Efficient Strategies for Channel Management in Wireless LANs

17 Pages·2006·0.29 MB·English

Efficient Strategies for Channel Management in Wireless
LANs
AruneshMishra,VladimirBrik,SumanBanerjee,AravindSrinivasan,WilliamArbaugh
(cid:0) arunesh,waa,srin @cs.umd.edu,(cid:0) vladimir,suman @cs.wisc.edu
(cid:1) (cid:1)
ComputerScienceTechnicalReportCS-TR-4729
UMIACSTechnicalReportUMIACS-TR-2005-36
ABSTRACT anemergingchallengeofefficientlysharingthescarcebandwidth
We define efficient algorithms for channel management (channel resourceamongstthenumerousclients. Inthispaperwefocuson
assignmentandloadbalancingamongAPs)in802.11-basedWLANs thisspecificresourcesharingproblemanddefineappropriatetech-
thatleadtobetterusageofthewirelessspectrum.Thesealgorithms niques for efficient channel assignment in the context of 802.11-
(called CFAssign) are based on a “conflict-free set coloring” for- basedWLANs.
mulation that jointly perform load balancing along with channel
assignment.Suchaformulationhasanumberofadvantages.First,
Existingapproaches forchannelassignment
itexplicitlycapturesinterferenceeffectsatclients.Next,itintrinsi-
EachWLANstandarddefinesafixednumberofchannelsforuseby
callyexposesopportunitiesforbetterchannelre-use.Finally,algo-
AccessPoints(APs)andmobileclients. Forexample,the802.11b
rithmsbasedonthisformulationdonotdependonspecificphysical
standarddefinesatotalof14frequencychannelsofwhich1through
RFmodelsandhencecanbeappliedefficientlytoawide-rangeof
11arepermittedintheUS,1through13arepermittedinEurope
in-buildingaswellasoutdoorscenarios.
andonlychannel14ispermittedinJapan. Eachchannelactually
representsthecenterfrequency onwhichatransmissionismade,
We have performed extensive packet-level simulations and mea-
e.g.,thecenterfrequenciesforchannels1and2are2.412GHzand
surements on a deployed wireless testbed of 70 APs to validate
2.417GHzrespectively. Thereisonly5MHzseparationbetween
theperformanceofourproposedalgorithms. Weshowthatinad-
thecenterfrequenciesofadjacentchannels. However,an802.11b
dition to single network scenarios, CFAssign algorithms are well
signaltransmittedonanychanneloccupiesapproximately30MHz
suitedforchannelassignmentinscenarioswheremultiplewireless
ofthefrequencyspectrum. Thesignalfallswithinabout15MHz
networkssharethesamephysicalspaceandcontendforthesame
ofeachsideofthecenterfrequency. Asaresult,an802.11bsignal
frequency spectrum. Our results over a wide range of scenarios
onanychanneloverlapswithseveraladjacentchannelfrequencies
indicatethatCFAssignreducestheinterferenceatclientsbyabout
causinginterference(alsoknownasadjacentchannelinterference).
50-70%incomparisontocurrentbest-knowntechniques.
Thisimpliesthatonlythreechannels(1,6,and11)intheUScan
beusedsimultaneouslywithoutcausinginterference.
1. INTRODUCTION
Wirelesslocalareanetworks(WLANs)havegainedimportancein EachAPoperatesonasingleadministrator-specifiedchannel.The
therecentyearsasanInternet-accesstechnology. Ascompetition mobileclientscansthewirelessmediumtoidentifyanAPwitha
hasdrivendowncostsofWLANequipment,wirelessInternetac- strongsignal. TheclientassociateswithsuchanAPusing802.11
cessmechanismsareincreasinglyavailableinnumerouspublichot protocolmechanismsandbeginstousethisAPforallInternetac-
spotslikecoffee-shops,airports,andhotels. cess. AllcommunicationbetweenanAPanditsassociatedclients
occurinthechannelassignedtotheAP.Asabasicdesignrule,APs
WLANsoperateinportionsofthefrequencyspectrumallottedby within range of each other are set to different “non-overlapping”
aregulatorybody,e.g.,theFederalCommunicationsCommission channels.Networkadministratorstypicallyusemultipletechniques
in the USA, for unlicensed use. For example, the 802.11b and to assign channels to APs to reduce interference between them.
802.11g based WLANs operate in the 2.4 GHz frequency band FirsttheyconductdetailedRadioFrequency(RF)sitesurveys,of-
whilethe802.11abasedWLANsoperateinthe5GHzfrequency ten using spectrum analyzers, prior to setting up APs within the
band.Suchunregulatedspectrumallocationhascontributedtosig- buildingandusethisinformationtomanuallyassignspecificchan-
nificantpopularityandgrowthofWLANs.Withtheincreasingde- nelstothem[1].Beyondsuchinitialassignment,eachAPcontinu-
ploymentofsuchWLANs,networkadministratorsarefacedwith ouslymonitorsitsassignedchannelfordatatransmissionsbyother
APsandtheirclients.Ifthevolumeoftrafficinthatchannel(from
Arunesh Mishra ([email protected]), Aravind Srinivasan
([email protected]) and William Arbaugh ([email protected]) are otherAPsorclientsofotherAPs)isgreaterthanathreshold,then
with the University of Maryland, College Park. Vladimir Brik thefirstAPtriestomoveovertoalesscongestedchannel.Wecall
([email protected]) and Suman Banerjee ([email protected]) this technique for channel assignment, Least Congested Channel
are with the University of Wisconsin, Madison. This document is Search(LCCS).
publishedasaUniversityofMaryland,ComputerScienceTechnicalReport
CS-TR-4729andUniversityofMarylandInstituteforAdvancedComputer
InthispaperwecontendthatwiththecontinuedgrowthofWLANs,
Studies(UMIACS)TechnicalReportUMIACS-TR-2005-36.Publishedon
16June2005. achannelassignmentschemebasedsolelyontheLCCSrulewill
notbeefficient. GiventheunlicensednatureofWLANtechnolo-
giesanddecreasingcostsofAPs,thenumberofAPslocatedina 3
physicalneighborhoodhasproliferated.Inmanycasesadministra- 2
torsincreasethenumberofAPswithinabuildingtoimprovethe
Region Y
wirelesscoverage. Additionallymultipleorganizationsco-resident 1 AP1 4
in thesame building deploy independentwirelessLANs, and the 10
Region X
channel assignmentsmadefortherespective APs aremadeinde- 5 11 12
pendentofeachother. Anyuncoordinatedassignmentofchannels AP2 6 AP3
toAPscanleadtosevereinefficienciesandperformancedegrada- 9
tionofthewirelessclients. 7
8
The end goal ofthiswork is toimprove applicationperformance
andefficienttechniquesforchannelassignmentsolveapartofthe
Figure1: Channelassignmentshouldbebasedonuserperfor-
problem. Load balancing of clients among APs along with effi-
mance. The unshadedcirclesindicatethe interferenceradius
cient channel assignment is vital for a complete solution. Prior
ofeachAP.
workbyBejeranoet. al[2]providesaprovably goodcentralized
loadbalancingmethodwhichassumesthatthechannelassignment
solutionwhichresultsinimprovedapplicationthroughput(Section
isperformedindependently. Itisnaturaltoexpect thatbyjointly
7). Also, the CFAssign algorithms adapt the channel assignment
consideringbothchannelassignmentandtheloadbalancingprob-
toreflectchangesinclientdistributionsattributingtomobility. We
lem, significantimprovements canbe achieved. Inthiswork, we
explore the tradeoff between frequent re-assignment of channels
providedistributedandcentralizedsolutionstothisjointproblem
foroptimalityandperformanceandshowhowsuchadaptationsare
ofchannelassignmentand loadbalancingtoimprove application
performedinthroughsimulations(Section7).
performance.Throughapplicationlevelmetricsweshowthatsuch
a joint solution has significant advantages compared to address-
IndependencefromRFpropagationmodels: Agoodalgorithm
ingthetwoproblemsindependently. Inthispaper,werefertothe
forchannelmanagementwillguaranteelowinterferenceatclients
jointproblemofchannelassignmentandloadbalancing,aschannel
withoutmakinganyassumptionsonthenatureofRFinterference
management.
orRFpropagation. This is particularlyuseful forin-buildingen-
vironmentswhereisotropicRFmodelsdonotholdduetovarious
Our Modeland Algorithms forEfficient Chan-
effectsofmulti-path,channelfading,etc. CFAssignmeetsthisob-
nel Management jectiveofpropagationmodelindependencebyusingempiricalsam-
In this paper we propose a class of channel management algo- plesoftheclients’experienceofinterferencetomakedecisionson
rithms,calledCFAssign(standsforConflict-FreechannelAssign- channelassignment.Suchclientparticipationexposesamoreaccu-
ment),thatoptimizesuserperformanceinwirelessLANenviron- rateviewofclientinterferenceandenablesthealgorithmstomake
mentswith multipleAPs. Thesealgorithmsemploy simplecoor- betterchannelassignmentdecisions.
