Optimal configuration of a resource-on-demand 802.11 WLAN with non-zero start-up times

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Computer Communications

journalhomepage:www.elsevier.com/locate/comcom

Optimal configuration of a resource-on-demand 802.11 WLAN with non-zero start-up times ^R

Jorge Ortín

^a

, Pablo Serrano

^b

, Carlos Donato

^b,c,∗

a Centro Universitario de la Defensa Zaragoza, Zaragoza, Spain

b Departamento de Ingeniería Telemática, Universidad Carlos III de Madrid, Leganés, Spain

c IMDEA Networks Institute, Leganés, Spain

a rt i c l e i n f o

Article history:

Received 28 August 2015 Revised 18 April 2016 Accepted 26 April 2016 Available online xxx Keywords:

WLAN 802.11

Resource on demand Energy consumption Infrastructure on demand

a b s t r a c t

ResourceonDemand in802.11WirelessLANs is receiving anincreasing attention,with itsfeasibility alreadyprovedinpracticeandsomeinitialanalyticalmodelsavailable.However,whilethesemodelshave assumedthataccesspoints(APs)startupinzerotime,experimentationhasshowedthatthisishardly thecase.Inthiswork,weprovideanewmodeltoaccountforthistimeinthesimplecaseofaWLAN formedbytwoAPswherethesecondAPisswitchedon/off dynamicallytoadapttothetrafficloadand reducetheoverallpowerconsumption,andshowthatitsignificantlyalterstheresultswhencomparedto thezerostart-uptimecase,bothqualitativelyand quantitatively.Ourfindingsshowthathavinganon- zero startuptimemodifies significantlythetrade-offs betweenpower consumption and performance thatappearsonResourceonDemandsolutions.Finally,weproposeanalgorithmtooptimizetheenergy consumptionofthenetworkwhileguaranteeingagivenperformancebound.

© 2016PublishedbyElsevierB.V.

1. Introduction

One of the most effective techniques to cope withthe grow- ing traffic demand in wireless networks is to deploy more ac- cess points (APs),thus reducing the per-cellcoverage and facili- tatingspectrumre-use.Thistechnique,though,challengesenergy- efficientoperation,asadeploymentplannedforahightrafficload resultsinahugewastageofenergyatalow loadifall theinfras- tructureiskeptpoweredon.

To achieve energy efficient operation in very dense scenar- ios, thenetwork has to implementa Resource-on-Demand (RoD) schemebywhichAPsareactivatedasthedemandgrowsandde- activated as it shrinks. Given that, in general, mobile networks are carefullyplanned, ownedby asingle operator,andconsist of equipmentwithveryhighenergydemands (and,correspondingly, highenergybills),itcomestonosurprisethatmostoftheresearch sofarinRoDhasfocusonthecaseofcellularnetworks[2,3].For the caseofWireless LAN(WLAN), though,fewer works havead- dressedtheproblemofRoD[4–6].

R This paper is an extended version of our paper [1] , which was presented at the Fourth IFIP Conference on Sustainable Internet and ICT for Sustainability.

∗ Corresponding author at: Avenida de la Universidad 30, Edif. Torres Quevedo, 28911 Leganés, Madrid, Spain.

E-mail address: [email protected] (C. Donato).

Veryrecently,twosurveyshaveaddressedtheimpactofsleep- mode techniques [7]and the impact of on-demand activation of resources [8]on theenergyefficiency ofwireless networks. Both surveys agree that the partial or full deactivation of base sta- tions/APswithlowtraffic isakeyenablerforenergyefficiency.In thisregard,twoofthemainconclusionsin[7],whosefocusiscel- lularnetworks,are:(i)dynamicapproachesoutperformstaticsolu- tions;and(ii)thereisawidespreaduseofover-simplifiedmodels, andfurther research analyzing theimpact of parameters such as thetimerequiredtoswitchon/off basestationsisneeded.

The review of on-demand approaches [8] considers both WLANs and cellular networks. In this survey, more than fifty strategies are classified according to the type of network (cel- lular, WLAN), performance metric (user demand, coverage, QoS, energyefficiency), type of algorithm (online fast reaction, online slowreaction,offline)andcontrolscheme(centralized,distributed, pseudo-distributed,cooperative).Inthiswork,itisalsohighlighted that the delay to switch on/off equipment should be considered whenimplementingthealgorithmsinrealenvironments.

Amongthe workscitedin[8],inthe seminalwork of[4],au- thorsdemonstratethefeasibilityandpotential savingsofRoD for 802.11WLANswith“Survey,Evaluate, Adapt, andRepeat” (SEAR), aRoD framework basedon heuristicsthatopportunistically pow- erson and off APs while maintaining coverage and user perfor- mance.Incontrasttothisexperimental-drivenapproach,in[5]au- thorspresent the first analytical model forRoD, focusing on the http://dx.doi.org/10.1016/j.comcom.2016.04.022

0140-3664/© 2016 Published by Elsevier B.V.

Please cite thisarticle as:J.Ortín etal., Optimal configurationof a resource-on-demand802.11 WLAN withnon-zero start-up times,

Table 1

Time required to switch from the ON state to the OFF state (and vice-versa) in a Linksys WRT54GL.

From (Power) To (Power) Time OFF (0 W) ON (2 .7 W) 45 s ON (2 .7 W) OFF (0 W) 3 s

caseof“clusters” ofAPs(i.e.,deviceswithoverlappingcoveragear- eas)andanalyzingtheimpactofthestrategyusedto (de)activate APsonparameters suchastheenergysavings andtheswitch-off rateofthedevices.In[6],authorsextendtheworkof[5]toana- lyzethecasewhen APsdonot completelyoverlaptheir coverage areas,tounderstandthetrade-offswhene.g.(re)associatingclients fromoneAPtoanotherAPinordertopowerdowntheformer.

