnetheworthofacoalition,likeconsideringthedualoftheirdeﬁnition,or

byassumingthatacoalitionofjobsareservedafterthejobsnotinthecoalition

areserved.

Yet,otherauthorsconsiderexplicitlyaﬁxedcostcomponentintheircost

sharing.In[39]forinstance,Anshelevichetal.studytheproblemoffaircost

allocationinnetworkdesign. Theauthorsshowthatsharingequallythedesign

costofeachnetworkedgebetweenuserswhoseconnections makeuseofitlead

tonear-optimal Nashequilibria. Anequalsharingofthedesigncostseems

rationalasitisnotdirectlyrelatedtoauser.Inourwork,anequalsharingof

theﬁxedenergyconsumptionbetweentheservicecategories maylookrational

tooasitisconsumedirrespectiveoftraﬃc. However,weconsiderthatanequal

sharingdoesnotreflecttheimpactoftrafficonthefixedenergyconsumption

increase,andso,weproposeasharingoftheﬁxedcostbasedonShapleyvalue.

2 .3 Shar

ingtherespons

ib

i

l

ity ofserv

icecate-gor

iesintheﬁxedenergyconsumpt

ion

Again,basedon[10]and measurementscarriedoutonarealoperationa

lEu-ropeannetworkbythenetworkoperator,thepowerconsumptionofanetwork

equipmentcanbe modeledasalinearfunctionoftheloadwithavariableand

aﬁxedcomponents.

LetPk(t)denotethepowerconsumptionofanetworkequipmentatinstant

t.Itisgivenby:

Pk(t)=Pkf(t)+(Pkmax(t)−Pkf(t))ρk(t) (2.1)

whereP_kf(t)istheﬁxedpowercomponent,Pmax

k (t)the max

imumpowercon-sumption,ρk(t)theloadand(Pkmax(t)−Pkf(t))ρk(t)thevariab

lepowercom-ponent.

LetEkdenotetheenergyconsumptionofthenetworkequipmentkoverthe

timeperiod ∆T.Itisgivenby:

Ek = ∆TPk(t)dt = ∆T(P f k(t)+(Pkmax(t)−Pkf(t))ρk(t))dt

LetE denotestheenergyconsumptionofanetworkcomposedofK equ

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LetEv_andEf_denotethevar_iab_{leandﬁxedenergycomponentso}_fthe networkrespectively: Ev₌ K k=1 ∆T (Pmax k (t)−Pkf(t))ρk(t)dt (2.2) Ef₌ K k=1 ∆T Pf k(t)dt (2.3)

Letusﬁrstconsideraradioaccessnetworkwithonlyoneradiotechnology

(homogeneousnetwork)transportingasetN ofN servicecategories,consuming

energyEwhichistobeassignedtotheservicecategories. Wehave,

E=Ev_+Ef ₍₂_.4)

LetEidenotetheenergyconsumptionassignedtoservicecategoryi,with

variableandﬁxedcomponentsEv

iandEif,respectively,

Ei=Eiv+Eif (2.5)

Theshareofservicecategory iinthevariableenergyconsumptionisits

traﬃcproportionϕiasitisload-dependent. Thatis,

Ev

i=ϕi×Ev (2.6)

Asoftheﬁxedenergycomponent,it mayseemrationaltoshareitequally

betweentheservicecategoriesasitisconsumedirrespectiveoftraﬃc. This

isactuallytheoutcome whenapplyingtheShapleyvaluetothetotalenergy

consumptionofthenetwork(theﬁxedcomponentisequallyassignedtothe

servicecategoriesandthevariablecomponentisassignedproportionallytotheir

traﬃc). However,thisenergycomponentincreaseswithtraﬃcovertimedue

tonetworkupgradeoperationsasdepictedinFig.1.9,andso,itissomehow

relatedtotheservices. Weproposethentoassigntoeachservicecategorya

shareoftheﬁxedenergyconsumptionbasedonitsimpactonthisincrease. To

doso,weusetheShapleyvalueforitsfairnesspropertyasaxiomaticallydeﬁned

byL.Shapleyandpresentedinthenextsection. Thatis,

Eif=φi×Ef (2.7)

whereφiistheShapleyvalueofservicecategoryi.

2 .4 Shap

leyva

lue

Ingametheory,acooperativegame(orcoalitionalgame)isagamewhichallows

groupingofplayerswithinso-calledcoalitions

,thanksforinstancetothepos-sibilityofexternalenforcementofcooperativebehavior(e.g.,throughcontract

law)[40,41,42]. Theseareopposedtonon-cooperativegamesinwhichthere

isnopossibilitytoforgealliances. Thepayoﬀofaplayerinacooperativegame

representsitsgainorlossinthegame. Anallocationrepresentsavectorof

payoﬀs. Cooperativegamesaretypicallyanalyzedintheframeworko

(21)

jointactionsthatgroupstakeandtheresultingcollectivepayoﬀs.Itisopposed

tonon-cooperativegametheorywhichfocusesonpredictingindividualplayers’

actionsandpayoﬀsandanalyzingNashequilibria.

Incooperativegametheory,asolutionisavectorofRN _{thatrepresents}

anallocationtotheplayers,withN thesetofplayers,andN thenumberof

players. Therearetwotypesofsolutionconceptsincooperativegames:the

unobjectionablesolutionsandtheequitablesolutions. Theformerguaranteea

sharingbetweentheplayerssuchthatanycoalition(groupingofplayers)cannot

increaseitsgainbyleavingthecoalitioncomposedofalltheplayers,called

thegrandcoalition. Animputationisasolutionthatexactlysplitsthetotal

valueofthegrandcoalitionamongtheplayers,suchthatnoplayerreceives

lessthan whathecouldgetonhisown. Thecoreisthesetofimputations

under whichnocoalitionhasavaluegreaterthanthesumofits members’

payoﬀs. Unobjectionablesolutionsincludethecore. Therefore,nocoalitionhas

anincentivetoleavethegrandcoalitionandreceivealargerpayoﬀ. Equitable

solutionstakeintoaccountsomeconsiderationofequitybetweenplayers.Such

solutionsincludetheShapleyvalue.

ThecharacteristicfunctionVinacooperativegameisafunctionwh

ichas-sociatestoeachcoalitionanumbercorrespondingtoitsvalue. Acooperative

gameiswithtransferableutilitywhentheplayerscansharetheircommonvalue

amongtheminanyway. Acooperativegamewithtransferableutil

ityisrep-resentedbythenumberofplayersinthegameandthecharacteristicfunction.

LetL(N)denotethesetofsubsetsofN. Acharacteristicfunctionisanelement

ofRL(N)_.