dination mechanisms between different APs in a shared wireless
environmenttoachievetheseobjectivesandhenceareeasytode- Interaction between channel assignments and load balancing
ploy. betweenAPs:Inordertoachievethemostefficientuseofwireless
channels, theproblemofchannel assignmentshouldnot bestud-
Wenowdescribesomeintuitiverequirementsinanysolutiontothe ied in isolation from the problem of client-AP association (load
channelmanagementproblemthatwillhelpinensuringlowinter- balancing).IncurrentWLANsystems,thesetwoproblemsaread-
ferenceatwirelessclients.Tothebestofourknowledge,CFAssign dressed independent of each other as follows. First, APs are as-
algorithmsarethefirstalgorithmsthatexplicitlyaddressthesere- signedtodifferentchannelsbasedontechniqueslikeRFsitesur-
quirementsofchannelmanagementinWLANs. veyandLCCS.Subsequently, eachclientindependentlyidentifies
anAPinitsvicinitywithgoodsignalstrengthandassociateswith
Client-driven approach: We call a channel management algo- it. Or,existingloadbalancingtechniquessuchas[2]canbeused
rithmclient-drivenifitaimstominimizeinterferenceorconflictsat todistributeclientloadamongtheAPs.Weshowinthispaperthat
wirelessclientsandnotatAPs.OurproposedCFAssignalgorithms more efficient use ofwirelesschannels is possiblewhen wecon-
implicitly model the location and distribution of wireless clients siderthechannelassignmentproblemintandemwiththeproblem
withrespecttotheAPswhilemakingchannelassignmentandload ofloadbalancingclient-APassociations,i.e. performingchannel
balancingdecisionsinordertomeettheminimizationobjective.In management. Theconflict-freesetcoloringapproachoftheCFAs-
particular,CFAssignmodelsthechannelassignmentproblemasa signalgorithmsimplicitlycouplesandsimultaneouslysolvesboth
conflict-freesetcoloringproblem,whereeachclientisrepresented theseproblemsforreducedinterferenceatwirelessclients.
byasingleset,andtheelementsofthesetcorrespondtodifferent
APsthatarewithintheclient’srange,therebydirectlycapturingthe Dynamicchannelre-useanddiscoveryofhidden-APs:Efficient
client-viewofinterferenceandconflicts. Inthispaperwedemon- channel re-use is an important requirement of all potential algo-
strate that such a client-driven approach leads to more efficient rithms.ConsiderthescenariodepictedinFigure1.Therearethree
channel managementatAPs that reduceinterferencefor wireless APs, namely , and . In this figure, mobile clients
(cid:0)(cid:2)(cid:1)(cid:4)(cid:3)(cid:6)(cid:5)(cid:7)(cid:0)(cid:8)(cid:1)(cid:10)(cid:9) (cid:0)(cid:8)(cid:1)(cid:12)(cid:11)
clients.WeelaboratemoreonthismodelinSection4.Existingap- (cid:13)(cid:15)(cid:14)(cid:17)(cid:16) are associated with , mobile clients (cid:14)(cid:21)(cid:20) are associ-
(cid:0)(cid:8)(cid:1)(cid:18)(cid:3) (cid:19)
proaches(LCCS)andotherpotentialalternativeapproaches(using atedwith ,andmobileclients (cid:14)(cid:23)(cid:13)(cid:6)(cid:24) areassociatedwith .
(cid:0)(cid:2)(cid:1) (cid:9) (cid:22) (cid:0)(cid:8)(cid:1) (cid:11)
vertex coloringmodel) capturethe interferenceatAPs instead of Transmissionsfrom and donotinterferewitheachother.
(cid:0)(cid:2)(cid:1)(cid:4)(cid:3) (cid:0)(cid:2)(cid:1)(cid:12)(cid:9)
theinterferenceatclientsandhenceperformpoorly(seeSection2 Hence we would ideally like to assign both of these APs to the
and 3). Additionally, the CFAssign algorithms perform load bal- samechanneltomaximize channelreuse. NotethatasimpleRF
ancingoftheclientsamongtheAPsandprovideacomprehensive sitesurvey(conductedbothat or )willalsoarriveatthe
(cid:0)(cid:2)(cid:1) (cid:3) (cid:0)(cid:8)(cid:1) (cid:9)
samedecision. (cid:4) Whiletheproposedalgorithmscanbeusedtoassignchan-
nels to multiple APs from a single wireless network, they
Transmissionsfrom and alsodonotinterferewitheach arequiteapplicableinchannelmanagementscenarioswhen
(cid:0)(cid:8)(cid:1) (cid:9) (cid:0)(cid:8)(cid:1)(cid:12)(cid:11)
other.However,theclientsof(cid:0)(cid:2)(cid:1) (cid:9) ((cid:19) (cid:14) (cid:20) )and(cid:0)(cid:2)(cid:1) (cid:11) ((cid:1)(cid:4)(cid:14) (cid:13) (cid:24) )arein multiplewirelessnetworksco-existinthesamephysicalen-
closeproximityofeachother. Henceif and operateon vironment. Such scenarios occur frequently in large office
(cid:0)(cid:2)(cid:1) (cid:9) (cid:0)(cid:2)(cid:1)(cid:12)(cid:11)
thesamewirelesschannel,onlyoneoftheseAPscanbeactively buildingssharedbydifferentcompanies,inresidentialneigh-
involvedincommunicationwithaclientinanygiveninstant. This borhoods with high density of wireless APs, and crowded
istheclassichiddenterminalprobleminwirelessnetworks[3,4]. downtown areas. CFAssign algorithms allow APs of these
The Distributed Coordinated Function (DCF) in 802.11b WLAN wirelessnetworkstoefficientlycontendforthespectrumboth
technologywillhandlesuchhiddenterminals(hiddenAPs)byus- in“cooperative”and“independent”modes. Inacooperative
ingthefour-wayhandshake(RTS-CTS-Data-Ack),therebyreduc- mode,theAPsfromdifferentwirelessnetworksareallowed
ingthedatathroughputachievedbythemobileclients.Howeverin tocoordinatewitheachother byexchangingprotocolmes-
thisscenario,anevenmoreefficientsolutionistoassignthesetwo sages for better channel management, whereas in an inde-
APstotwodifferentnon-overlappingchannels,ifpossible. Unfor- pendentmode,suchprotocolinteractionsarenotpermitted.
tunately,anRFsitesurveyateitheroftheAPlocationsortheLCCS Weexplorebothscenariosinourevaluations.
heuristicdoesnotexposethisinformationtothesiteadministrator.
(cid:4) Thealgorithmslendthemselvestoincrementaldeployment.
Theaboveexampleillustratesthatthedecisiontoassigntwodif- This is because CFAssign-enhanced APs can co-exist with
ferent APstothesame wirelesschannelsignificantlydependson legacy APs and still lead to performance improvement for
the potentialinterferenceexperiencedby themobile clientsinan clients.Ourevaluationindicatesthatinmanyscenarios,even
“overlap”region,i.e.,Regions and inFigure1. Ifboththese if10%oftheAPsusetheproposedtechniques,thenetwork
(cid:2) (cid:3)
regionsareempty,thenallthreeAPscanbeassignedtothesame as a whole achieves upto 40% reduction in client interfer-
channel to maximize channel reuse. Our proposed solutions dy- ence.
namicallyidentifyopportunitiesforchannelreusewhensuchover-
lapregionsaredevoidofmobileclients,butquicklyrevertbackto
are-assignmentofchannelsastheoverlapregionsbecomepopu- WealsopresentadetailedevaluationoftheCFAssignalgorithms,
latedwithclients.(Weignoresmalltimescale,transientmigrations usingbothextensivepacket-levelsimulationsthatevaluatetheim-
ofuserpopulations.) pactonapplicationlevelmetricsaswellasmeasurementsperformed
onalargetestbedconsistingof70APsdistributedoverfourfloors
ofanofficebuilding.
KeyBenefits andContributions ofthisWork
In this paper we present two versions of CFAssign that are ap- Our results indicate that the proposed techniques lead to signifi-
plicable to a wide range of WLANs technologies, e.g., 802.11b, cantlylowerinterferenceatwirelessclients.Forexample,in802.11b
802.11a,802.11g.Thefirsttechnique,calledCFAssign-BiS(CFAs- networks (with only 3 non-overlapping channels), the techniques
sign with “biased sampling”) does not require any collaboration achievebetween (cid:14) (cid:20) reductioninclientinterferenceinvari-
amongtheAPsandcanbeappliedtoawirelessnetworkformedby oussimulatedand(cid:5)(cid:7)(cid:6)measu(cid:6)(cid:9)r(cid:8)edtopologies.
APs belongingto differentWLANs. In thistechniqueAPs inde-
pendentlyandgreedilytrytominimizetheinterferencewithintheir Roadmap: Therestofthepaperisstructuredasfollows: InSec-
areaofcoveragewithoutbeingmalicious. Thesecondtechnique, tion 2 we discuss the limitations of current approaches based on
calledCFAssign-RaC(CFAssignwith“randomizedcompaction”), LCCS. Section 3 discusses the limitations of vertex coloring ap-
utilizes collaboration between APs in vicinity to minimize inter- proaches, popularincellularnetworks, whenappliedtoWLANs.
ferencein thenetwork as awhole. CFAssign-RaCis particularly Wepresent our conflict-freecoloringformulationfor thechannel
suitedforefficientchannelallocationforasinglewirelessnetwork, assignmentprobleminSection4,andpresentourCFAssignalgo-
orformultiplewirelessnetworksiftheadministratorsarewilling rithmsinSection5. Section6presentsthemodificationstoCFAs-
tocooperate. signalgorithmsforloadbalancing. Section7discussesthesimu-
lationresults, and theexperimentsarediscussed inSection8. In
The following characteristics of the CFAssign algorithms are the Section 9 we describe the related work. We conclude in Section
keycontributionsofourwork: 10.