Inboth analyticalworks[5,6],aswellasinarecentfollow-up analysis[9],amongothersimplifyingassumptions,authorsneglect thetimerequiredtopoweronanAP.Thisassumptionisalsomade in[10],wheretheimpactoftheAPpowermodelontheenergyef- ficiencyofaWLANisanalyzed.However, in[4]itisreportedthat typicalstart-uptimesrangebetween12and35s.Toconfirmthese results,weperformanexperimentalcharacterizationofthepower consumedbyaLinksysWRT54GLrouterrunningOpenWRT10.03.1, whichisavery popularwireless routerthat hasbeenwidelyde- ployed,followingthe methodology wedescribedin [11] andalso measuringthe averagetime requiredtopower iton (i.e.,thede- vicestartsbroadcastingtheSSID)andtopoweritoff (i.e.,noSSID isbroadcasted).Wenotethat,forthisexperiment,thereisnotraf- fic being transmitted or received in the ON state, which signifi- cantlyimpacts the energyconsumed asreportedin [11]. The re- sultsareprovided inTable 1.As ourresultsconfirm, thesetimes arefarfromnegligible,inparticularwhencomparedagainstinter- arrivalsand/or servicetimes.Inthisworkwerevisit thisassump- tionandassessitsimpactonperformance.

Morespecifically,inthisworkweaddresstheproblemofmod- elingthe time required to start-up an AP ina RoD scenario.We considerthecaseofanetworkwithtwooverlappingAPsandshow that,even in thissimplescenario, considering the start-up times altersbothqualitativelyandquantitativelytheresults,ascompared tothecaseof“immediate” boottimes.Ouranalysisisvalidatedby extensiveevent-drivensimulations, which confirm the validity of themodelforavarietyofscenarios.

2. Systemmodel

Oursystemisasimplifiedversionoftheclustermodelanalyzed in[5],consistingoftwoidenticalAPsserving thesamearea.One of the APs is always on, in order to maintain the WLAN cover- age,while the other AP is opportunistically powered on (off) as usersarrive(leave)thesystem.However, incontrasttothemodel in[5],poweringonthesecond APtakesTon unitsoftime;during thistime,thesecond APisnotavailable andarrivingrequestsare servedbythefirstAP.EachAPconsumesP_AP unitsofpowerwhen active (i.e., during start-up and when powered on) and 0 other- wise.Althoughcommodityhardwarecan supportanintermediate state(i.e.,switchingon/off the wireless card),thisdoesnotbring asmuchsavingsaspoweringon/off thecompletedevice[11].

Inourmodel,a“user” isanewconnectiongeneratedbyawire- lessclient.Following[12],thesearegeneratedaccordingtoaPois- son process at rate

λ

^{and are always served by the lessloaded}

AP.TheAPbandwidthisevenlysharedamongalltheusers,which demand an exponentially distributed amount of work. We argue that although in real systems these amounts of work may devi- ate from the exponential distribution, this assumption serves to illustratethe impact of boot-up timeson performance. Based on

theseassumptions,servicetimesarealsoexponentiallydistributed, withthe departure rate being

μ

^{when there is only one serving}

APand2

μ

^{whenbothAPsareserving,i.e.,weneglecttheimpact}

of channel sharing. We assume a load-balancing algorithm such thatusers(re)associatewhiletheyare beingserved,andthatthis (re)association time is negligible –note that thiscan be achieved with the recent 802.11 v and 802.11 r amendments [13], which supporttriggering re-associations andperforming fasttransitions, respectively, with minor disruption of the service. Following our previousmeasurements, wewillalsoneglectthetimerequiredto poweroff anAP.

We set the maximum number of users per APto K. This as- sumptiononthe“hardcapacity” onthenumberofusers,alsoused in [5], emulates the provisioning ofa minimumbandwidth (e.g., QoS)orthefinitesizeoftheaddresspool.Basedonthis,themax- imumnumberof usersallowed intothe networkis2K;however, despite thereshould be atmostK usersper APwhen thismaxi- mum isreached, weallow up to2K usersintothe firstAPwhile thesecondoneisbeingpoweredon,asuserswillre-associateonce itbecomesavailable.

In orderto power on andoff the second AP, we assume that there is a threshold-based policy with hysteresis: the second AP is powered onwhen there are N_h usersassociated withthe first APandanotheruserarrives,anditispoweredoff whenthereare N_l+1users inthesystemandone ofthem leaves.Therefore,the poweron-off processhasahysteresisofsizeN_h− Nl.Weillustrate inFig.1anexampleoftheprocessofswitchingon/off APsforthe caseofN_h=5andN_l=3. Asthefigure shows,when thereare5 usersinthe WLANonlyone APispoweredon,butwhena sixth userarrivesthesecondAPstartstobootup(althoughitmaytake some time beforeit canserve users).Then, atsome point auser leaves,butbothAPs arekepton,andevenwithfourusersnoAP isdeactivated. Onlywhen thelimit N_l=3isreached, the second APisswitched off andonly oneAPremains active. Thisexample correspondstoahysteresisofN_h− Nl=2.

Wecharacterizetheperformanceofthesystemwiththefollow- ingfigures:

• TheaveragepowerconsumedbytheinfrastructureP.

• TheaveragetimespentinthesystembyauserTs.

• Theprobability thata userisnot allowedinto thesystembe- causeofreaching thehard limit of2K users, i.e., theblocking probabilityp_B.

• TherateatwhichthesecondAPispoweredon/off

ω

^,whichis

anotherkeyvariable ofinterestasitcan affectthelifetimeof theequipment.

The focus of the work is first to model the impact of Ton on thesevariables,thentounderstandthedifferenttrade-offsinper- formance,andfinallytoderivetheoptimalconfigurationofanRoD schemebasedonanoptimizationcriterion.

3. Performanceanalysis

We modelour systemwith theregenerative process [14] illus- tratedinFig.2.Thisregenerativeprocessisformedbythreestages, whichdependonthestatusofthesecondAP:

• StageA,inwhichthesecondAPisinactive.

• Stage B, in which it is being powered on but cannot serve clientsyet.