L.ShapleyapproachestheShapleyvalueaxiomatically. Thatis,heasked

whatkindofpropertieswe mightexpectsuchasolutionconcepttosatisfy,and

hecharacterizedthe mappingφthatsatisﬁestheseproperties.

Shapley’sﬁrstaxiomassertsthatonlytheroleofaplayerinthegameshould

matter,nothisspeciﬁcnameorlabelintheset N.

Axiom1 (Symmetry).ForanyV inRL(N)_,anypermutat_{ionπ:N → N,}

andanyplayeriinN,φπ(i)(πV)=φi(V)

ApermutationofthesetofplayersN isanyfunctionπ:N →N suchthat,

foreveryjinN,thereexistsexactlyoneiinN suchthatπ(i)=j. Givenany

suchpermutationπandanycoalitionalgameV,weletπV bethecoalitional

gamesuchthat

πV({π(i)|i∈S})=V(S),∀S⊆N

Thatis,theroleofanyplayeriinV isessentiallythesameastheroleof

theplayerπ(i)inπV.

Shapley’ssecondaxiomassertsthattheplayersinacarriersetshoulddivide

theirjoint worth(whichisequaltothe worthofthegrandcoalition)among

themselves,andallocatenothingtothedummies.

Axiom2 (Carrier).ForanyVinRL(N)_andanycoa_l_it_ionR,i_fRisacarr_ier

ofV,then _i∈Rφi(V)=V(R).

Wesaythatacoalition RisacarrierofacoalitionalgameV iﬀ

V(S∩R)=V(S),∀S⊆N (2.8)

IfRisacarrierofV,thenalltheplayerswhoarenotinRarecalleddummies

(22)

Axiom3 (Linearity).ForanytwocoalitionalgamesV andW inRL(N)_,any

numbersuchthat0≤p≤1,andanyplayeriinN,

φi(pV+(1−p)W)=pφi(V)+(1−p)φi(W) (2.9)

Shapleyshowedthatthereisaunique mappingφcalledtheShapleyvalue

thatsatisﬁesthesethreeaxioms.

Theorem1. Thereisexactlyonefunctionφ:RL(N)_{→ R}N _thatsat_isﬁesthe

threeaxiomsoftheShapleyvalue. Thisfunctionsatisﬁesthefollowingequation,

foreveryiinN andeveryV inRL(N)_:

φi(V)=

S⊆N−i

|S|!(|N|−|S|−1)!

|N|! (V(S∪{i})−V(S)) (2.10)

VissuperadditiveifforanycoalitionsSandTinL(N)suchthatS∩T=∅,

wehave

V(S∪T)≥V(S)+V(T)

IfV issuperadditive,thentheShapleyvalue mustbeindividuallyrational,

inthesensethat

φi(V)≥V({i}),∀i∈N

TheformulafortheShapleyvaluecanbeequivalentlywritten

φi(V)=

S⊆N−i

|S|!(|N|−|S|−1)!

|N|! (V(N\S)−V(S)) (2.11)

2 .5 Shar

ingscenar

ios

2 .5

.1 Case w

ithno mandatoryp

layers

Sharesoftheservicecategoriesandvaluesofthecoalitionsarenormalizedby

theﬁxedenergyconsumption,unlessotherwisestated.

LetSdenoteasetofservicecategories,whichwedenotea"coalition",and

sitssize,i.e.,thenumberofservicecategoriesinthecoalition.

Weassumethatthevalueofcoalition Sistheratioofitstraﬃcvolumeto

thetraﬃcvolumeofcoalitionshavingthesamesizeasS. Thatis,

V(S)= s k1=1vk1,S (N s) j2=1 s k1=1vk1,Sj2 (2.12) where N

s isthenumberofcoalitionsofsizesandvk,Sisthetraﬃcvolume

ofthekth_e_lemento_facoa_l_it_ion_.k

1spansovertheservicecategoriesinsidea

coalition,j2spansovercoalitionsofsizesand(·)isthebinomialcoeﬃcient.

Theintuitionbehindthecharacteristicfunctioncanbeseenasfollows. Over

thelongterm,traﬃcofdiﬀerentservicecategoriesincreases,andsodoesthe

energyconsumption. Ourfocusisontheﬁxedcomponentofth

isenergycon-sumption. Weassumethattheimpactofaservicecategoryintheﬁxedenergy

consumptionincreaseisequaltoitstraﬃcproportion. Andso, wesharethe

ﬁxedcomponentoftheenergyconsumptionbetweentheservicecategor

(23)

theshortterm,theﬁxedenergycomponentisconstant,andso,atthisscale,

what mattersisthenumberofplayerspercoalition,andnotthetraﬃcvolume

ofeachplayer. Andso,theproportionalsharingdoneatthelongerscaleisdone

onlyoncoalitionsofthesamesize.

Thischaracteristicfunctionisaparticularchoice motivatedbytheabove

rationale. Otherchoicesforothercharacteristicfunctionsarepossible.

Thischaracteristicfunctioncanbeexpressedasfollows:

V(S)=ϕ(S)_N−1

s−1

whereϕ(S)isthetraﬃcproportionofcoalitionS.

ThederivationofthisexpressioncanbefoundinAppendixA.

BasedonEqn.(2.10),theshareφiofplayericanbeequivalentlywritten

asEqn.(2.13)[43], φi(V,S)=_N!1 N s=1 (N −s)!(s−1)! (N −1 s−1) j1=1 δ({i},S) (2.13)

where δ({i},S) =V(Sj1,{i})−V(Sj1,{i}\{i})isthe marginalcontributionof

playeriincoalitionS. ItrepresentsthecostgainedorlostbycoalitionS

becauseofplayeri.

Thecomputationalcomplexityof(2.13)growsexponentiallyinthenumber

ofservicecategories,whichcouldrepresentanobstacleforimplementation.So,

weproposeaclosed-formexpressionwhichlowerthecomputationalcomplexity,

derivedfrom(2.13).

Theclosed-formexpressionoftheShapleyvalueofplayeriisgivenby:

φi(N,ϕi)=( N s=1 1 sN s )ϕi+( N s=2 (N−1 s−2 − N−1s−1)N−2s−2 N−1 s−1 N−1s−2sNs )(1−ϕi) (2.14)

ThederivationofthisexpressioncanbefoundinAppendixA.

2 .5

.2 Case w

itha mandatoryp

layer

Letusnowconsiderascenariowitha mandatoryplayer. Thisisthecasefor

instance whenanoperatorhastheobligation,bythestate,tooﬀeragiven

service,notably Voice, whendeployinganetworkinfrastructure. Therefore,

wesupposethatthenetworkcannotprovideasetofservicecategoriesnot

containingthe mandatoryservicecategory. Thatis:

V(S) = ₍ϕ(S)N −1

s−1) ifi

∗_∈S

V(S) = 0 ifi∗_∈S (2.15)

wherei∗_{denotethe mandatoryp}_layer_.