(cid:4) Theyarethefirstclient-drivenalgorithmsforchannelman- 2. EXISTINGAPPROACHESANDLIMITA-
agementinWLANsthataredesignedexplicitlytoreducein- TIONS
terferenceatwirelessclients.UnliketheRFsitesurveybased
Current best practice for channel assignment [1] is to perform a
static techniques, our proposed solutions enable automated
LeastCongestedChannelSearch(LCCS).IndependentofLCCS,
channelassignmenttoAPs,loadbalancetheclientsamong
there exist approaches for load balancing after a channel assign-
APs based on continuously evolving channel conditions in
ment has been computed [2]. We first perform a simple analytic
the wireless environment and gracefully adapt to changing
modeling of LCCS and discuss its limitations. Next we discuss
distributionofclients(duetomobility).
someoftheinherentshortcomingsofusinganyexistingloadbal-
ancingtechniqueafterperformingachannelassignment.
(cid:4) TheymakenoassumptionsaboutRFinterferenceorRFprop-
agationmodels. In particularthese algorithms are efficient
forin-buildingenvironments,wherearbitrarymulti-pathand LCCS andits GeometricAnalysis
attenuationeffectsinvalidaterelativelysimplephysicalmod- Apart from manual channel assignment based on computation of
elsthatarecommonlyusedinvariouswirelessproblems. radio-maps [1], some AP vendors provide for a more automated
2R 2R 2R 2R
AP 1 AP 2 AP 1R AP 2 AP 1R AP 2 AP 1 AP 2
RBSS RC1 C2 RBSS C1 C2 RBSS C1 C2 RBSS RC1 C2
> DRBSS+ R [R B S S to RD B S S + R] [ 2R toD RB S S ] <D 2R
(a)NoConflict (b)Type-1Conflict (c)Type-2Conflict (d)Type-3Conflict
Figure2: FigureshowsfourdifferentconflictsituationswithAPs and sharingthesamechannel. Theinnermostcircle(of
(cid:0)(cid:2)(cid:1) (cid:3) (cid:0)(cid:8)(cid:1)(cid:10)(cid:9)
radiusR)aroundanAPindicatesitstransmissionradius.Thenextlargercircle(ofradius2R)indicatesthemaximumtransmission
radius among all mobile users associated with this AP. The outermost circle indicates the maximum interference radius of users
associatedwiththeAP.
techniquecalledLCCS.Inthisscheme,anAP,ondetectinginter- terferewitheachother. Notethatonly (cid:14) (cid:3) or (cid:14) (cid:9) candetect
ferencefromotherAPsorclientsassociatedtootherAPs,searches suchinterference.
fora“less-congested”channelofoperationonaperiodicbasis.We
Type-2conflict: Inthiscase (Figure2(c))the distancebe-
nowshowthattherearemanypotentialscenariosinwhichanAP (cid:4)
usingtheLCCSalgorithmisunabledetectconflictswithneighbor- tween the two APs is such that (cid:24) (cid:0)(cid:26)(cid:20) (cid:17)(cid:27)(cid:22) (cid:0) (cid:10)(cid:13)(cid:12)(cid:9)(cid:12) . In
ingAPsandclients. this case the client (cid:14)(cid:2)(cid:3) will cause interference at (cid:0)(cid:2)(cid:1) (cid:9) and
client (cid:14) (cid:9) willcauseinterferenceat(cid:0)(cid:2)(cid:1)(cid:4)(cid:3) . Theclientsthem-
selveswillalsointerferewitheachother(infacttheclients
In order to evaluate the efficacy of LCCS, we perform a simple
can potentially demodulate the transmissions of each other
geometricanalysisofthisscheme.Forthesakeofsimplicityinthis
correctlyandhencerealizetheconflict).However, can-
analysisweassumeanopen-spaceenvironmentinwhichthepath (cid:0)(cid:2)(cid:1)(cid:18)(cid:3)
lossofasignalfollowsatwo-raygroundmodel[5].Forsimplicity notcorrectlydemodulatethetransmissionsof (cid:14) (cid:9) ,sincethe
of illustration we assume that the clients and APs have the same (cid:0)(cid:2)(cid:1)(cid:4)(cid:3) iswithinthecarrier-senserangeof(cid:14) (cid:9) butnotwithinits
transmission range1 (cid:0) . Based on our path loss model, it can be transmissionrange. HenceneitherAPcanaccuratelydetect
shownthatatransmissionradiusof(cid:0) cancauseinterferenceuptoa thatthisinterferenceisduetoanotheranotherAPlocatedin
radiusof(cid:1) (cid:0) ,where(cid:1)(cid:3)(cid:2) (cid:13)(cid:5)(cid:4)(cid:20) (cid:22) [5].Receiverswithinthearadiusof itsvicinityandisusingthesamechannel.
(cid:1) (cid:0) mightnotbeabletodemodulatethepacketscorrectly,however, Type-3conflict: Inthiscase(Figure2(d))thedistancebe-
(cid:4)
thesignalisstrongenoughtocauseinterferenceatthereceiver. tweenthetwoAPsislessthan(cid:24) (cid:0) .Inthisscenario, will
(cid:0)(cid:8)(cid:1)(cid:18)(cid:3)
beabletocorrectlydemodulatetransmissionsby(cid:14) (cid:9) andwill
InFigure2,theinnermostcirclearoundanAPindicatesittransmis- realizethatthereisanotherAPinitsvicinityusingthesame
sionradius(cid:0) .Awirelessusermustbelocatedwithinthistransmis- channel,i.e.willbeabletodetecttheconflict.
sionradiusinordertoassociatewiththeAP.Sinceclientscanbe
situated upto a distance (cid:0) from an AP, transmissions from such
clientscanbereceiveduptoadistanceof(cid:24) (cid:0) indicatedbythesec- Amongthesefourscenarios,thetwoAPsshouldbeallocatedthe
ondconcentriccircle. Also,suchtransmissionswillinterfereupto samechannelonlyintheNo-conflictcase.Intheotherthreecases,
adistanceof(cid:0)(cid:7)(cid:6) (cid:13)(cid:8)(cid:4)(cid:20) (cid:22) (cid:0) (cid:2) (cid:24)(cid:9)(cid:4)(cid:20) (cid:22) (cid:0) . SinceeachAPandallthemo- thetwoAPsshouldbeassignedtodifferentnon-overlappingchan-
bileuserstogetherdefineaBasicServiceSet(BSS)inthe802.11 nels,ifpossible.
terminology,wedenotethisrange((cid:24)(cid:9)(cid:4)(cid:20) (cid:0) )by(cid:0)(cid:11)(cid:10)(cid:13)(cid:12)(cid:9)(cid:12) .
(cid:22)
However,outofthethreeconflictcasesshowninFigure2,anAP
ConsiderFigure2withtwoAPs,( and )andtheirclients usingtheLCCSalgorithmisonlyabletodetectType-3conflicts.
(cid:0)(cid:2)(cid:1)(cid:4)(cid:3) (cid:0)(cid:8)(cid:1)(cid:10)(cid:9)
((cid:14)(cid:8)(cid:3) and (cid:14) (cid:9) ). Client (cid:14)(cid:8)(cid:3) is associatedwith (cid:0)(cid:8)(cid:1) (cid:3) and client (cid:14) (cid:9) is Theothertwoconflictscenarioswillgoundetected. However,the
associatedwith . AssumebothAPshavebeenassignedtothe frequency of Type-1 and Type-2 conflicts is expected to be quite
(cid:0)(cid:2)(cid:1)(cid:10)(cid:9)
samechannel.Wedistinguishbetweenthefollowingscenarios: high. This can be shown both using simple geometric analysis
(72% ofall conflictsassumingauniform distributionofAPsand
homogeneoustransmissionradii)aswellasinreal-life(seemea-
(cid:4) Noconflict: Inthisscenario(Figure2(a))thetwoAPsare surementstakenonouroperationalWLANtestbedinSection8).
separatedbyadistancegreaterthan(cid:0) (cid:10)(cid:13)(cid:12)(cid:9)(cid:12) (cid:6)(cid:15)(cid:0) ,i.e.,(cid:16)(cid:16)(cid:4)(cid:20) (cid:0) .
(cid:22)
InthiscasethemobileclientsofthetwoAPsdonotinterfere LoadBalancing afterLCCS
witheachother.