• StageC,inwhichbothAPsareactiveandservingusers.

Followingthedescriptionofthesystemmodel,therearethree transitions:

• The transition A → B, which is produced when there are N_h usersassociatedwiththefirstAPandanewuserarrives.

Fig. 1. Example of the powering on/off process for N h = 5 and N l = 3 .

two APs

A B

C _T

on

N

_h

+1 N

_l

one AP second AP

boong up

Fig. 2. Regenerative process to model the system.

• ThetransitionB→C,which istriggeredby thecompletionof theTonunitsoftimerequiredtopoweronthesecondAP.

• ThetransitionC→A,whichoccurswhenthereareN_l+1users inthesystemandoneofthemleaves.

Wenotethat,incasethereareN_lorfeweruserswhenthetran- sitionB→Chappens(i.e.,anumberofusershigherthanthehys- teresis left whilethe second APwas switchingon), we will con- sider that the systemtraversesstate C witha zerosojourn time, andthentransitionstostateA.

Inthefollowing,we firstdescribehowtocompute theperfor- mance figures of the complete system, based on per-stage vari- ables, andthen presenta modelforthe dynamicsofthe system, basedonaMarkovchainmodelforeachstage.Throughoutthear- ticle, we will refer with“stage” to the three statesof theregen- erativeprocess illustratedinFig.2,andreservethe useof“state”

forthedescriptionoftheMarkovchains.Wenotethatthisanaly- sisofatwo-APscenarioisexactaslongastheassumptionsonthe arrivalanddepartureprocesses,andthe(re)associationtimeshold.

3.1. Computingtheoverallperformancefigures

Theaverageduration Tofacompletecycleoftheregenerative processcanbecomputedas

T=T^A+T^B+T^C, ⁽¹⁾

whereT^jistheaveragesojourntimeofstagej.

Notethat,inourscenario,wehavebydefinitionthatT^B=Ton, whilethecomputationofT^A andT^C willbe performedinthefol- lowingsubsection.

BasedontheT^j,theaveragepowerconsumedbythenetworkis

P=PAPT^A+2PAP

(

^TB+T^C

)

T . ⁽²⁾

Tocompute the other performance figures, we needto obtain theexpectedamountoftime thatthereare iusers inthe system duringthedurationofacycle,T_i.Similarlyto(1),thisvaluecanbe expressedas

Ti=T_i^A+T_i^B+T_i^C, ⁽³⁾

whereT_i^j is theaverageamount oftime thatthere arei usersin thesystemduringthesojourntime ofstagej.Withthe valuesof T_i andT,theprobability p_i thatthereare iusers inthesystemis

givenby p_i=Ti

T =T_i^A+T_i^B+T_i^C

T^A+T^B+T^C. ⁽⁴⁾

Basedonthe p_i,theblockingprobabilityisequal totheproba- bilitythatthereare2Kusersinthesystem,i.e.

p_B=p_2K, ⁽⁵⁾

whiletheaveragetimespentbyauserinthesystemTsisgivenby Little’sformula

Ts= Nt

λ (

^{1− pB}

)

^{, (6)}

whereNt corresponds totheaveragenumberofusers inthesys- tem,whichiscomputedas

Nt=

2K



i=0

ip_i. (7)

Finally,thederivationofthedeactivationrateofthesecondAP

ω

^{isalmostimmediate,giventhatit}correspondstotheinverseof acompletepoweron–poweroff cycle,i.e.,theaveragedurationof acycleoftheregenerativeprocess.Therefore,it canbecomputed as

ω

⁼_TA+T¹_B+TC^{. (8)}

Withtheabove,wecancomputetheperformancefiguresofthe systemwith (2),(5),(6), and(8), giventhe times T_i^j and T^j. We next describe how to compute these times by modeling the dy- namicsofeachstageoftheregenerativeprocess.

3.2.Modelingeachstageoftheregenerativeprocess

The three stages of the regenerative process can be modeled withthree differentContinuous-Time MarkovChains (CTMCs),il- lustratedinFig.3.Inall thechains,thestate modelsthenumber ofusersbeingservedbythesystem,eachchainhavingadifferent numberofstates:

• CTMC_A models the systemwhen only one AP is powered on, and thereforeits numberof statesranges from0(empty sys- tem)toN_h+1(thesystemtransitionstothenextstage).

• CTMC_BmodelsthesystemduringtheTonunitsoftimeittakes forthesecondAPtopower,andthereforeitcanservebetween 0andthemaximumnumberofusers2K.

• CTMC_CmodelsthesystemwhenthetwoAPsareservingusers, andthereforerangesbetweenN_land2K(thesystemtransitions tostageA).

WenextanalyzeeachoftheseCTMCsseparately,startingwith CTMC_B (theonewiththelargestnumberofstates).

3.2.1. CTMCB

Thiscaseis illustrated inFig.3b, whereusers arriveat arate

λ

^{andareservedatarate}

μ

^{.Ouraimistocomputetheexpected}

Fig. 3. CTMCs representing the different stages of the regenerative process.

totaltime the CTMC spends in each state duringthe interval [0, Ton). Ifwedefine

π

i(t)astheprobabilitythat aCTMCisinstatei attime t,the expectedtotal timespent inthat statei duringthe interval[0,t)is

Li

(

^t

)

^=t

0

π

i

(

^u

)

^{du, (9)}

andbasedonthis,wecancomputeT_i^B=L^B_i(^Ton),whichisrequired toderivetheperformancefiguresofthesystemasexplainedinthe previoussection.

Tocompute

π

i(t),wemustsolvethedifferentialequation d

π (

^t

)

dt =

π (

^t

)

^{Q, (10)}

where

π

^{(t)andQarethevectorofstate}probabilitiesandthegen- eratormatrixoftheCTMCrespectively.