Sharesφi∗ andφ_oofthe mandatoryplayeri∗andanon mandatoryplayer

o,respectively,areobtainedfrom(2.13).

Theclosed-formexpressionoftheShapleyvalueofthe mandatoryplayeris

(24)

φi∗(N,ϕ_i∗)=( N s=1 1 sN s )ϕi∗+( N s=2 N−2 s−2 N−1 s−1 sNs )(1−ϕi∗) (2.16)

ThederivationofthisexpressioncanbefoundinAppendixB.1.

Theclosed-formexpressionoftheShapleyvalueofanon mandatoryplayer

isgivenby: φo(N,ϕi∗,ϕ_o)=( N s=2 (N−1 s−2 − N−1s−1)N−2s−2 N−1 s−1 N−1s−2sNs )ϕi∗+( N s=2 N−2 s−2 N−1 s−1 sNs )ϕo +(N s=3 (N−1 s−2 − N−1s−1)N−3s−3 N−1 s−1 N−1s−2sNs )(1−ϕi∗−ϕo) (2.17)

ThederivationofthisexpressioncanbefoundinAppendixB.2.

2 .5

.3 Case w

ithon

ly mandatoryp

layers

Letusconsiderascenariowherealltheplayersaremandatory. Theclosed-form

Shapleyvalueofplayeriisgivenby:

φi(N)=_N1 (2.18)

ThederivationofthisexpressioncanbefoundinAppendixC.

Thus, whenalltheplayersare mandatory,theﬁxedenergycomponentis

equallyassignedtotheservicecategories. Auniformsharingisthenaspecial

caseoftheShapley-based model.

2 .5

.4 Heterogeneousrad

ioaccessnetwork

Whenthenetworkiscomposedofseveralradioaccesstechnologies, weshare

theresponsibilityoftheservicecategoriespertechnology.

LetT denotethesetofradiotechnologies,Ftthesetofservicecategories

providedbythesub-networkimplementingtheradiotechnologyt,Ev

t(Etf)

thevariable(ﬁxed)energyconsumptionofsub-networktandϕi,tthetraﬃc

proportionofservicecategoryiregardingthesub-networkt. Thetotalnetwork

energyconsumption(variableandﬁxed)assignedtoservicecategoryiisgiven

by:

Ei=

t∈T

ϕi,tEtv+φi,tEtf (2.19)

Ifθtistheshareofthevariablecomponent,then,

Ei=

t∈T

(θtϕi,t+(1−θt)φi,t)Et (2.20)

(25)

2 .5

.5 Evo

lv

ingnetworkinfrastructure

Overlongperiodsoftime,typicallyontheorderofyears,thenetworkin

fras-tructureneedstobeupgradedinordertokeepupwithloadincrease,asdepicted

inFig.1.9.

Whenthereareseveralupgradelevels,theshareofaservicecategoryinthe

ﬁxedenergycomponentofthenetworkisderivedfromitssharespertechnology

andperupgradelevel. LetLdenotethesetofupgradelevels,ϕi,t,lthetraﬃc

proportionofservicecategoryionsub-networktconsideringupgradelevell

andEv

t,l(Eft,l)thevariable(ﬁxed)energyconsumedbysub-networktregarding

upgradelevell.

Ei=

l∈Lt∈T

(ϕi,t,lEt,lv+φi,t,lE_t,lf) (2.21)

Traﬃcvariationsstronglyimpactnetworkupgrade,andso,oneneedsto

makeasharingofenergyandequipmentcosts whichtakesintoaccountthis

aspect. Forthispurpose,onecanconsiderthevariationsoftraﬃc,δv,instead

ofthetraﬃcvolumes,v,inthe model. Traﬃcvariationδvofaservicecategory

representsitstraﬃcincreasebetweentwoupgradelevels. Attheﬁrstupgrade

level,traﬃcvariationscorrespondtotraﬃcvolumes.

Ei= l∈Lt∈T ( δvi,t,l k∈Ftδvk,t,l Ev t,l+φi,t,lE_t,lf) (2.22)

2 .6 Imp

lementat

ionissues

Fig.2.1showstheruntime(inseconds)oftwoalgorithmsforthecomputation

oftheShapleyvaluesoftheservicecategories,oneusingtheShapleyvalue

function (2.13)-denotedby Classical-andtheotherusingtheclosed-form

expressionoftheShapleyvalue(2.14)-denotedbyOptimized.

Thealgorithmusingtheclosed-formexpression(2.14)hasaruntimealmost

independentofthenumberofservicecategoriesinthenetwork(lessthan1

secondforupto50servicecategories,themaximumnumberofservicecategories

we measureintheconsiderednetwork), whilethealgorithmusing(2.13)has

acomputationalcomplexitygrowingexponentiallyinthenumberofservice

categories,doesnotconvergeandhassomeresourcelimitationstartingfroma

certainnumberofservicecategories(dependingonthesimulationenvironment).

ThisisbecausetheShapleyvaluefunctioncomputesthemarginalcontributions

ofeachservicecategoryin2N_−1coa_l_it_ions_,un_l_ikethec_losed-_formexpress_ions

wederivefromit. Theseexpressionsarelinearintraﬃcproportionandcanbe

writteninthefollowinggeneralforms:

φi(N,ϕi)=A(N)ϕi+B(N) (2.23)

for(2.14),

φi∗(N,ϕ_i∗)=C(N)ϕ_i∗+D(N) (2.24)

for(2.16)and

(26)

0 100 200 300 0.08 0.10 0.12 0.14 0.16 Cla ssi cal alg orit h m Opti miz ed alg orit h m 0 10 20 30 40 50

Number of service categories

Ru

nti

me

(

s)

Figure2.1: Runtimesoftheclassical-basedandclosed-form-basedShapleyvalue

algorithms.

for(2.17),whereA(N)istheimpactofplayeritraﬃcinitsshare,C(N)the

impactofthe mandatoryplayeri∗_{traﬃcinitsshare}_{,E(N)theimpacto}_fthe

mandatoryplayer i∗_{traﬃcinanopt}_iona_lp_layeroshare_{,andF(N)theimpact}

ofanoptionalplayeroinitsshare.B(N)isthelowerboundonplayerishare,

D(N)thelowerboundonthe mandatoryplayeri∗_{shareandG(N)thelower}

boundonanoptionalplayeroshare.