Once a channel assignment is known, it is possible to improve
user performance by carefully balancing load across APs. Given
Type-1conflict: Inthiscase(Figure2(b))thetwoAPsare
(cid:4) achannel assignment, one ofthe bestknown techniques forload
separatedbyadistance,(cid:17) ,suchthat(cid:0)(cid:18)(cid:10)(cid:19)(cid:12)(cid:16)(cid:12)(cid:21)(cid:20) (cid:17)(cid:23)(cid:22) (cid:0)(cid:24)(cid:10)(cid:13)(cid:12)(cid:9)(cid:12)(cid:25)(cid:6)
balancingisgivenbyBejeranoet.al[2],whichprovidesanLinear
(cid:0) . Thisimpliesthattransmissionsofclients(cid:14) (cid:3) and (cid:14) (cid:9) in- Programming(LP)basedcentralizedschemeforfairnessandload
1Theanalysisextendstriviallytoheterogeneoustransmissionchar- balancing in a WLAN. The approachis well suited for scenarios
acteristics. where thechannel assignment strategyis fixed and static. Inour
anoptimalmin-maxloadbalancewouldresultinabandwidthal-
M2 users location of (cid:13)(cid:9)(cid:0) (cid:2) to the (cid:2) users of , and a bandwidth of
(cid:9) (cid:9) (cid:0)(cid:8)(cid:1) (cid:9)
(cid:13)(cid:9)(cid:0)(cid:11)(cid:10) (cid:2) (cid:6) (cid:2) (cid:6) (cid:2)(cid:4)(cid:3)(cid:9)(cid:12) toeachofthe(cid:2) (cid:6) (cid:2) (cid:6) (cid:2)(cid:4)(cid:3) users(since
(cid:3) (cid:11) (cid:3) (cid:11)
AP2
theyalongwith theirAPsshare thesamechannel). Ontheother
hand,ourCFAssignalgorithmsallocatechannelsbasedonloadand
AP1 AP3 wouldassignAPs(cid:0)(cid:8)(cid:1)(cid:18)(cid:3) and(cid:0)(cid:2)(cid:1)(cid:10)(cid:9) tothesamechannel,and(cid:0)(cid:2)(cid:1)(cid:12)(cid:11) toa
differentchanneltobalancetheload(Sections5and6). Although
M1 users APs and interfere,theusersassociatedto and
(cid:0)(cid:8)(cid:1)(cid:4)(cid:3) (cid:0)(cid:2)(cid:1)(cid:12)(cid:9) (cid:0)(cid:2)(cid:1)(cid:4)(cid:3) (cid:0)(cid:2)(cid:1)(cid:10)(cid:9)
M3 users would geta bandwidthofatleast (cid:13)(cid:9)(cid:0)(cid:11)(cid:10) (cid:2) (cid:6) (cid:2) (cid:12) , whiletheusers
(cid:3) (cid:9)
M4 users associatedto wouldgetabandwidthof (cid:13)(cid:9)(cid:0)(cid:13)(cid:10) (cid:2) (cid:6) (cid:2)(cid:4)(cid:3)(cid:9)(cid:12) . For
(cid:0)(cid:2)(cid:1)(cid:12)(cid:11) (cid:11)
(in range of M1 and M3) example, let (cid:2) (cid:3) (cid:2) (cid:2) (cid:9) (cid:2) (cid:2) (cid:11)(cid:21)(cid:2) (cid:2) (cid:3) (cid:2) (cid:13) . Assumingperfect
(cid:6)
bandwidth sharing after applying LCCS, each user associated to
Figure3:FigureshowsanexampletopologywhereLCCSwith gets a bandwidth of (cid:13)(cid:9)(cid:0) (cid:13) and any user associated to
(cid:0)(cid:2)(cid:1)(cid:12)(cid:9) (cid:0)(cid:2)(cid:1)(cid:18)(cid:3)
optimalloadbalancingproducesanunfairsolutioncompared or getsabandwidthof (cid:13)(cid:9)(cid:0)(cid:6) (cid:16) . However, ifour CFAssignal-
(cid:0)(cid:2)(cid:1)(cid:12)(cid:11)
toCFAssign. gorithms are used for channel as(cid:6)signment, all users get an equal
bandwidthof(cid:13)(cid:9)(cid:0) (cid:24) ,ineffectachievingbetterloadbalancingdueto
work,weaddressWLANscenarioswherethechannelassignment (cid:6)
betteropportunitiesprovidedbyefficientchannelassignment.
canbecontrolledeitherinacentralizedoradistributedmanner.We
willnowshowusingsomesimplescenariosthatitsessentialtoper-
3. AVERTEXCOLORINGBASEDAPPROACH
formloadbalancingduringchannelassignment. Specifically, we
show thatLCCS basedchannelassignmentcan createhigh inter- ANDITS LIMITATIONS
ferencetopologies. Usinganefficientloadbalancetechniquesuch Basedonthediscussionintheprevioussection,itmayappearnat-
as[2]canstillyieldasuboptimalsolutionontheoverallapplica- uraltomodelthechannelassignmentprobleminWLANsasaver-
tionperformance. Belowwediscusstwoimportantshortcomings texcoloringproblem. Suchvertexcoloringbasedapproacheshave
of performing load balance using techniques suchas [2] after an beenapplied successfullyinthe context of frequency assignment
LCCSbasedchannelassignment: incellularnetworks[6,7,8].
HiddenTerminals-Type1and2conflicts: Consideracaseoftwo Inthissectionweoutlineapotentialvertexcoloringapproachand
APsandtwoclientswithoneclientassociatedtoeachAP.Saythe itsmodelinglimitations. Inthisapproach,agraphisusedtorep-
APsarenotinrangeofoneanother, however, thetwoclientsare resentconflictsorinterferencebetweennodes.Theverticesofthis
within transmission range of each other. Thus, since the clients graphcorrespondtoAPs,andedgescorrespondtoimpactofinter-
interferewitheachother,atanygiventimeonlyoneoftheclients ferencebetweenpairsofAPs. Theobjectiveofthisproblemisto
canbeactive. Thus,eachgetsanormalizedthroughputof (cid:13)(cid:1)(cid:0) (cid:24) if assignafixednumberofcolors(channels)tothevertices(APs)of
theywereassignedtoAPsonthesamechannel.NotethatanLCCS thisgraphthatminimizesinterference.Eachedge (cid:10)(cid:15)(cid:14) (cid:12) isassoci-
(cid:5)(cid:17)(cid:16)
basedchannelassignmentcannotdetectsuchscenarios(bothType- atedwithapenaltyfunction (cid:10)(cid:15)(cid:23) (cid:12) ,suchthatifAP(cid:14) isassigned
(cid:18)(cid:20)(cid:19)(cid:20)(cid:21)(cid:22) (cid:5)(cid:25)(cid:24)
1andType-2conflicts),and hencewilllikelyassignboth APsto achannel(cid:23) and isassignedachannel , apenaltyof (cid:10)(cid:15)(cid:23) (cid:12)
(cid:16) (cid:24) (cid:18)(cid:26)(cid:19)(cid:20)(cid:21)(cid:22) (cid:5)(cid:27)(cid:24)
the same channel. Performing load balancing after LCCS based isincurred.Thefollowingisanintuitivewaytochoosethepenalty
channel assignment using schemes such as [2] will be unable to function. If(cid:23) and arenon-overlappingchannels,thenthepenalty
(cid:24)
improvethethroughputforsuchclientsandcanresultinunfairness functioniszero. If(cid:23) (cid:2) (cid:24) ,i.e.,bothAPsareassignedtothesame
(discussedbelow).However,ourconflictbasedchannelassignment channel,thenthepenaltyfunctionincreasesmonotonicallywiththe
solutionwouldcapturethisintoaclient’sinterferenceset(Section numberofclientsofthetwoAPsexperiencingconflictsofTypes
5)andallocatenon-overlappingchannelsaccordingly. 1, 2, or 3 as defined in Section 2. Examples include clients (cid:14) (cid:3)
and (cid:14) (cid:9) inFigure2(b), (c), and(d). (Notethatsuchinterference
Unfairness: Throughanexampleweshowthatbecauseofthein- is experiencedif and only if both the APs are assigned the same
efficaciesinherentinLCCS,performingoptimalloadbalancecan channel.)
result in max-min unfairness, while performing our conflict-free
channel assignment (described later) with load balance yields a Inordertoachievelowinterferenceatclients,wemustchoosean
better solution. Consider the scenario shown in Figure 3. Here assignmentofcolorstovertices(channelstoAPs)suchthattheag-
(cid:2) ,(cid:2) and(cid:2) usersareexclusivelyinrangeofAPs , gregate value of the penaltyfunctions on all edges is minimized.
(cid:3) (cid:9) (cid:11) (cid:0)(cid:8)(cid:1)(cid:18)(cid:3) (cid:0)(cid:2)(cid:1)(cid:12)(cid:9)
and respectively. (cid:2)(cid:4)(cid:3) usersarewithinrangeofAPs and Inourworkwehaveexploredspecificdistributedimplementations
(cid:0)(cid:2)(cid:1)(cid:12)(cid:11) (cid:0)(cid:8)(cid:1)(cid:18)(cid:3)
. Also assume that the users (cid:2) , (cid:2) , (cid:2) are in range of ofthisvertexcoloringbasedchannelassignmentinWLANs. Due
(cid:0)(cid:8)(cid:1) (cid:11) (cid:3) (cid:9) (cid:11)
eachother.Theoverlapbetween and cannotbedetected tospaceconstraintswedonotreportonspecificdetailsofthisap-
(cid:0)(cid:8)(cid:1)(cid:18)(cid:3) (cid:0)(cid:2)(cid:1) (cid:11)
by LCCS (as the overlap region does not involve the APs them- proach. Insteadwefocusonspecificshortcomingsofsuchanap-
selves). However,LCCScandetectoverlapbetween proach which form the intuition behind the CFAssign algorithms
(cid:5) (cid:0)(cid:2)(cid:1)(cid:18)(cid:3) (cid:5)(cid:7)(cid:0)(cid:2)(cid:1)(cid:12)(cid:9)(cid:7)(cid:6)
and .Thus, and wouldbeassignedthesame thatweproposeinthispaper.