ForCTMC_Bwehavethat

π

^B

(

^t

)

⁼



π

0^B

(

^t

)

^,...,

π

2^BK

(

^t

) 

and Q^B=



q_{i j}



,i,j∈

{

^0,...,2K

}

^,

withtheelementsofthismatrixbeing

qi j=

⎧ ⎪

⎪ ⎪

⎪ ⎪

⎪ ⎪

⎪ ⎪

⎨

⎪ ⎪

⎪ ⎪

⎪ ⎪

⎪ ⎪

⎪ ⎩

−

λ

^{fori=0and j=0}

−

μ

^fori=2K,j=2K

−

λ

−

μ

^fori=

{

^{1,...,2K− 1}

}

andj=i

λ

^fori=

{

^{0,...,2K− 1}

}

andj=i+1

μ

^fori=

{

^1,...,2K

}

andj=i− 1 0 inanyothercase

(11)

We also need theset ofinitial conditions

π

^{B(0)to solve (10).}

Giventhat stage B startswhen there are N_h users inthe system andanewarrivalhappens,wehavethat

π

i^B

(

⁰

)

=

1 fori=N_h+1 0 inanyothercase

Withthese,wecansolvethesystemspecifiedby(10)andcom- puteT_i^Bwith(9)asexplainedabove.¹Notethatwecanalsoobtain

π

^{B(Ton), whichisrequiredtocomputethesetofinitialconditions}

forboththenextstageCandstageA,asexplainednext.

3.2.2. CTMC_C

This caseis illustrated in Fig. 3c, withthe departure rate be- ing 2

μ

^{asbothAPs areserving users.In contrasttothe previous}

chain,CTMC_C hasanabsorbingstate,namely,N_l.Whenthesystem reaches thisnumber ofusers, the second AP is powered off and thesystemtransitionstostageA.

Asintheprevious case, weneedtocompute theexpectedto- tal time the chain spends in each state during the sojourn time T^C. Thesevalues correspond to the timeuntil absorption spent in each ofthenon-absorbingstatesofCTMC_C, whichare definedas limt→∞L_i(t)forthesetofstates



T_N

l+1,...,T_2K



.Thetimesbefore absorptioncanbecomputedas[15]

L^C

(

^∞

)

^QC=−

π

^C

(

⁰

)

^{, (12)}

where L^C

(

^t

)

⁼



L^C_Nl+1

(

^t

)

^,...,LC2K

(

^t

) 

,

π

^C

(

^t

)

⁼



π

N^Cl+1

(

^t

)

^,...,

π

2^CK

(

^t

) 

, and

Q^C=



qi j



,i,j∈

{

^Nl+1,...,2K

}

^,

with

qi j=

⎧ ⎪

⎪ ⎪

⎪ ⎪

⎪ ⎪

⎨

⎪ ⎪

⎪ ⎪

⎪ ⎪

⎪ ⎩

−2

μ

^fori=2K,j=2K

−

λ

− 2

μ

^fori=

{

^{Nl+1,...,2K− 1}

}

andj=i

λ

^fori=

{

^Nl+1,...,2K− 1

}

andj=i+1

2

μ

^fori=

{

^Nl+2,...,2K

}

andj=i− 1 0 inanyothercase

(13)

Theinitialconditions

π

^{C(0)aredetermined bythe}distribution ofthestateprobabilitiesattheendofstageB,i.e.,

π

i^B(^Ton)^:ifthere arelessthanN_l+1usersinthesystem,thesecondAPisimmedi- atelypoweredoff andthesystemtransitionstostageA;otherwise, thenumberofusersattheendofstageBcorrespondstothenum- berofusersatthebeginningofstageC.

Followingtheabove,wehavethat

π

i^C

(

⁰

)

=

π

i^B

(

^Ton

)

^fori=

{

^Nl+1,...,2K

}

0 inanyothercase

Therefore,the systemwill spendzerosojourn time atstage C withprobability1− 2K

N_l+1

π

i^C(⁰)^.

Once (12)is solved, the sojourn time ofstage Ccan be com- putedas

T^C=

2K



i=Nl+1

L^C_i

(

^∞

)

^{, (14)}

andT_i^C=L^C_i(∞)^fori=

{

^Nl+1,...,2K

}

^{and0elsewhere.}

3.2.3. CTMC_A

This case, illustrated in Fig. 3a,is also modeled with a CTMC withanabsorbingstate,namely,N_h+1.Thisstatetriggerstheac- tivation ofthe second AP, whichcorresponds to the transitionto stageB.

1 Instead of solving (10) and then computing (9) , πi ( t ) and L i ( t ) can be efficiently evaluated for a given t = T on value using the uniformization method.

The times before absorption can be computed also with(12), wherenowwehave

L^A

(

^t

)

⁼



L^A₀

(

^t

)

^,...,LANh

(

^t

) 

,

π

^A

(

^t

)

⁼



π

0^A

(

^t

)

^,...,

π

N^Ah

(

^t

) 

, and

Q^A=



qi j



,i,j∈

{

^0,...,Nh

}

^,

with

qi j=

⎧ ⎪

⎪ ⎪

⎪ ⎪

⎪ ⎪

⎨

⎪ ⎪

⎪ ⎪

⎪ ⎪

⎪ ⎩

−

λ

^fori=0 and j=0

−

λ

−

μ

^fori=

{

^1,...,Nh

}

and j=i

λ

^fori=

{

^0,...,Nh− 1

}

and j=i+1

μ

^fori=

{

^1,...,Nh

}

and j=i− 1 0 in anyothercase

(15)

Similarly to the case of CTMC_C, the set of initial conditions

π

^{A(0)isdeterminedbythestatusofthesystemattheendofstage}

B: in case there were less than N_l users once the second AP is available,thesystemwilltransitiondirectlytostageA,i.e.

π

i^A

(

⁰

)

=

π

i^B

(

^Ton

)

,fori=

{

^{0,...,Nl− 1}

}

^{, (16)}

otherwise,the transitiontostage A willhappen throughstate N_l, i.e.

π

i^A

(

⁰

)

⁼¹⁻

Nl−1

j=0

π

j^B

(

^Ton

)

^,fori=Nl (17)

andcorrespondingly

π

i^A(⁰)=0foranyotherstate.