Forexample,forN =5, φi(ϕi) =A(5)ϕi+B(5) =0.417ϕi+0.117. As

depictedinFigs.2.2and2.3,A(N),B(N),C(N),D(N),G(N)areasymptot

i-callyequivalentto1/N.E(N)andF(N)tendfasterto0. Thatis(2.14),(2.16)

and(2.17)becomerespectivelyφi(N,ϕi) =1+ϕ_Ni,φi∗(N,ϕ_i∗) =1+ϕ_Ni∗ and

φo(N)=_N1foralargenumberofservicecategories.

Itis worthtonotethatφi(ϕi) =A(2)ϕi+B(2) =ϕiforN =2, which

meansthattheShapley-based modelisequivalenttoaproportionalsharing

whenconsideringjust2servicecategoriesandifnoneiscons

ideredasamanda-toryservice.

Inaddition,besidesthereductionofthecomputationalcomplexity,the

closed-formexpressionsgivethelowerboundontheplayerssharesintheﬁxed

energyconsumption. Consideringforinstancethescenariowithouta

manda-toryplayer,and5servicecategories,thelowerboundontheplayerssharesis

B(5)=12%.

AsillustratedinFig.2.3,thelowerboundontheplayerssharesisafunction

ofthenumberofservicecategoriesdeﬁnedinthe model. Consideringagainthe

scenariowithouta mandatoryplayer,thelowerboundontheplayerssharesis

thehighestwhenconsidering5servicecategories(12%)andthelowestwhen

(27)

0% 25% 50% 75% 100% 0 10 20 30 40 50

I mp ac t of tr aff ic o n f ix ed e ne rg y sh ar es 1/N A(N) C(N) E(N) F(N)

Figure2.2:Impactoftraﬃcproportionsonsharesinﬁxedenergyconsumption.

0% 10% 20% 30% 40% 50% 0 10 20 30 40 50

Lo we r bo un d on fi xe d en er gy s ha re s 1/N B(N) D(N) G(N)

Figure2.3:Lowerboundonsharesinﬁxedenergyconsumption.

2 .7 Numer

ica

lapp

l

icat

ions

We considerarealoperationalEuropeanradioaccessnetwork. Theperiodof

thestudycoverstwoyearsrepresentinga mature2G/3Gnetwork withearly

(28)

servicesthataretransmittedinthenetwork withthefollowingsegmentation

fortheservicecategories:twolargeones,namelystreamingandwebbrowsing,

andthreesmallerones:download,voiceandotherdataservices.Fig.2.4shows

theirtraﬃcproportionsastakenfromtherealdataset. Weconsidertraﬃcand

energyconsumptionofthe3Gsub-network.

Voice 9% Download 13% Other data 13% Web 30% Streaming 35%

Figure2.4: Traﬃcproportionsperservicecategory.

Theshareofaservicecategoryinthevariableenergyconsumptionequals

itstraﬃcproportionasthisenergycomponentisload-dependent. Thisimplies

thatdataservicesareresponsibleforabout90%oftheUMTSTerrestrialRadio

Access Network(UTRAN)variableenergyconsumption. Theseservicesare

dominatedbyOverTheTop(OTT)actorslikeGoogle.

Wenextturntothesharingoftheresponsibilityoftheservicecategoriesin

theﬁxedenergyconsumption.

2 .7

.1 Case w

ithno mandatoryp

layer

WeshowinFig. 2.5thesharingachieved withourShapley-basedproposal

alongsidewithtwootherapproaches:uniformandproportionalsharing. Again,

auniformsharingconsistsinassigningtheﬁxedenergyconsumptionequallyto

theservicecategories,andaproportionalsharingconsistsinassigningtoeach

servicecategoryashareequaltoitstraﬃcproportion.

Auniformsharingfavorsservicecategorieshavingalargetraﬃcvolumeas

(29)

20% 20% 20% 20% 20% 15% 17% 17% 24% 26% 9% 13% 13% 30% 35% Unif or m Sh apl ey −b as ed Pr op orti on al

Streaming Web DownloadOther data Voice

Sh ar es i n f ix ed e ne rg y co ns u mp ti on

Figure2.5: Sharesinﬁxedenergyconsumption: uniform,proportionaland

Shapley-basedsharing.

havingasmalltraﬃcvolume. OurShapley-based modelachievesatrade-oﬀ

giventhatservicecategorieshavingalargetraﬃcvolume,namelystreaming

and web,areassignedalowersharethan withaproportionalapproach,and

thosehavingasmalltraﬃcvolume,namelyvoice,downloadandotherdata

servicesareassignedalowersharewithregardtoauniformsharing.

Thisisanappreciableoutcomeforstreamingandwebasitdoesnotpenalize

themalotandacknowledgesthefactthattheyare majordriversfornetwork

activity,andsoitisforservicecategorieshavingasmalltraﬃcvolumeasit

doesnotmakethemtoomuchresponsiblefortheﬁxedenergyconsumptionand

encouragestheirtransportaswellastheintroductionofnewones.

BasedonourShapley-based model,dataservicesareresponsiblefor85%of

theUTRANﬁxedenergycomponent.

2 .7

.2 Case w

itha mandatoryp

layer

WenowturntothecasewhenVoiceis mandatoryduetolegalconstraints.

AsdepictedinFig.2.6,the mandatorynatureof Voiceisreﬂectedinour

Shapley-based modelwhichincreasessigniﬁcantlyitssharefrom15%to29%.

Itisanexpectedoutcomebecausetheoperatorwouldbe mandatedbythelaw

toimplementandoﬀeritonanationalbasis.Indeed,tooﬀerthisservice,the

operator wouldneedtodeployanetworkanddimensionitinsucha wayto

reachallthecitizensofthegivencountry.Inthiscase,thenetworkcanbeseen

asinitiallydeployedtotransportprimarily Voice,andsoitisnaturalthatit

wouldtakealargepartoftheshareintheenergyconsumption(yetnotallof

(30)

TheaimoftheregulatorisnotnecessarilytoincreasetheshareofVoicein

theenergyconsumptionofthenetwork,butnotablytoguaranteesomebasic

servicesonanationalbasis.

Heretoo,theShapley-basedmodelisatrade-oﬀ. Atrade-oﬀisnotrequired

forVoiceasa mandatoryplayerbecauseitisobligedtobedeliveredwhatever

thesharing model.

20% 20% 20% 20% 20% 29% 17% 17% 19% 19% 9% 13% 13% 30% 35% Unif or m Sh apl ey −b as ed Pr op orti on al

Figure2.6:Sharesinﬁxedenergyconsumption-Voiceisa mandatoryplayer.