(cid:5) (cid:0)(cid:8)(cid:1) (cid:9) (cid:5)(cid:7)(cid:0)(cid:8)(cid:1) (cid:11) (cid:6) (cid:0)(cid:8)(cid:1) (cid:3) (cid:0)(cid:8)(cid:1) (cid:11)
channelwhile wouldbeassignedadifferentchannel(forsake
(cid:0)(cid:2)(cid:1)(cid:10)(cid:9)
of simplicity assume only two channels are available). Then, in Consider Figure 4(a), in which there are four APs: , ,
(cid:0)(cid:8)(cid:1)(cid:18)(cid:3) (cid:0)(cid:8)(cid:1)(cid:10)(cid:9)
any load balancing scheme, all (cid:2) can only will be assigned to , (cid:3) . Let us assume that none of these APs are in inter-
(cid:9) (cid:0)(cid:2)(cid:1) (cid:11) (cid:0)(cid:2)(cid:1)
(cid:0)(cid:8)(cid:1)(cid:10)(cid:9) ,andtheusers(cid:2) (cid:3) (cid:6) (cid:2) (cid:11) (cid:6) (cid:2)(cid:4)(cid:3) willbeequallysharedbythe ferencerange of eachother. Clients (cid:14) (cid:3)(cid:6)(cid:5) (cid:14) (cid:9) (cid:5) (cid:14) (cid:11) (cid:5) (cid:14) (cid:3) are indirect
APs, and . Letusassume(onlyforthisdiscussion)that communicationrangeofAPs , , , (cid:3) respectively
(cid:0)(cid:8)(cid:1) (cid:3) (cid:0)(cid:2)(cid:1) (cid:11) (cid:0)(cid:2)(cid:1) (cid:3) (cid:0)(cid:8)(cid:1) (cid:9) (cid:0)(cid:8)(cid:1) (cid:11) (cid:0)(cid:8)(cid:1)
802.11 achieved perfect bandwidth sharing between nodes in di- and no other APs. Therefore, (cid:14) (cid:3) associateswith (cid:0)(cid:2)(cid:1)(cid:4)(cid:3) , (cid:14) (cid:9) asso-
rectinterferencerangeandcontendingforthechannel,i.e.,ifthere ciateswith(cid:0)(cid:2)(cid:1) (cid:9) ,andsoon. Client(cid:14)(cid:29)(cid:28) isindirectcommunication
are node gets exactly (cid:13)(cid:9)(cid:0) of the channel bandwidth. Then rangeofallthefourAPs.Withoutlossofgenerality,letusassume
(cid:8) (cid:8)
using the channel assignment determined by LCCS, performing that(cid:14)(cid:30)(cid:28) associateswith(cid:0)(cid:2)(cid:1) (cid:3) .Figure4(b)showsthecorresponding
conflictgraph,whichisa4-clique. Thereisanedgebetweeneach
pairAPssinceclient (cid:14)(cid:29)(cid:28) isincommunicationrangeofbothAPs.
Thereforebasedonthevertexcoloringapproach,eachAPwillbe
assignedadistinctcolor(channel)andwewillneedfourdifferent
non-overlappingchannelstoguaranteeconflictfreedom. C2 C1
C3 AP2
AP1
However, in reality only two channels are sufficient to guarantee
C2" C1"
conflictfreedominthisexample.Forexample,wecanassign(cid:0)(cid:8)(cid:1)(cid:18)(cid:3) C3"
(anditsclients(cid:14)(cid:8)(cid:3) (cid:5) (cid:14)(cid:30)(cid:28) )toonechannelandallotherAPstothesame
secondchannel.Notethat (cid:3) andtheirclientsdonot
(cid:0)(cid:2)(cid:1)(cid:10)(cid:9) (cid:5)(cid:7)(cid:0)(cid:2)(cid:1) (cid:11) (cid:5)(cid:7)(cid:0)(cid:2)(cid:1)
interferewitheachother.
While such a solution is not realizable in the vertex coloring ap- Figure5: Exampletoillustraterangeandinterferencesetsfor
proach, we next describe our CFAssign algorithms based on the clients.
minimumconflict-freesetcoloringformulationwheresuchanas-
Interferencesetofaclient:Therangesetofaclientcapturessome
signmentcanbeachieved.
oftheinterferenceexperiencedbytheclient,butdoesnotcapture
thetotalinterferenceobservedbyit. Aclientcansufferadditional
interference from clients of other APs, if the client is within the
C4 transmissionrangeofsuchclients. Notethatiftheclientiswithin
C3 AP4 AP3 AP4 the transmission rangeof suchan AP, then theAP will be inthe
rangeset.Ontheotherhand,iftheclientisoutsidethetransmission
AP3
rangeofsuchanAP,thelatterwillnotbepartoftherangeset.This
C5
isillustratedinFigure5. Thesolidlinesshowthecommunication
AP1 ranges. Here, client is not within the transmission range of
AP2 AP2 AP1 (cid:0)(cid:9)(cid:1)
C1 . However,itisincommunicationrangeofclient whichis
C2 a(cid:10)(cid:2)s(cid:11)so(cid:1)ciatedwith . Insuchascenariowesaythatc(cid:0) li(cid:13)ent is
(cid:10)(cid:2)(cid:11) (cid:1) (cid:0)(cid:28)(cid:27)
withininterferencerangeof (duetoclient associatedwith
(cid:10)(cid:9)(cid:11)(cid:29)(cid:1) (cid:0)(cid:14)(cid:13)
);Aclient issaidtobeintheinterferencerangeofanAP
(a) (b) i(cid:10)(cid:2)f(cid:11)(i)(cid:1) isnotwit(cid:30)hintransmissionrangeofAP and,(ii) iswithi(cid:31)n
(cid:30) (cid:31) (cid:30)
transmissionrangeofsomeclient and iswithintransmission
(cid:30)! (cid:30)!
Figure4: (a)AWLANexampleand(b)thegraphcreatedby rangeofAP . (Notethat neednotbeassociatedtoAP .) The
(cid:31) (cid:30) (cid:31)
thevertexcoloringformulation. set of all APs within interference range of a client constitute the
interferencesetcorrespondingtotheclient.
4. CONFLICT-FREESETCOLORINGFOR-
Each clientis, thus, associatedwith twosets: a rangeset and an
MULATION interferenceset. ForthesetupofFigure5,therangeandinterfer-
Weformulatetheproblemofchannelassignmentinwirelesslocal- encesetsforthethreeclientsareshowninTable1.ThesetofAPs
area networks as a conflict-free set coloring problem and assign- togetherwiththerangeandinterferencesetsforeachclientcreates
ing colorscorrespondtoassigningchannels. Considerawireless theconflict-freesetsystem.
network comprising ofa setof APs and clients. As discussed in
Section 3, avertex coloringapproachfor channelassignment for Informally, a client is said to be in conflict if there is more than
thenetworkinFigure4yieldsasolutionthatrequiresfourcolors oneAPinitsrangeorinterferencesetthatisoperatingonthesame
(channels),whileinrealitywecanachievethesameconflictfree- channel as the client. A clientin conflictcan suffer fromdrastic
dom(andsameAPload)usingjusttwocolors. Wearrivedatthis reduction in throughput — the reduction factor can be exponen-
channelassignmentinthefollowingmanner.Clients are tialinthetotalnumberofclientsoverallAPsinconflictwiththis
(cid:0)(cid:2)(cid:1)(cid:4)(cid:3)(cid:5)(cid:3)(cid:5)(cid:3)(cid:6)(cid:0)(cid:8)(cid:7)
eachinrangeofasingleAPandareassignedtotheirin-rangeAP, client[9]. Aclientissaidtobeconflict-freeifthereisexactlyone
e.g., to , to andsoon. Client isinrangeofall APinitschannelfromitsrangeset(thisistheAPtheclientwillbe
(cid:0)(cid:9)(cid:1) (cid:10)(cid:2)(cid:11)(cid:12)(cid:1) (cid:0)(cid:14)(cid:13) (cid:10)(cid:2)(cid:11)(cid:15)(cid:13) (cid:0)(cid:17)(cid:16)
fourAPs: . Giventhisset,weneedacol- associatedto),andthereisnootherAPinitsrangeorinterference
(cid:18)(cid:19)(cid:10)(cid:2)(cid:11) (cid:1)(cid:19)(cid:20) (cid:10)(cid:9)(cid:11) (cid:13)(cid:21)(cid:20) (cid:10)(cid:9)(cid:11)(cid:23)(cid:22) (cid:20) (cid:10)(cid:9)(cid:11) (cid:7)(cid:25)(cid:24)
oringoftheAPssuchthatthissethasatleastoneAPwithaunique setusingthesamechannel.
color,i.e.,thatcolorisnotusedbyanotherAPwithintheset.This
canbetriviallyachievedifweselectexactlyoneAPandassignit Ourobjectiveistoassigncolorssuchthatthetotalnumberofconflict-
aparticularcolor(associateclient toit),andthenassigndiffer- free sets (and hence the number of conflict-free clients) is maxi-
(cid:0)(cid:14)(cid:7)
entcolorstotherest. Forexample, couldbeassignedcolor1 mized. Thisassignmentofcolorsalsoyieldstheassociationmap-
(cid:10)(cid:2)(cid:11) (cid:1)
while couldbeassignedcolor2.Inordertomodel pingforeachclient,i.e.,theclientassociatestotheAPthatholds
(cid:10)(cid:9)(cid:11)(cid:15)(cid:13) (cid:20) (cid:10)(cid:2)(cid:11) (cid:22) (cid:20) (cid:10)(cid:2)(cid:11)(cid:23)(cid:7)
thisapproachofassigningchannelsusingtheconflict-freesetfor- theconflict-freecolorforitsrangeandinterferencesets.