Finally,thesojourntimeofstageAiscomputedas T^A=

Nh



i=0

L^A_i

(

^∞

)

^{, (18)}

andT_i^A=L^A_i(∞)^fori=

{

^0,...,Nh

}

^{and0elsewhere.}

4. ImpactofT_ononperformance

ToanalyzetheimpactofTon ontheperformance,weassumea systeminwhichupto2K=10usersareallowed,afixedvalue of P_AP=3.5W,² and

λ

=0.1arrivals/s and1/

μ

=10s, whichcorre- spondsto an averageloadofapprox.50%.³ Weconsider fourdif- ferentactivationpolicies:

• N_l=N_h=4: no hysteresis and the activation threshold lower thanthemaximumnumberofuserperAP(K).

• N_l=N_h=5:nohysteresisandtheactivationthresholdsettoK.

• N_l=2andN_h=4:ahysteresisoftwousersandtheactivation thresholdsettoK− 1.

• N_l=2andN_h=5:ahysteresisofthreeusersandtheactivation thresholdequaltoK.

When presenting the results, we depict withlines the values fromouranalyticalmodelandwithpointstheresultsofadiscrete eventsimulatorthatiswritten inCandwhoseoperationweval- idatedthoroughly.Eachpointrepresentstheaverageoftensimu- lationruns,andeachrunconsistingonmorethan10⁶userdepar- tures (we do not represent the 95%-confidence intervalsas their relativesizeiswellbelow1%).

2 For simplicity, we assume a constant power consumption figure throughout all scenarios. Following our previous work of [11] , the consumption of a Linksys AP ranges between approx. 2.7 W when there is no activity and 4.4 W when the ac- tivity is maximum. The average of these figures results approx. 3.5 W, which is the value used.

3 These service times can emulate a scenario where a user downloads e.g. 20 MB using 802.11g, assuming an effective throughput of approximately 15 Mbps.

22 24 26 28 30 32 34 36 38 40

0 5 10 15 20 25 30 35 40

Ts(s)

T_on (s)

N_h = 5, N_l = 5 N_h = 4, N_l = 4 N_h = 5, N_l = 2 N_h = 4, N_l = 2

Fig. 4. Impact of the activation time T on on the total delay T s .

3.8 4 4.2 4.4 4.6 4.8 5 5.2

0 10 20 30 40 50

Power (W)

T_on (s)

N_h = 5, N_l = 5 N_h = 4, N_l = 4 N_h = 5, N_l = 2 N_h = 4, N_l = 2

Fig. 5. Impact of the activation time T on on the power consumed P .

4.1. TotaldelayTs

Wefirst analyze,forthe fourconsidered policies listed above, theimpactofTon onthetotaldelayTs,withtheresultsshownin Fig.4.Thereareseveralobservationsthat canbe drawnfromthe figure. First,the results from the modelcoincide with the simu- lations values for all considered configurations (we obtained the same accuracy for other configurations of the load, omitted for space reasons), which confirms the validity of our analysis.Sec- ond,theresultsalsoconfirmthatT_on hasanon-negligible impact onperformance, as itincreases delayfigures by 25–35% ascom- paredto thecaseof zerostart-up times.Finally,the policy more reluctanttopoweronthesecondAP(i.e.,N_h=5,N_l=5)resultsin thelargestdelaysforall valuesof Ton, whilethepolicy moreea- gertopoweronthe secondAP(i.e.,N_h=4,N_l=2) resultsinthe smallestdelayvalues.

4.2.PowerconsumedP

WenextanalyzetheimpactofT_ononthetotalpowerconsumed bythenetworkwiththefourconsideredpolicies,withtheresults showninFig.5.First,asinthepreviouscase,itisclearthatTonhas significant impacton theperformance w.r.t. thisvariableaswell, asit increases power consumption by up to 20%. In addition to theabove,whichconfirmsthequantitativeimpactofTononperfor- mance,wenotethatnon-zerostart-uptimesintroducequalitatively different results. For instance, when Ton=0, the less consuming schemeisN_h=5,N_l=5(whichisinlinewithintuition,giventhat

0 0.005 0.01 0.015 0.02 0.025

0 5 10 15 20 25 30 35 40

pB

T_on(s) N_h = 5, N_l = 5

N_h = 4, N_l = 4 N_h = 5, N_l = 2 N_h = 4, N_l = 2

Fig. 6. Impact of the activation time T on on the blocking probability p B .

thesystemspends mostofthetime instage A andtherefore the termPAPT^A prevailsin(2));however,whenTon>5s,thelesscon- sumingpolicybecomesN_h=5,N_l=2.Wealsonotethatthepolicy thatresultedinthesmallestdelays(N_h=4,N_l=2)hasthelargest powerconsumptiononlyforTon<5s.Morespecifically,thereisa trade-off betweendelayperformance andpowerconsumption for Ton ≈ 0, i.e., lessconsumingstrategieslead to thelargest delays;

however,when Ton > 5 s, this trade-off disappears partially un- dersome configurations (we willfurther explorethese trade-offs inthenextsection).Inthisway,a strategydesignedtominimize thepowerconsumptionforTon=0canbe outperformedbyother policieswhenT_on>0(indeed,forT_on≥ 20sitisoutperformedby twostrategies).

4.3.Blockingprobabilityp_B

Concerningthe resultsontheprobability p_B that auserisnot allowed into the system, because the maximum capacity2K has beenreached, they are presented in Fig. 6. The observed behav- ior inthis caseis expected, given the results on Ts presented in Fig.4andtherelationshipbetweenTsandp_Bgivenin(6),withthe relativeorder ofthe different activation policiesbeing thesame:

thehigher the delays(because the second AP ispowered off for relativelylongerperiodsoftime),thehighertheprobabilitythata usercannotbeadmittedintothesystem.