2 .7

.3 Caseofanevo

lv

ingnetworkinfrastructure

Wenowstudythecasewhenthenetworkinfrastructureisupgradedinorder

tokeepupwithtraﬃcincrease. Fig.2.7depictsthetraﬃcproportionsofthe

sameservicecategoriesovertwoperiodsoftimecorrespondingtotwonetwork

upgradelevels,termedlevels1and2intheﬁgure. Weconsidertraﬃcprediction

inthisscenario.

Heretoo,eachservicecategoryisassignedashareinthevariableenergy

consumptionequaltoitstraﬃcproportion,andso,thecorrespondingﬁgureis

omitted. Asoftheﬁxedenergyconsumption,Fig. 2.8showsthenewshares

basedonourShapley-basedmodel(2.14),ateachupgradelevel,consideringthe

traﬃcvolumesandthetraﬃcvariationsatlevel2.

Consideringthetraﬃcvolumesputstheweightonservicecategorieshaving

alargetraﬃcvolume. Consideringthetraﬃcvariationsputsthe weighton

servicecategorieswhosetraﬃcincreasesrapidly,reﬂectingtheiractualrolein

thenecessityofupgradingthenetworkinfrastructure(addingnewequipment

inthenetwork),whichinturnincreasesthenetworkenergyconsumption.

Itisimportanttonotethattraﬃcincreaseandtraﬃcvolumesarecorrelated

(31)

9% 13% 13% 30% 35% 4% 13% 12% 32% 39% Le vel 1 Le vel 2

Tr aff ic p ro po rti on s

Figure2.7:Traﬃcperservicecategory-caseofevolvingnetworkinfrastructure.

toincreasefasterintermsoftraﬃc. Asaresult, wenoteasimilarsharing

(intermsofweights)oftheresponsibilityoftheservicecategoriesintheﬁxed

energyconsumptionwhetherweconsidertraﬃcvolumesortraﬃcincreases.

15% 17% 17% 24% 26% 13% 17% 17% 25% 28% 12% 16% 17% 25% 30% Le vel 1 Le vel 2 ( ab sol ut e tr affi c) Le vel 2 (i ncr ea sin g tr affi c)

Streaming Web Download Other data Voice

Figure2.8:Sharesinﬁxedenergyconsumption-caseofevolv

(32)

2 .8 Conc

lus

ion

Weinvestigated inthischapterhowtosharetheresponsibilityofserv

icecate-goriesintheﬁxedenergyconsumptionofaradioaccessnetwork.It mayseem

rationaltoequallyassignedtheﬁxedenergyconsumptiontoservicecategories

asitisconsumedirrespectiveoftraﬃc. However,itincreaseswithtraﬃcover

timeduetonetworkupgradeoperationsandisthensomehowrelatedtoservices.

Becauseofthis,weassignedtoeachservicecategoryashareoftheﬁxedenergy

consumptionbasedonitsimpactonthisincrease. WeusedtheShapleyvalue

todoso. OurShapley-basedmodelputslessweightonservicecategorieshaving

asmallamountoftraﬃcthananequalsharing,andlessweightonserv

icecat-egorieshavingalargeamountoftraﬃcthanasharingproportionaltotraﬃc.

Thisisanappreciableoutcomeasitencouragestransportandintroductionof

smallservices,andacknowledgestheroleoflargerservicesas majordriversfor

networkactivity.

AstheShapleyvaluehasahugecomputationalcomplexity, weprovided

closed-formexpressionsallowingtocomputethesharesoftheservicecategories

withsigniﬁcantlesscomplexity.

Weconsideredtwosettings:onewithaconstantnetworkinfrastructureand

onewithanevolvingnetworkinfrastructureoverlongerperiodsoftime.

More-over,weconsideredthecasewhensomeservicecategoriesarelegallyobligedto

beprovided,suchas Voiceinseveraldeployedoperatornetworks. Theshare

ofa mandatoryservicecategoryincreasessigniﬁcantlyascomparedtothecase

(33)

Chapter3

Shar

ingthe Respons

ib

i

l

ity

ofServ

ice Categor

iesinthe

F

ixedEnergy Consumpt

ion

ofaEnd-to-End Network

3 .1 Contextandprob

lemstatement

Thischapterisageneralizationofchapter2whosemotivationconsistsinsharing

theresponsibilityofservicecategoriesintheﬁxedenergyconsumptionofaradio

accessnetwork.Inthischapter,weconsiderthewholenetworkinfrastructure.

Wedecomposethenetworkinto7blocks,namely,theradioaccess,theﬁxed

access,theaggregation,themobilecore,theregisters,theIPcoreandtheservice

platforms. Weconsider5servicecategories:Streaming, Web,Download,other

dataandVoice. AccordingtoETSI[30],theusefuloutputofanequipmentis

deﬁnedtobeitsmaximumcapacity,andisexpressedasthenumberofErlangs,

packets/s,subscribers,orsimultaneouslyattachedusers.Eachservicecategory

isassignedashareintheﬁxedenergyconsumptionofablockwithourShap

ley-based modelintroducedin[44]. Weﬁrstapplyittotraﬃc,thentoso-called

usefuloutputs.

ApplyingourShapley-based modeltousefuloutputsinsteado

ftraﬃcim-pactsthesharesoftheservicecategoriesregardingthe mobilecoreonly.In

fact,the mobilecoreiscomposedofequipmentwhoseusefu

loutputisnotnec-essarilytraﬃcthroughput.Forexample,theusefuloutputoftheservingGPRS

supportnode(SGSN)isthenumberofsimultaneouslyattachedusersandnot

traﬃcthroughput[30].

Theremainderofthischapterisorganizedasfollows.Insection3.2

,wein-troduceourmodelforsharingtheresponsibilityofservicecategoriesintheﬁxed

energyconsumptionofaend-to-endnetwork.Section3.3showssomenumer

i-calapplicationsofour modelrunonarealdatasettakenfromanoperational

(34)

3 .2 Shar

ing mode

l

Atypicalnetworkiscomposedofanumberofblocks,asillustratedinFig.3.1. A

blockisasetofelementswithacommongeneralfunctionfromanarchitectural

pointofview. Forexample,forradioaccessnetworks,wecandeﬁnetwo main

blocks:theblockofbasestationsandtheblockofcontrollers,whenapplicable.

End-usersshouldalsobeconsideredasoneormoreblocks. Thepartitionofone

blockintosub-blocksshouldbepossiblefollowingtheneedandthecoherence

ofthe model. Eachblockorsub-blockiscomposedofalistofelements. An

elementmaybeanetworkequipment,aserveroradevicethatisusedtodeliver

theservicetotheend-user. Onebasestationisforexampleanelement.

Figure3.1:Exampleofa mobilenetworkdecompositionperblock.