mulationweusethefollowingdefinitions:
Range set of a client: Foreach client wedefine its range set as Someadvantagesofconflict-freesetcoloringformulation:There
thesetofallAPssuchthattheclientlieswithinthetransmission aremultipleadvantagesofusingtheconflict-freesetcoloringfor-
rangeofeachsuchAP,regardlessofthecurrentchannelofoper- mulationtoobtainanefficientchannelassignmentinWLANs.First,
ation of the APs. In the above example, the range set for is this formulationdirectly captures the effectof interference atthe
(cid:0)(cid:26)(cid:16)
. Notethataclientcancomputeitsrange clientsusingtherangeandtheinterferencesets. Thus,algorithms
(cid:18)(cid:19)(cid:10)(cid:2)(cid:11) (cid:1)(cid:19)(cid:20) (cid:10)(cid:2)(cid:11) (cid:13)(cid:21)(cid:20) (cid:10)(cid:2)(cid:11)(cid:23)(cid:22) (cid:20) (cid:10)(cid:9)(cid:11) (cid:7)(cid:21)(cid:24)
setempiricallybymonitoringAPsinitsvicinity. thatprovidesolutionstothisproblemaimtodirectlyoptimizethe
metricofinterest—conflictatthewirelessclients. Thereforewe is conflict-freeif the coloring satisfies the above property forthe
callthisapproachaclient-drivenapproach.Thisisakeydifference client. The coloring also implicitly defines the association map-
fromthevertexcoloringapproach(Section3)wheretheverticesto pingfortheclienttobeconflict-free,i.e.,theclientwillassociates
becoloredrepresenttheAPsandtheedgesindirectlyaccountfor totheAPwhichholdstheconflict-freecolor, ,initsrangeset.
(cid:24)
theinterferenceonclientsduetotheassignmentofsamecolorto
twoneighboringAPs. A trivial conflict-free coloring is achieved by assigning a unique
color to each AP. This assignment would use colors (chan-
(cid:24)(cid:2)5(cid:24)
Next, the conflict-free coloring formulation intrinsically captures nels). TheminimumCFcoloringproblemistominimizethetotal
opportunities for channel re-use. In Figure 5, we would need 2 numberofcolorstoachieveconflict-freecoloringforthesetsystem
channelstoobtainaconflict-freecoloringoftheformulationshown onagiveninstanceoftheproblem. Inanotherform,givenafixed
intable1.Letsassumethattheclients(cid:14)(cid:2)(cid:3) (cid:5) (cid:14) (cid:9) (cid:5) (cid:14) (cid:11) movetoanalter- numberofcolors/channels,theproblemistomaximizethenumber
natelocation, (cid:14) (cid:3)(cid:1)(cid:0) (cid:5) (cid:14) (cid:9)(cid:2)(cid:0) (cid:5) (cid:14) (cid:11)(cid:3)(cid:0) , respectively. Now, theinterference ofclientsthatareconflict-free.
setsofallclientsareempty,andtheirrangesetsare(cid:4) (cid:24)(cid:6)(cid:5) (cid:4) (cid:5) (cid:4) (cid:5)
(cid:0)(cid:2)(cid:1) (cid:5) (cid:0)(cid:8)(cid:1)(cid:18)(cid:3) (cid:5) (cid:0)(cid:2)(cid:1)(cid:4)(cid:3)
respectively. WecanassignthesamechanneltobothAPsandstill ThesolutiontotheCFproblemprovidesthefollowing:
get a conflict-free assignment. Thus, the conflict-free set system
capturessuchopportunitiesofchannelre-useinherently. Bykeep-
ingthemodelupdatedonaperiodicyetcoarse-grainedbasis, we 1. (cid:28) givesthechannelassignmentfortheAPs.
will be able to neglect fine-grained user migrations, and capture
mediumandlarge-scalevariationsofclientdistributions. 2. For (cid:10)(cid:12)(cid:11)6(cid:8)7(cid:21) , define 8 (cid:10)(cid:7) (cid:12) (cid:2) ( (cid:29) color of ( is conflict free
in . (( is the AP that leads to conflict-freedom for this
(cid:10) (cid:11)
Finally, the conflict-free coloring formulation captures effects of client.) 8 (cid:10)(cid:7) (cid:12) providestheassociationmapping, i.e.,theAP
interference through sets (range and interference sets) instead of toassociatetoforeachclient(cid:7) .
physicalRFmodels, e.g., circularcommunicationranges. There-
forealgorithms thatcanefficientlysolve thisconflict-freeformu-
Ithasbeenshownthat,ingeneral,theCFproblemisnoteasierthan
lation will be efficient irrespective ofthe underlying physical RF
vertexcoloring,andishardtoapproximate[10]. Ourobjectivein
propertiesofthewirelessenvironment.
thisworkistodefineefficientstrategiesthatmaximizethenumber
ofconflict-freeclientsinthesetsystem.
RangeSet InterferenceSet
(cid:4) (cid:5) (cid:4) (cid:5)
(cid:14)(cid:8)(cid:3) (cid:0)(cid:2)(cid:1) (cid:9) (cid:0)(cid:2)(cid:1) (cid:3)
(cid:4) (cid:5) (cid:4) (cid:5) 5. CHANNELASSIGNMENTALGORITHMS
(cid:14) (cid:9) (cid:0)(cid:2)(cid:1) (cid:3) (cid:0)(cid:2)(cid:1) (cid:9)
(cid:14) (cid:11) (cid:4) (cid:0)(cid:8)(cid:1)(cid:4)(cid:3)(cid:6)(cid:5)(cid:7)(cid:0)(cid:8)(cid:1)(cid:10)(cid:9) (cid:5) (cid:4) (cid:5) We describe two randomized algorithms for the CF formulation
discussedintheprevioussection. Inthissection,weignoretheis-
Table 1: Table shows the range and interference sets for the sueofloadbalancingclientsamongAPsandinsteadconcentrateon
exampleofFigure5. thetheparadigmofconflict-freechannelassignment.LaterinSec-
tion 6, we discuss modifications to reduce intra-AP interference,
FormalDefinition
i.e.loadbalancingamongAPs.
Let us denote a wireless network as (cid:10) (cid:5) (cid:14) (cid:12) , where is the set
(cid:2) (cid:2)
ofallAPsand (cid:14) isthesetofallclients. Foreachclient (cid:7)(cid:9)(cid:8) (cid:14) , The first algorithm, called CFAssign-RaC (CFAssign using “ran-
weassociateatuple(cid:10)(cid:12)(cid:11) (cid:2) (cid:20)(cid:14)(cid:13) (cid:11) (cid:5) (cid:23) (cid:11)(cid:16)(cid:15) where(cid:13) (cid:11)(cid:17)(cid:8) (cid:24)(cid:19)(cid:18) istherange domizedcompaction”)isasophisticatedcentralizedapproach.Such
setfor(cid:7) and(cid:20) (cid:11) (cid:8) (cid:24) (cid:18) istheinterferencesetfor(cid:7) ((cid:24) (cid:18) denotesthe analgorithmisparticularlysuitedforcentrallymanagedwireless
(p(cid:10)o(cid:2)orw(cid:5)(cid:27)se(cid:21)imr(cid:12)specltoy,noasftr(cid:2)suect).tseyLdsetitenm(cid:21)th)e(cid:2)foar(cid:4)bt(cid:10)(cid:12)oh(cid:11)vee(cid:2)nme(cid:20)(cid:22)tawn(cid:13)on(cid:11)re(cid:5)kr(cid:23),(cid:11)(cid:23)(cid:10)a(cid:15)(cid:25)c(cid:5)o(cid:14)(cid:24)n(cid:26) fl(cid:12)c.iclite-nfrtese(cid:7) s(cid:5)e.tWsyestceamll naTsehetewdosserakcmosnpwdliintahglg”m)oruiistlhtiamplseicmaAlplPelesd,dCaissFtArisisbstuiygtpendi-cBaaillSgion(rCimtFhoAmsstsriogerqnguauinrsiiinznaggtizo“enbrsio-.
(cid:2)
coordination between APs. Therefore such an algorithm is par-
Acolcoorns,flficotr-fareseet(sCyFs)tecmolo(cid:10)(cid:2)ra(cid:5)(cid:12)s(cid:21)si(cid:12)g,ndmefiennetd(cid:28)(cid:30)in(cid:29) (cid:2) the(cid:31)abo(cid:4)v(cid:13)e(cid:4)m(cid:4) (cid:4)"a!#n(cid:5)neursisnagtis!- aticruelsairdleyntsiuailteadreafowrhsceerenaeraiochs AwPithiosuitndanepyencednetnrtallyamutahnoargiteyd, bey.g.a,
fiesthefollowingproperty: separate household. By using greater coordination, the central-
izedCFAssign-RaCalgorithmperformsbetterthanthedistributed
CFAssign-BiSalgorithm. Boththesealgorithmsareclient-driven,
(cid:26)#- (cid:24)(cid:30)(cid:10)(cid:12)(cid:11) (cid:8)(cid:2) (cid:4)(cid:20)$(cid:13) (cid:13)(cid:4) (cid:11)(cid:4) (cid:5)(cid:4)"(cid:23)!.(cid:11)%(cid:5) ,(cid:15)(cid:23)s(cid:8)(cid:30)uc(cid:21)h,thdaetfi(nie) &(cid:2)(cid:24)&/’’0(cid:2)(cid:24) (cid:2) (cid:4))((cid:13) a(cid:8) nd(cid:13) (cid:11)+(i*i)(cid:23)l(cid:11)%et(cid:29),&(cid:2)(cid:28)’(cid:10)((cid:2) (cid:12) (cid:2)(cid:4))( (cid:24)’ (cid:5)(cid:5) ,,tthheenn pheavrfeornmodexepisetnindgenteccehonfiqpuheyssliickaelLRCFCmSo.dels,andsignificantlyout-
( (cid:13) .Inotherwords:
’1(cid:8) (cid:11)
AssignmentofcolorstotheAPsisinsuchawaythatforeachclient
( )thereisatleastoneAP( )intherangesetof whichisassigned 5.1 CFAssign-RaC– RandomizedCompaction
(cid:7) 2 (cid:7)
acolor, ! , andnootherAPintherangesetorinterferencesetof Inthiscentralizedalgorithm,eachclientperiodicallymonitorsits
has been assigned to this same color, ! . We shall refer to this rangesetandinterferencesetandsendsthisinformationtothecen-
(cid:7)
propertyastheconflict-freecoloringpropertyforthesetsystem. tralentity. Thecentralentityusesthisinformationtocomputean
appropriate channel assignment using the algorithm described in
thissectionandcommunicatesthisassignmenttoeachAP.