4.4.Activationrate

ω

Finally,we analyzetheimpactofT_on ontherateatwhich the secondAP ispowered onandoff

ω

^{,withthe resultsbeingillus-}

tratedinFig.7.Asexpected,theresultsshowthat,ingeneral, the longer ittakes the AP to boot(and consequently, the longer the systemremains instage B),the lower theactivation ratewillbe, asexpressedin(8).Thefigurealsoshowsthatthosepolicieswith morehysteresis(i.e.,N_l=2) obtainlower activation ratesandre- sultlesssensitive toTon,the reasonbeingthat the hysteresis in- creasestheaveragesojourntimesofstagesAandC,thusdecreas- ingtheinfluenceofthetermT^Bin(8).Finally,givenaspecifichys- teresis,thepoliciesmorereluctanttopoweronthesecondAPalso obtainloweractivationsrates,sincetheconditiontoswitchonthe secondAP(i.e.,reachingN_h users)ishardertosatisfy.

5. Onthetrade-offsinaRoDscheme

Buildingonthepreviousresults,inthissectionweanalyzethe differenttrade-offsthatappearinanetworkthatimplementsare- sourceondemandscheme.Morespecifically,inthe previoussec-

0 0.2 0.4 0.6 0.8 1 1.2

0 10 20 30 40 50 60

(cycles/min)

T_on (s)

N_h = 5, N_l = 5 N_h = 4, N_l = 4 N_h = 5, N_l = 2 N_h = 4, N_l = 2

Fig. 7. Impact of the activation time T on on the activation rate ω.

tionwehaveseenthat,dependingontheN_handN_lconfiguration, andthevalue ofTon,the performanceintermsofTs,P,p_B and

ω

changesboth qualitativelyandqualitatively. Now wewantto fur- therexplorethesechanges,consideringalsodifferentvaluesofthe systemload

ρ

^.

Throughoutthissectionwewillfocusourfindingsonthemost illustrativetrade-offs,namely:

1. Totaldelay(Ts)vs.powerconsumption(P).Thistrade-off serves torepresentthecostintermsofpowerconsumptionforagiven gainintermsofperformance,e.g.,howmanywattscostagiven reductioninseconds.

2. Power consumption (P) vs. activation rate (

ω

^{). This trade-off}

illustrates that the resource consumption hastwo dimensions that must be carefully considered when configuring the RoD scheme,sincea decreaseofthe powerconsumption maylead toan undesirableincrease oftheactivation rateofthesecond AP.⁴

5.1. ImpactofTon

We startour analysiswiththeimpact ofTon onthe twocon- sideredtrade-offs. To thisaim, we build on the results fromthe previous section (i.e.,

ρ

=1/2), anddepict theminFigs. 8and9, whereeachpointcorrespondstoapairofvalues({P,Ts}forFig.8, and{

ω

^{,P}forFig.9)foradifferentvalueofT}on.⁵

Onthe one hand, Fig.8 illustrates that, asalready showedin the previous section, the longer the value of Ton, the worse the performance of the system both in terms of T_s and P, and that differentN_h,N_l configurationsresultindifferentperformance fig- ures, both quantitatively and qualitatively. The figure also shows anothereffectofnon-zeroT_on,namely,thattherearesomeconfig- urationsworse than others underall circumstances. Indeed,while forthecaseofTon=0,ifoneconfigurationresultsinalower de- lay thanother it alsoresultsina largerpower consumption,this isnolongertruewhenTon >0.Forinstance,whenTon=60s,the configurationsN_h=N_l=5andN_h=N_l=4obtainworsefiguresof bothPandTsthantheothertwoconfigurations.

On the other hand, Fig. 9 reveals one “positive” aspect of a longer Ton: given that it takes longer to complete a cycleof the

4 For instance, in our previous experimental works (e.g. [16,17] ) we have expe- rienced faulty behavior from the power sources due to frequent rebooting of the devices. As a high rate of switching on/off an AP may impact its lifetime, we con- sider as “very large” values of ω those in the same order of magnitude as 1/ T on .

5 Given the tight matching between analytical and simulation values, from now we will only represent the values corresponding to the analysis.

20 25 30 35 40 45

3.5 4 4.5 5 5.5

Ts(s)

Power (W) N_h = 5, N_l = 5

N_h = 4, N_l = 4 N_h = 5, N_l = 2 N_h = 4, N_l = 2

T_on = 0

T_on = 60

Fig. 8. Impact of the activation time T on on the T s vs. P trade-off.

2 3 4 5 6 7 8

0 0.2 0.4 0.6 0.8 1 1.2

Power (W)

(cycles/min) N_h = 5, N_l = 5

N_h = 4, N_l = 4 N_h = 5, N_l = 2 N_h = 4, N_l = 2

T_on = 0 T_on = 60

Fig. 9. Impact of the activation time T on on the P vs. ω trade-off.

regenerativemodel,thepowerconsumptionincreasesbuttheac- tivationratedecreases,whichcould helptoextendthelifetimeof thesecondAP.

5.2. Impactof

ρ

We nextanalyze howthetrade-offs variesfordifferentvalues ofthe networkload

ρ

^{.Tothisaim,we setT}on equal to30s and plot the two considered trade-offs for

ρ

^{values ranging between}

0.05and0.95insteps of0.05,withtheresults beingdepictedin Figs. 10and11.Forthe caseoftheT_s vs.P trade-off (Fig.10),we canderivethefollowingmainresults:

• When the load is very low, there is very little difference be- tween the(de)activation policies,asonlyone APison almost allthetime.

• When the load is very high, though, there are non-negligible differences interms of power (approx. 4%) and, in particular, delay (approx. 30%) between the best and worst performing case.Inallcases,thepowerconsumptionisverycloseto7W, hintingthatthesecondAPisonmostofthetime,eitherboot- ing(stageB)oractivated(stageC).Thedifferenceindelayper- formancedependsonthevalueofN_l:thesmallerthisvalue,the longer the systemstays in stage C, thus providing users with betterservice.