3 .2

.1 Componentsofab

lockenergyconsumpt

ion

Asstatedearlier,theenergyconsumptionofanetworkequipmentiscomposed

of2components:avariableandaﬁxedone. LetEf_kdenotetheﬁxedenergy

componentofequipmentkovertimeperiod ∆T,andEv

kitsvariableenergy

component.

Theoverallenergyconsumptionofablockisthesumofindividualenergy

consumptionsofitselements.LetK denotethenumberofelementsinblockj,

andEjtheenergyconsumptionofblockj. Wehave:

Ej=

K k=1

Ef

k+Ekv (3.1)

Hence,thevariableenergycomponentofblockjisgivenbyEv

j= Kk=1Ekv

anditsﬁxedcomponentisgivenbyE_jf= K_k=1E_kf.

3 .2

.2 Shar

ingtherespons

ib

i

l

ityofserv

icecategor

iesina

b

lockﬁxedenergyconsumpt

ion

Letidenoteaservicecategory,Efi,jtheﬁxedenergyassignedtoservicecategory

iregardingblockjandEv

i,jthevariableenergyassignedtoservicecategoryi

regardingblockj. Letϕi,jdenotethetraﬃcproportionofservicecategoryi

(35)

Aservicecategoryisassignedashareinthevariableenergyconsumption

equaltoitstraﬃcproportionsincethisenergycomponentisload-dependent.

So,

Ev

i,j=ϕi,j×Ejv (3.2)

Eachservicecategoryisassignedashareintheﬁxedenergyconsumption

withourShapley-based modelintroducedintheprecedingchapter. So,the

shareofservicecategoryiintheﬁxedenergyconsumptionofblockjisgiven

by:

Ef

i,j=(A(N)ϕi,j+B(N))×Ejf (3.3)

where A(N)=_N1+ N s=2 1 sN s −(N−1s−2_N−1− N−1s−1)N−2s−2 s−1 N−1s−2sNs (3.4) B(N)= N s=2 (N−1 s−2 − N−1s−1)N−2s−2 N−1 s−1 N−1s−2sNs (3.5)

whereN isthenumberofservicecategoriesand(·)isthebinomialcoeﬃcient.

3 .3 Numer

ica

lapp

l

icat

ions

Inthissection, weconsiderthearchitectureofareal Europeannetworkas

illustratedinFig.3.2.

Figure3.2:End-to-endarchitectureofatelecommunicationnetwork.

Thestudiednetworkconsistsofaﬁxedaccess,a mobileaccess

,anaggrega-tion,amobilecore,theregisters,anIPcoreandastreamingserver. We,again,

consider5servicecategories,namely,Streaming, Web, Download,otherdata

servicesandVoice.

3 .3

.1 Shap

leyva

lueapp

l

iedtotraﬃc

Thenumberofservicecategories N tobeconsideredinthesharingdepends

ontheequipmentunderconsideration. Forexample, mobileswitchingcenters

(36)

Table3.1:Sharing modelparameters Parameters Values A(1) 1 B(1) 0 A(4) 0.556 B(4) 0.111 A(5) 0.417 B(5) 0.117

Table3.2: Weightcoeﬃcients

Networkblock Weight

CScoreenergyconsumption 0.21×Mobilecoreenergyconsumption

PScoreenergyconsumption 0.21×Mobilecoreenergyconsumption

EPCcoreenergyconsumption 0.48×Mobilecoreenergyconsumption

IMScoreenergyconsumption 0.10×Mobilecoreenergyconsumption

SGSNnetworkenergyconsumption 0.16×PScoreenergyconsumption

HSSnetworkenergyconsumption 0.92×Registersenergyconsumption

work,Voicereferstocircuitswitchedvoice. BasedonthepossiblevaluesofN

inourstudy,thevaluesofparametersA(N)ofEqn.(3.4)andB(N)ofEqn.

(3.5)canbefoundinTab.3.1.

The mobilecoreiscomposedofdiﬀerentsub-blocks,namely,thecircuit

switchedcore(CScore),packetswitchedcore(PScore),evolvedpacketcore

(EPC)andIP multimediasubsystemcore(IMScore). Thesesub-blockshave

theirowntraﬃcproportions,andso,theservicecategoriesareassigneddiﬀerent

shares.Inordertocomputethesharesoftheservicecategoriesregardingthe

mobilecore,weneedtoknowtheweightsofthesub-blocksinthe mobilecore

energyconsumption. ValuesoftheseweightsaredepictedinTab.3.2. They

comefrom measurementscarriedoutonthestudiednetworkandcanbefound

inAppendixD(weconsiderenergyconsumptionvaluesofyear2016,knowing

thattheIMSenergyconsumptionwas619 MWhthesameyear).

Givenablock,theshareofaservicecategoryisthe weightedsumofits

sharesintheﬁxedandvariableenergycomponentsoftheblock. Itsshare

inthevariableenergycomponentisweightedwiththeproportionofvariable

energyinthetotalenergyconsumptionoftheblock. Weconsiderthevariable

energycomponenttoaccountfor20%ofablockenergyconsumption[11,45].

Fig.3.3depictsthesharesoftheservicecategor

iesintheenergyconsump-tionofthestudiedoperationalEuropeannetworkperblock. Weobservethe

following:

•Energyconsumptionofthestreamingserverisallocatedintotaltothe

streamingservice.

(37)

30% 50% 49% 36% _20% 49% 100% 24% 16% 16% 27% 20% _16% 0% 11% 17% 17% _9% 20% 16% 0% 16% 18% 18% 14% 20% 18% 0% 19% 0% 0% 14% 20% 0% 0% Str ea min g We b Do wnl oa d Ot her d at a Voi ce RAN Fixed acce ss Aggre gatio n Mobil e core Regis ters IP cor e Strea ming serv er Sh ar es i n en er gy c on su mp ti on

Figure3.3:Sharesinend-to-endnetworkenergyconsumption.

sincewedonotconsider mobilecontrollers,i.e.,BSCsandRNCs,inthe

scopeofthisinvestigation. So,theaggregationnetworkiscomposedof

Ethernetswitchestransportingthetraﬃcoriginatingfromtheﬁxedaccess.

Asaresult,theseblockshavethesametraﬃcdistribution,andso,the

samesharesfortheservicecategories.

•Streamingistheservicethatconsumesthe most,whatevertheb

lockun-derconsideration,exceptfortheregistersgiventhattheirtraﬃcconsists

essentiallyofrequeststhataresupposedtobeevenlydistributedamong

theservicecategories.Streamingconsumesnearlyhalftheenergyofthe

ﬁxedaccess,aggregationandIPcore.Infact,Streamingrepresentsthe

vast majorityoftraﬃcinthenetwork,around60%oftheﬁxedaccess,

aggregationandIPcoretraﬃcregardingthestudiednetwork.