Even if the conflict-free property does not hold for the entire set
system,itmayholdindependentlyforafewindividualclients. In- TheCFAssign-RaCalgorithm(Algorithm1)progressivelychoses
tuitivelythispropertyistrueforaclient, , ifacolor is’repre- the’best’color(channel)foranAPthatmaximizesthenumberof
(cid:7) (cid:24)
sented’onlyonceintheset (cid:13) (cid:23) byasingleelement( (cid:13) . clientsthat areconflict-free. Wefirst describeacompaction step
(cid:11)3* (cid:11) ’4(cid:8) (cid:11)
This is our formal definition for a conflict-free client. A client whichcanbeappliedtoanyexistingcolorassignmenttoincrease
Algorithm1CFAssign-RaC (cid:10) ! (cid:12) setofallpossiblechannels. Nowconsideraclientwithrangeand
(cid:2) (cid:5)(cid:12)(cid:21) (cid:5) (cid:5)(cid:1)(cid:0)
X=setofaccesspoints, interference set of APs with size, (cid:6) . Then we can calculate the
T=setof range,interference tuplesforeachclient, probabilityofthissetbeingconflict-freeusingasimpleapplication
(cid:5) (cid:6)
! =numberofcolors oftheunionbound(andisgivenbyEquation4intheappendix).
L=numberofrounds Itisintuitivethattheuniformsamplingapproachcanachievegood
(cid:4) (cid:13) (cid:4) (cid:4) (cid:4)"!.(cid:5) isthereturnedchannelassignment conflict-freedompropertiesonlywhenthesizesoftherangeandin-
(cid:28) (cid:29) (cid:2) (cid:31) terferencesetsaresmall.Forexampleinan802.11bnetwork(with
3non-overlappingchannels)ifthesizeofthesesetsis3APs,then
1: bearandompermutationof .
2: L(cid:2)(cid:3)e(cid:2)t (cid:2) (cid:2) (cid:4))( (cid:3) (cid:5) ( (cid:9) (cid:5) (cid:4) (cid:4) (cid:4) (cid:5) ((cid:5)(cid:4) (cid:5) . (cid:2) theprobabilityofconflict-freedomforeachclientis77%.Henceby
45736::::: fSoertfo(cid:24)(cid:26)(cid:2)r(cid:6)((cid:2)(cid:23)(cid:10)(cid:7)(cid:1)((cid:8)(cid:18)(cid:8)(cid:2)(cid:13)(cid:4) (cid:12)(cid:2)(cid:7)(cid:4)(cid:13)(cid:4)(cid:5)"(cid:4)(cid:4)N(cid:28)(cid:0)(cid:4) (cid:10)(cid:4)uC(d(cid:24)m(cid:2)5o(cid:12)om(cid:2)(cid:24)Cdpoao(cid:14)ncfl(cid:13)tiio/c*nt-FS1rteeinepd(cid:10)(cid:21)(cid:10)ic( (cid:5)(cid:1)a(cid:4)(cid:28)te(cid:12)sanu! n(cid:12)assignedAP*/ swtcehixooeeennncflcua(cid:6)itchtni(cid:4)ten(cid:10)-g(cid:24)(cid:26)fgpur(cid:0)erat(cid:16)oehr(cid:12)(cid:19)b.ai(cid:23)(cid:25)sna(cid:24)Hbtsei(cid:3)ioelmiw(twoypeblivoettheafrui,cnhnoeiiignndfhoflbtrihpmycertao-ssfsbarasaemimbgeipdnelloiiint8mnyg0g2t!ihs.a1al(cid:2)bt1gobo7(cid:16)ur7inn%itenhdtmewEodfqombutrhkyaue,tlittohicifpnleil(cid:6)(cid:22)ee4enxittp(cid:21)nismrateher(cid:19)sees-,
8: i(cid:28)fNum(cid:7) Conflict Free(cid:10)(cid:21) (cid:5)"(cid:28) (cid:12) (cid:2) (cid:6) (cid:5)"(cid:7)(cid:1)(cid:28)(cid:18)(cid:5)(cid:12)(cid:21)th(cid:5)en taoptpiceanldlyixgaonedsstoubzseerqouwenitthailngcerberaasiicnagpp.roximations)whichasymp-
9: stop (cid:6)
10: endif
InparticularifthenumberofAPsintherangeandinterferenceset
11: endfor
islargerthanthenumberofavailablechannels,andwechooseuni-
12: endfor
formlyatrandom,thereisagoodchancethatforeachAPassigned
conflict-freedom among clients, and later describe the algorithm toaspecificchannelthereisatleastanotherAPinthesetthatis
whichleveragesthis. alsoassignedtothischannel. Hence, uniform samplingdoesnot
scalewellwithincreasingset-sizes,i.e.,increasingdensityofAPs
CompactionStep:Considerawirelessnetwork(cid:10) (cid:5) (cid:14) (cid:12) , (cid:2) setof inthenetwork.
fAmoPursltah,te(cid:14)ioAn(cid:2)P.sLsweetth(cid:28)(cid:17)oicfh(cid:29)c(cid:2)uliseen(cid:31)sts!.(cid:4)cL(cid:13)oel(cid:4)to(cid:4)r(cid:10)(cid:4)(cid:1)s(cid:2)!..(cid:5)C(cid:5)(cid:27)(cid:21)obne(cid:12) stbihdeeetrehxaenisctAoinrPrge(cid:2)2(cid:10)sc(cid:9)(cid:9)pool(cid:8)onrd(cid:2)ia(cid:2)ns.gsKigCenFempfieonnrg-t OpruoracChF,Aessspiegcni-aBlliySwalhgeonritthhme riamnpgreovaensdtihneteurnfeifroenrmcessaemtpsliiznegs aapre-
allothercolorassignmentsthesame,thecompactionstepassigns large,bybiasingthesamplingprocessasfollows.EachAPchooses
acolorto2(cid:10)(cid:9) whichmaximizesthenumberofconflict-freeclients onespecificchannelwithhighprobability(i.e.biased)(cid:9) ,whilethe
ontheoverallforthesetsystem (cid:10)(cid:2) (cid:5)(cid:27)(cid:21) (cid:12) . Suchacolorischosenas otherchannelsarechosenwithequalprobability, (cid:10) (cid:13)(cid:18)(cid:14) (cid:9) (cid:12) (cid:0)(cid:11)(cid:10) ! (cid:14) (cid:13) (cid:12) ,
thenewassignmentfor 2(cid:10)(cid:9) . Notethatthenumberofconflict-free where ! isthenumberofchannels. Asaconsequenceofthisap-
clientscanbeeasilycomputedusingtheinterferencesetsavailable proach,ifthenumberofAPsintherangeandinterferencesetsof
atthecentralentity. aclientis ,mostoftheAPs( (cid:4) ofthem)willselectthe“biased”
(cid:6) (cid:9) (cid:6)
channel. WecalltheseAPs,biased-APs. Onlytheremainingfew
TheCFAssign-RaCalgorithmoperatesbyrepeatedlyinvokingthe APs from the conflict sets((cid:10) (cid:13) (cid:14) (cid:12) (cid:4) ofthem) will choose from
(cid:9) (cid:6)
compaction step for each AP in succession. We traverse the se- theremainingchannels. WecalltheseAPs,unbiasedAPs. Since
quenceofAPsmultipletimes,boundedbyaparameter(cid:0) (empiri- thenumberofunbiasedAPsisfarsmallerthantheoriginalnumber
callywefoundthat(cid:0) (cid:2) (cid:19) wasadequateforconvergence),starting ofAPsintherangeandinterferencesetofeachclient, auniform
initiallywitharandompermutationoftheAPs. Notethattheso- samplingapproachtochannelassignmentfortheseAPscanpoten-
lutionimprovesmonotonicallyineachrun.However,itispossible tiallybeeffectiveinmakingthissetofremainingAPs(andhence
thatthealgorithmgetsstuckinalocaloptima. Therefore,inprac- the original set) conflict-free. This is why the unbiased APs use
tice,weinvokethealgorithmmultipletimesandchoosethebestso- uniformsamplingtochoosefromtheunbiasedchannels. Itisim-
lutionthatwasobtainedacrosstheseruns.Eachseparateinvocation portant to re-iterate that it is an unbiased AP from the range set
ofthealgorithm,therefore,usesadifferentrandompermutation. whichistypicallyresponsibleformakingtheclientconflict-free.