• LikeforthecaseofTon,seenintheprevioussection,thereare qualitativelyvariationsintheTsvs.Ptrade-off when

ρ

^changes,

5 10 15 20 25 30 35 40 45 50

3 3.5 4 4.5 5 5.5 6 6.5 7

Ts(s)

Power (W)

N_h = 5, N_l = 5 N_h = 4, N_l = 4 N_h = 5, N_l = 2 N_h = 4, N_l = 2 = 0.05

= 0.95

Fig. 10. Impact of the load ρon the T s vs. P trade-off.

2 3 4 5 6 7 8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Power (W)

(cycles/min)

N_h = 5, N_l = 5 N_h = 4, N_l = 4 N_h = 5, N_l = 2 N_h = 4, N_l = 2 = 0.95

= 0.05

Fig. 11. Impact of the load ρon the P vs. ω trade-off.

asthelinescorrespondingtodifferentN_h,N_l configurationsnot onlychangetheirslopebutalsomightcrosseachother.

• Given a N_h value, a configuration withouthysteresis (N_l=N_h) obtains a poorerperformance bothin terms ofTs andP than theconfigurationwithhysteresis(N_l <N_h)forallthevaluesof

ρ

^.

WenextanalyzehowthePvs.

ω

trade-off varieswith

ρ

^,which

isillustratedinFig.11andshowsavery-differentbehaviorascom- paredwiththecaseofthevariationwithTon.Basedonthefigure, wecanderivethefollowingmainconclusions:

• Again, for small

ρ

^{values,there are little} differencesbetween configurations, withPbeingvery closetothe useofonlyone APand

ω

^{beingcloseto0.}

• As

ρ

^increases, performance worsens for both variables, i.e., thereisan increaseofthepowerconsumptionandtheactiva- tionrate,theformeralreadyseeninthepreviousfigure,while thelatterbeingcausedbythecrossingoftheN_hthresholddue tothelargerload.

• However, once a certain

ρ

^{threshold is crossed, power con-}

sumption keeps increasing but the activation rate decreases:

thisisbecause,thehighertheload,thelesslikelytheN_lthresh- old willbe reached,andthereforethesystemwillincreasethe amountoftimewithbothAPsactive,whichresultsinasmaller

ω

^.

• Like inthe previous case, strategieswithout hysteresis obtain worse figuresthanthosewithhysteresis,sincethetotalpower

18 20 22 24 26 28 30 32 34

3.9 4 4.1 4.2 4.3 4.4

Ts(s)

Power (W)

N_h = 5

N_l = 0 N_l = 5

N_h = 4

N_l = 0 N_l = 4

Fig. 12. Impact of N l on the T s vs. P trade-off, T on = 0 .

3.8 3.9 4 4.1 4.2 4.3 4.4 4.5

0.2 0.4 0.6 0.8 1 1.2

Power (W)

(cycles/min)

N_h = 5

N_l = 5 N_h = 4

N_l = 0

N_l = 0

N_l = 4

Fig. 13. Impact of N l on the P vs. ω trade-off, T on = 0 .

issimilarforbothtypesofRoDschemesbuttheactivationrate ismuchhigherwhennohysteresisisemployed.

5.3.ImpactofN_l

Finally,we analyzetheimpact oftheconfigurationoftheRoD onperformance.Tothisaim,wefix

ρ

=1/2andperformasweep onN_l fortwovaluesofN_h=

{

⁴,5

}

^{.Tofurther analyzetheimpact}

ofnon-zerostart-up times onperformance, we first considerthe caseofTon=0,andthenthecaseofTon=30s.

ScenarioI:Ton=0. Theresultscorrespondingtothisconfiguration aredepictedinFig.12(T_svs.P)andFig.13(Pvs.

ω

^{).Inbothcases,}

thetrade-offsaremonotonous:givena N_h configuration,decreas- ingthedelayimpliesincreasingthepowerconsumptionand,sim- ilarly,decreasingthe powerconsumption impliesahigheractiva- tionrate.Additionally,ahigherN_h valueresultsinsmaller power consumptionsandactivationrates.

ScenarioII:Ton=30s. Werepresenttheresults correspondingto thisconfigurationinFig.14(Tsvs.P)andFig.15(Pvs.

ω

^).Inthis

case, there is no monotonous behavior forany of the trade-offs, whichfurtherconfirmsthequalitativeimpactofhavinganon-zero Ton. More specifically, when there isa notable hysteresis (i.e., N_l

≤ 2), theprevious trade-offs still exist, witha decrease of delay (power)resulting inan increase of power(activation rate).How- ever,when there is no orvery small hysteresis (i.e., N_l closer to

20 25 30 35 40 45

4.4 4.5 4.6 4.7 4.8 4.9 5

Ts(s)

Power (W) N_h = 5

N_l = 0

N_l = 5 N_h = 4

N_l = 0

N_l = 4

Fig. 14. Impact of N l on the T s vs. P trade-off, T on = 30 s.

4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5

0.1 0.2 0.3 0.4 0.5 0.6

Power (W)

(cycles/min) N_h = 5

N_l = 0

N_l = 5 N_h = 4

N_l = 0

N_l = 4

Fig. 15. Impact of N l on the P vs. ω trade-off, T on = 30 s.

N_h),the performanceworsensforboththedelay(power)andthe powerconsumption(activationrate).Additionally,thegraphshows that,ingeneral,givenadelaybound,ahighervalueofN_hisprefer- ablesinceitleadstosmallerpowerconsumption.

6. OptimalconfigurationofaRoDscheme

Ourmodelnotonlyservestoanalyzethetrade-offsinaWLAN implementing a RoD scheme,but alsocan be used to derive the optimalconfigurationofits parameters (namely, N_h andN_l) fora givenscenario (in termsof

ρ

^{andTon), aswe illustrate next. We}

note that there are many different algorithms and configuration criteriathat could be usedto configurethe WLAN,andtherefore thatourproposalonlyservestoillustrateoneapproach.