•Sharesregardingthe mobilecorearediﬀerentfromthoseofthe mobile

access(RAN),althoughtheseblocksdealwiththesametraﬃc.Indeed,

traﬃcoriginatingfromthe mobileaccessisnotoperatedbythesame

equipmentinthe mobilecoredependingonthenatureoftheservice.

Be-causeofthis,the mobilecorehasdiﬀerentsharespersub-block,resulting

inglobalsharesdiﬀerentfromthoseofthe mobileaccess.

•SharesregardingtheIPcorearequitesimilartothoseoftheﬁxedaccess,

eventhoughtheIPcoredealswithtraﬃcoriginatingbothfromtheﬁxed

and mobileaccesses. Indeed,thisoutcomeisbecausetheﬁxedtraﬃc

accountsforahugeamountofIPtraffic. Forexample,thefixedtraffic

(including WiFitraﬃc)accountsforaround80%ofoverallIPtraﬃcon

(38)

3 .3

.2 Shap

leyva

lueapp

l

iedtousefu

loutputs

Intheaboveanalysis, weassignedashareoftheblocksenergyconsumption

toeachservicecategorybasedontraﬃc.Inthissection, wecons

idertheso-calledusefuloutputstoassigntoeachservicecategoryashareintheend-to-end

networkenergyconsumption. Again,theusefuloutputofanequ

ipmentisde-ﬁnedtobeits maximumcapacityandisexpressedasthenumberofErlangs,

packets/s,subscribers,orsimultaneouslyattachedusersaccordingtoETSI[30].

It mightbe morerationaltoconsiderusefuloutputinsteadoftraﬃcforsome

equipment. Forexample,it makes moresensetod

iscusstheenergyconsump-tionofthehomesubscriberserver(HSS)intermsofnumberofsubscribers

insteadoftraﬃcthroughput,becausethisequipmentisdesignedforregistering

subscribers.

Simulationsetup

TheusefuloutputsofnetworkequipmentunderinvestigationaregiveninTab.

3.3. Theﬁrstcolumnshowsthenetworkequipmentweconsiderinthescope

ofthisinvestigation,column2givesthecorrespondingusefuloutput,basedon

ETSI[30].Incolumn3,wegivethenumberofservicecategoriesoperatedby

thegivenequipment. Thelastcolumnshowstheusefuloutputproportionsof

theservicecategories.

Traﬃcproportionsofthemobileandﬁxedaccessescomefrommeasurements

carriedoutonthenetworkunderinvestigationbythenetworkoperator.

MSCsdealwithcircuitswitchedservices,andso,wesupposethatonlyVoice

impactstheseequipment.

Weassumethateveryend-userusesallthedataservices,andso,dataservice

categorieshavethesameimpactonSGSNsintermsofsimultaneouslyattached

users. VoicedoesnotimpactSGSNsgiventhattheseequipmentprovidedata

servicesonly. Thesamereasoningappliesforgateway GPRSsupportnodes

(GGSNs),mobilitymanagemententities(MMEs),packetgateways(PGWs)and

signalinggateways(SGWs).

Wealsoassumethatdataserviceshavethesame meanpacketsize,andso,

proportionswhichshouldbecomputedbasedonthroughputexpressedinpacket

persecondcanbeapproximatedwithtraﬃcproportions,whichare moreeasily

measurable.InthecaseofGGSNs,weconsider3Gdatatraﬃcproportionsonly.

Infact, GGSNsdeliver2Gand3Gdatatraﬃc,however,the2Gdatatraﬃcis

negligiblecomparedtothe3Gtraﬃc. Forexample,we measured1%2Gdata

traﬃcversus34%3Gdatatraﬃconthestudiednetwork. Whenitcomesto

PGWsandSGWs,weconsider4Gtraﬃcproportionsinstead.

UsersregisteredintheHSSusealltheservicecategories(Voiceanddata),

andso,theservicecategorieshavethesameimpactonthisequipmentinterms

ofnumberofregisteredsubscribers.Infact,2Gsubscriberscannotbeconsidered

asvoice-onlyusersgiventhattheydogeneratedatatraﬃc;Forexample,there

are4%of2Gsubscribersonthestudiednetwork,andtheygenerate1%oftotal

datatraﬃc. Wekeepthesamereasoning withequipmentidentityregisters

(EIRs)intermsofnumberofregistered mobilephones.

Ethernetswitchescarrytraﬃcoriginatingfromtheﬁxedaccess,andso,

thesetwoblockshavethesametraﬃcproportions.

(39)

accessestrafficproportions;Thefixedtrafficaccountingfor80%oftotaltraffic,

basedon measurementscarriedoutontheinvestigatednetworkbythenetwork

operator. Weconsider WiFitraffictobepartofthefixedaccesstraffic.

Asweconsiderastreamingserver,100%ofitstraﬃcisduetoStreaming.

Useful-output-basedsharingoftheresponsibilityofservicecategories

inthe mobilecoreenergyconsumption

Asstatedabove,onlythesharesofthemobilecoreareimpactedwhenapplying

ourShapley-based modeltousefuloutputsinsteadoftraﬃc.Infact,theuseful

outputofthenetworkblocks,exceptthe mobilecoreandregisters,istraﬃc

throughput,andso,thesharesoftheservicecategoriesarenotalteredcompared

tothecasewhenweapplytheShapley-basedmodeltotraﬃc. Whenitcomesto

the mobilecoreblock,someequipmentusefuloutputisnottraﬃcthroughput.

ThisisthecaseforSGSNs,forexample,whoseusefuloutputisthenumberof

simultaneouslyattachedusers.

Althoughtheusefuloutputofregistersisnottraﬃcthroughput,westillhave

anequalsharingoftheenergyconsumptiongiventhatthenumberofregistered

subscribersinthe HSSandthenumberof mobiledevicesinEIRsareequally

distributedovertheservicecategories,liketherequests. Asaresult,onlythe

ﬁgureofthe mobilecoreblockis modiﬁedasshowninFig.3.4.

Itisimportanttonotethattheuseful-output-basedsharingisbeneﬁcial

toservicecategorieshavingalargetraﬃcvo

lumeascomparedtothetraﬃc-basedsharing.Indeed, moreequipmenthavetheirenergyconsumptionequally

assignedtotheservicecategoriessincetheirusefuloutputisuniformlyd

is-tributed. ThisisthecasefortheSGSN,the HSSandtheEIRforexample.

Replacingasharingproportionaltotraﬃcproportionswithauniformsharing

isnaturallybeneﬁcialtoservicecategorieshavingalargetraﬃcvolumeasi

l-lustratedintheﬁgure. However,theshareofVoiceremainsunchangedbecause

theenergyconsumptionoftheCScoreisthesame.