6.1. Optimizationalgorithm

Our optimizationcriterion isas follows. Forour 2-AP setting, thebestperformanceintermsofdelayforany

ρ

^{valueistheone}

provided whenboth APsare always active.We denotethis mini- mumaverage delayasT_s^∗.Then,we assumethat thenetworkad- ministratoriswillingtotrade-off anincreaseofthisaveragedelay bye.g.

α

^{%inexchangeforabetterpower}consumptionbymeans ofaRoD scheme.Tothisaim,wesweep onallpossiblevaluesof N_h andN_l,andselectthatconfigurationwiththeminimumpower consumption(denotedasP_min)amongalltheoneswithanaverage

0 1 2 3 4 5 6

0 0.2 0.4 0.6 0.8 1

T_on = 0 s

N

N_h N_l

0 1 2 3 4 5 6

0 0.2 0.4 0.6 0.8 1

T_on = 30 s

Fig. 16. Optimal configuration of N h and N l vs. ρwith T on = 0 and T on = 30 s.

delaysmallerthan(¹+

α

/100)^Ts^∗.Wedenotethisconfigurationas

{

^N∗h,N^∗_l

}

^.

We summarize the operation of this scheme in Algorithm 1, whosecomputational complexityisquadraticandrelativelysmall (i.e., it consists of two sweeps over a small number of possible configurations).Wenotethatthesweepincludestheconfiguration withN_h=0andN_l=−1,i.e.,the caseofthetwo APsalways on, andthereforethealgorithmwillalways provideatleastthiscon- figurationasaresult.

Algorithm1 Centralizedadaptivecontrolalgorithm 1: ComputeT_s^∗

2: SetP_min=∞ 3: forN_h=0. . .K do

4: forN_l=−1...N_h− 1do 5: ComputeT_swith(6) 6: ifTs<T_s^∗(¹+

α

/100)^then

7: ComputePwith(2) 8: ifP<P_min then

9: P_min←P

10:

{

^N∗h,N_l^∗

}

←

{

^Nh,N_l

}

11: endif

12: endif

13: endfor 14: endfor 15: Return:

{

^N∗_h,N_l^∗

}

6.2. Results

Fig. 16 showsthe optimal configuration for Ton=0 (top) and Ton=30s(bottom).Inbothcases,whentheloadislow(

ρ

<0.2), the most efficient strategy is to use large values of N_h (and N_l), since the probability that the system reaches a high number of users is very small and therefore there is no need to power on thesecondAP.Thesevaluesarealmostthesameforboththezero andnon-zerostart-upcase.

Asloadincreases,thevalue ofN_h decreases,toensurethatthe total delaydoes not exceed the imposed threshold. Similarly, N_l also decreases toensure that the second APis active forenough time to maintain the total delay below the threshold. We note that herethe configurationbetweenthe zeroandnon-zerocases changes: whenTon is 30s,highervaluesofhysteresis (andlower valuesofN_h)arerequiredtokeepthetotaldelaybelowthethresh- old whileminimizing theconsumedpower,whichalsoleadstoa

3 3.5 4 4.5 5 5.5 6 6.5 7

0 0.2 0.4 0.6 0.8 1

Power (W)

T_on = 0 s T_on = 30 s

Fig. 17. Power consumption with { N ^∗_h , N ^∗l} , T on = 0 and T on = 30 s.

loweractivationrateofthesecondAP.Additionally,thevalueofN_h isalsolower thanin thezerostart-up case,to prevent situations inwhichtherearemanyusersinthesystemwhilethesecondAP isbeingpoweredon.Incontrast,whenTonis0theoptimalvalues ofbothN_handN_l arehigher,thankstothebetterdynamicsofthe system.

Forhigh loads (

ρ

> 0.8),the value ofN^∗_h is increased in one unit. This is because N_h and N_l cannot be but natural numbers, andthereforethis“rounding” hasanotableimpactontheresulting configuration.Forourconsidered systemand

α

^{value, when}

ρ

^is

above0.8boththeresultingoptimalN_h^∗,andN_h^∗− 1fulfillthecon- ditiononthedelay(notethat itisarelativecondition),whilethe former results insmaller values of the power consumption (this canbe seeninFig.17,astheincrease inthepowerconsumption changesslightly).

Wenextanalyzethepowerconsumptionoftheoptimalstrate- giesforTon=0andTon=30s,withtheresultsbeingdepictedin Fig.17.We notethat the configurationwithminimumdelaycor- respondstobothAPspoweredon,i.e., a7Wconsumption forall valuesof

ρ

^{,andthattheoptimalstrategyallowanincreaseofthis}

minimumdelayof(atmost)10%inordertominimizepowercon- sumption. For low values of the load (

ρ

< 0.2), performance is identical forthe zero and non-zero Ton cases, as only one AP is poweredon.Whentheloadislarger(

ρ

≥ 0.2),thereisa notable differencebetweenthetwocases,thisbeingcausedbythelower valuesofN_h andN_l fortheTon=30scase,thatincrease thetime spentbythesysteminstagesBandC.Comparedtotheconfigura- tionwithminimumdelay,thesavingsrangebetweenapprox.10%

(highload)and50%(lowload),whichfurthermotivatestheuseof RoDschemes.

7. Conclusionsandfuturework

Inthisworkwehavepresentedananalyticalmodelforthecase of a simple RoD system, which takes into account the time re- quired to power on an AP. The accuracy of the model has been validatedvia simulations, andresultshaveshowed that,even for the simple scenario considered, the time required to start-up an APhasadramaticimpactonperformance.Indeed,thistimealters both the quantitative and qualitative results as compared to the caseofzerostart-uptime.Wehavealsoobtainedtheoptimalcon- figurationofasimpleRoDschemetakingintoaccountthestart-up time,findingthatthistimemodifiestheoptimalparametersofthe RoD system.As a consequence,we believethat thestart-up time shouldbetakenintoaccountwhendesigninginfrastructureonde- mandpoliciesinreal-lifedeployments.