Hybridsharingoftheresponsibilityofservicecategoriesinthe mobile

coreenergyconsumption

Sincethevariableenergyconsumptionisconsumedproportionallytotheload

[10],theshareofaservicecategoryinthisenergycomponentisequaltoits

traﬃcproportion.

Asoftheﬁxedenergyconsumption, weassignittotheservicecategories

basedontheirutilityfortheblock,expressedbytheusefuloutput.

Forexam-ple,theshareofadataservicecategoryinthevariableenergyconsumptionof

SGSNsisequaltoitstraﬃcproportion,whiletheﬁxedenergyconsumptionis

equallyassignedsincethesimultaneouslyattachedusersonaSGSNareequally

distributedoverthedataservicecategories.

Asaresult,wehaveahybridsharingofthemobilecoreenergyconsumption

inthesensethatitsvariableenergyconsumptionisassignedtotheservice

categoriesbasedontheirtraﬃcproportions,whileitsﬁxedenergyconsumption

isassignedbasedonusefuloutputs. Thesharesoftheservicecategoriesinthe

mobilecoreenergyconsumptionconsideringahybridsharingareshowninFig.

(40)

22%

20%

17% 18%

23%

Sh ar es i n en er gy c on su mp ti on

Figure3.4: Sharesin mobilecoreenergyconsumption: useful-output-based

sharing.

Letusnotethatthehybridsharingliesbetweenthetraﬃc-basedandusefu

l-output-basedsharing,soitisatrade-oﬀbetweentheservicecategoriesinthe

sensethatthosehavingalargevolumeoftraﬃcgetalowersharethanwitha

traﬃc-basedsharing,andsoitisforservicecategorieshavingasmallervolume

oftraﬃcascomparedtoauseful-output-basedsharing.

3 .4 Conc

lus

ion

Inthischapter, wesharedtheresponsibilityofservicecategoriesintheﬁxed

energyconsumptionofaend-to-endnetwork. Wedecomposedtheent

irenet-workinto7blocks,namely,theradioaccess,theﬁxedaccess,theaggregation,

themobilecore,theregisters,theIPcoreandtheserviceplatforms. Weapplied

ourShapley-basedmodelperblock. Weconsidered5servicecategories,namely,

Streaming, Web,Download,otherdataandVoice.

Streamingistheservicethatconsumesmostwhateverthenetworkblock.In

fact,thisserviceaccountsforthevast majorityofInternettraﬃc,around60%

oftheﬁxedaccess,aggregationandIPcoretraﬃcregardingtheoperational

Europeannetworkunderinvestigation.

The mobileaccessand mobilecorehavenotthesamesharesalthoughthey

dealwiththesametraﬃc.Indeed,the mobilecoreiscomposedofsub-blocks

withdifferenttrafficproportionsresultingindifferentglobalsharesascompared

tothe mobileaccess.

WealsoappliedourShapley-basedmodeltousefuloutputs. Onlytheshares

ofthe mobilecoreare modiﬁed,consideringthestudiednetwork.Indeed,the

(41)

24%

21%

15% 17%

23%

Sh ar es i n en er gy c on su mp ti on

Figure3.5:Sharesin mobilecoreenergyconsumption:hybridsharing.

(42)

Ta ble 3.3: Use ful out put s

Usefuloutputproportionsperservicecategory

Networkequipment Usefuloutput Numberofplayers Streaming Web Download Otherdata Voice

MobileBasestations Datathroughput 5 43% 31% 8% 16% 3%

DSLAM/OLT Datathroughput 4 63% 10% 12% 14% 0%

MSC Subscriber 1 0% 0% 0% 0% 100%

SGSN SimultaneouslyAttachedUsers 4 25% 25% 25% 25% 0%

GGSN Paquets/s 4 43% 32% 9% 16% 0%

GGSN SimultaneouslyAttachedUsers 4 25% 25% 25% 25% 0%

MME SimultaneouslyAttachedUsers 4 25% 25% 25% 25% 0%

PGW/SGW Paquets/s 4 45% 32% 8% 15% 0%

PGW/SGW SimultaneouslyAttachedUsers 4 25% 25% 25% 25% 0%

HSS/AuC Subscriber 5 20% 20% 20% 20% 20%

EIR Mobilephones 5 20% 20% 20% 20% 20%

Ethernetswitch Datathroughput 4 63% 10% 12% 14% 0%

IProuter Datathroughput 5 59% 15% 11% 15% 0%

StreamingServer Datathroughput 1 100% 0% 0% 0% 0%

(43)

Chapter4

EnergyEﬃc

iencyofthe

Serv

iceCategor

ies

De

l

iveredbya Mob

i

le

Access Network

4 .1 Contextandprob

lemstatement

Once wehavesharedtheresponsibilityofservicecategoriesinthenetwork

energyconsumption,thischapteraimsatcomputingtheirenergyeﬃciency.

AccordingtoETSI[31],theenergyeﬃciencyofaradioaccessnetworkisthe

ratioofitstraﬃcvolumetoitsenergyconsumption.

Extendingthisdeﬁnition,weintroduceanew metricforcomput

ingtheen-ergyeﬃciencyofservicecategoriesdeliveredbyaradioaccessnetwork

,ex-pressedinbits/imputedJoule. This metricshouldbevalidforallservicesto

bedeﬁnedsuchasvoice,data,videostreaming,onlinegaming,etc,andforall

possiblearchitectures:classicalreferencearchitecture,centralizedradioaccess,

virtualizedradioarchitecture,etc.

Wedeﬁnetheenergyeﬃciencyofaservicecategorytobetheratioofits

traﬃcvolumetoitsenergyconsumption.

Weconsiderﬁrstanetworkequipment. Theenergyeﬃciencyofaservice

categorycanbeexpressedastheratioo

fitstraﬃcthroughputtoitspowercon-sumptionconsideringthe meantraﬃcthroughputand

meanpowerconsump-tion. Wespeciﬁcallyconsider5servicecategories:Streaming, Web,Download,

otherdataservicesandVoice. Weconsidertwocases

:thecasewhenthenet-workequipmenthasnosleep modefeatureandthecase whenitisputinto

sleep modeduringidleperiods,thatis,periodsoftimetheequipmenthasno

packets.Intheformer,weuseourShapley-based modelintroducedpreviously

toassignashareoftheﬁxedpowerconsumptiontoeachservicecategoryand

thenderivetheenergyeﬃciency. Inthelatter,thepowerconsumedbythe

equipmentirrespectiveoftraﬃcistheaverageoftheﬁxedpowerconsumed

whenitisactiveandthepowerconsumedwhenitisinsleep mode. Wegive