Algorithm2CFAssign-BiS (cid:10) ! (cid:12) Conceptually, ahighbiasprobabilityisexpectedtoperformwell.
(cid:5) (cid:5)(cid:12)(cid:11)
(cid:2) However, toachievethebestresults,acarefulchoiceof should
=setofaccesspoints, (cid:9)
(cid:2)! =numberofcolors, bemade. Thebestvalueofthebiasprobability,called(cid:9) (cid:14)(cid:26)(cid:16)(cid:15)(cid:18) ,de-
=maximumsizeofarange/interferenceset. pends on the maximum size of the range and interference set in
(cid:11)
Biased-Sample(cid:10) ! (cid:12) returnscolor withprobability the network and the number of available channels. We calculate
(cid:5)(cid:13)(cid:9) (cid:9)
andcolor(cid:4)(cid:23) (cid:10)(cid:13)(cid:6) (cid:4) (cid:20)(cid:4) (cid:4)"!.(cid:23) (cid:5)(cid:22) is!t(cid:12)hewriethtuprnroebdacb(cid:6)hilaintyne(cid:10)l(cid:13) a(cid:14)ssi(cid:9)g(cid:12)n(cid:0)(cid:13)m(cid:10) !en(cid:14)t (cid:13) (cid:12) . (cid:9)(cid:27)ap(cid:14)(cid:26)p(cid:16)(cid:27)e(cid:18)ndaixn.alNytoitcealtlhyatussuincghtahecsoemtpwuotaptiaornamneeetedrsstoasodnelyscersibtiemdaitnetthhee
(cid:28) (cid:29) (cid:2) (cid:31) maximumconflictsetsizeinthenetwork. EachAPcanperform
1: Choose Bias Probability: (cid:9) (cid:2) (cid:9)(cid:15)(cid:14)(cid:17)(cid:16)(cid:15)(cid:18) (cid:10) ! (cid:5)(cid:19)(cid:11) (cid:12) /*This is dis- aalo‘lnoec,aal’sedsetsicmriabteedoifnthSiesctviaolnue5.b4y.Ainltgeorraicthtimon2wpirtehseitnstsoCwFnAcslsieignnts-
cussedindetailintheappendix.*/
2: Color: ( set (cid:10)( (cid:12) Biased-Sample(cid:10) ! (cid:12) BiSinpseudo-code.
(cid:26) (cid:8) (cid:2) (cid:29) (cid:28) (cid:7) (cid:5)(cid:20)(cid:9)
TheperformanceofCFAssign-BiScanbeimprovedbyiteratingthis
5.2 CFAssign-BiS– BiasedSampling processovermultipleroundswithsomeextracoordinationbetween
APs. In eachround we run an instanceof CFAssign-BiS and se-
Wenowpresentasimplerdistributedalgorithmthatrequiresmini-
lectthechannel(andthecorrespondingsetofAPsassignedtothat
malcoordinationbetweenAPsforchannelassignment.Letusfirst
channel) which was responsible for the most number of conflict-
considerauniformsamplingapproachforchannelassignment,in
freeclientsintheround. Wethenmakethechannelassignmentof
which eachAP chooses a channel uniformly atrandom from the
theseAPspermanent,andproceedtothenextroundbyexcluding
theseAPs,thecorrespondingchannel,andtheconflict-freeclients 1 1
cfwnB(cid:13)ra,oioilSlt(cid:13)lmla-tt1ihinotirchsne(cid:13)re,qe,ituacrAeesiurrelqaregruttsoiehivnrrneeietotsnharumcslogomouomon2brrdieedtc.rhisanmounCafctlhwcbieooeaicnntrohclflbyoai(cid:13)erlcedltterwvi-odnfeeurareeCnytneidFoiscAAnt,elisPrCtesoasniFtgiitwAmosnsnh-ipsnBiillogieetSfhmn-Ce-t1ehBFn.niiAsetStCs-twash(cid:13)Flieog.gAronIdsknr-is.ifBittfgWhhieSnmires--- Probability of conflict-free 000000000......... 1234567890 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Percentage of Conflict-free Users 000000000......... 1234567890 3 4 5 6 7NNNmmmaaaxx x==8 = 11 802 9 10
(cid:15) Value of the Bias Probability Number of Colors
entrounds. Hence,inthispaperwefocusonlyonCFAssign-BiS-1
asacompletelydistributedsolution. (a)Plotof(cid:0) (cid:10) ! (cid:12) for (b) Lower Bound on the
(cid:6)(cid:10)(cid:5) (cid:5)(cid:13)(cid:9)
5.3 Analysis (cid:6) (cid:2) (cid:22) and! (cid:2) (cid:19) . expected conflict-free
probabilityat(cid:9) (cid:2) (cid:9) (cid:14)(cid:26)(cid:16)(cid:27)(cid:18)
WepresentasummaryofouranalyticalevaluationfortheCFAssign- for various values of !
BiS algorithm (more details in the appendix). For simplicity, we and
(cid:6)!(cid:24)(cid:27)(cid:26) (cid:28)
consideronlyrangesets,althoughtheresultshereextendtrivially
toincorporateinterferencesetsaswell.
Figure6:Figure(a)showshowtoget (b)plotsthelower
(cid:9)(cid:15)(cid:14)(cid:26)(cid:16)(cid:27)(cid:18)
Let(cid:0) (cid:10) ! (cid:12) denotetheprobabilitythatarangesetofAPswith boundontheexpectedpercentageofconflict-freeusersfor(cid:9) (cid:2)
(cid:6)(cid:10)(cid:5) (cid:5)(cid:13)(cid:9)
size(cid:6) iscoloredconflict-freewith! channelsusingCFAssign-BiS (cid:9)(cid:27)L(cid:14)(cid:26)o(cid:16)(cid:27)w(cid:18)e.rBoundforCFAssign-RaC
algorithmwithabiasprobabilityof . Wecalculateanexactex-
(cid:9) DetailedanalyticevaluationoftheCFAssign-RaCalgorithmismore
pressionfor(cid:0) (cid:10) ! (cid:12) intheappendix,asshownbelow:
(cid:6)(cid:10)(cid:5) (cid:5)(cid:20)(cid:9) involvedandhenceomittedduetospaceconstraints(willbemade
availablethroughacompaniontechnicalreport). SinceCFAssign-
RaCiscentralized,itcanbeinitializedwiththecoloringobtained
(cid:23)(cid:25)(cid:24) (cid:9) (cid:9) fromexecutingCFAssign-BiS.Also, sinceineachiterationofthe
(cid:0) (cid:10)(cid:6) (cid:5) ! (cid:5)(cid:13)(cid:9) (cid:12) (cid:2) (cid:6) (cid:9) (cid:1)(cid:23) (cid:24) (cid:3)(cid:3)(cid:2) (cid:10) (cid:13) (cid:14) (cid:9) (cid:12) (cid:6) (cid:4) (cid:6) (cid:9) ’ (cid:10) (cid:13) (cid:14) (cid:9) (cid:12) (cid:1)(cid:23) (cid:24) ’(cid:6)(cid:2)(cid:13)(cid:12) (cid:10)(cid:6) (cid:14) (cid:24) (cid:5) ! (cid:14) (cid:13) (cid:12) loop (steps (cid:19) (cid:4) (cid:4) (cid:4) (cid:13) ), the conflict freedom of clients is only im-
’(cid:6)(cid:5)(cid:8)(cid:7) (cid:24)(cid:11)(cid:10) proved, the perform(cid:6) ance results of CFAssign-BiS (discussed ear-
(1) lier) act as a lower bound for CFAssign-RaC. This is confirmed
where throughextensivesimulationsinSection7andmeasurementsona
realtestbedinSection8.
(cid:12) (cid:10)(cid:6) (cid:5) ! (cid:12) (cid:2) (cid:4) (cid:4) (cid:10) (cid:14) (cid:13) (cid:12) (cid:1)(cid:4)(cid:18)(cid:17) (cid:3)(cid:3)(cid:2) (cid:9) !(cid:23) (cid:10)(cid:20)(cid:19) (cid:23)(cid:4)(cid:15)(cid:21) (cid:10)(cid:15)(cid:23)(cid:15)(cid:22)(cid:12) (cid:10) !! (cid:23)(cid:14) (cid:23) (cid:12) (cid:1)(cid:23)(cid:25)(cid:24) (cid:4)(cid:2) (2) CAsondvisecrugsseendceearlier in section 5.1, the CFAssign-RaCalgorithm
(cid:5)(cid:12)(cid:3)(cid:15)(cid:14)(cid:14)(cid:14)(cid:16) convergesrapidly(4rounds)inpractice. Itcanbeeasilyseenthat
thealgorithmwillconvergeprovably: ineachiterationoftheloop
Figure 6(a) plots (cid:0) (cid:10) ! (cid:12) forvarious values of the bias proba- (steps (cid:4) (cid:4) (cid:4) (cid:13) )eitherthealgorithmterminates(valueoftheobjec-
(cid:6)(cid:10)(cid:5) (cid:5)(cid:13)(cid:9) (cid:19)
bility(cid:9) keeping (cid:6) and ! fixed at (cid:6) (cid:2) (cid:22) (cid:5) ! (cid:2) (cid:19) . The point(cid:9) at tive function(cid:6) cannot be improved) or the algorithm improves the
which(cid:0) (cid:10) ! (cid:12) ismaximizedgivesustheoptimalbiasprobabil- objective function i.e., the number of conflict-free clients. Since
(cid:6)(cid:10)(cid:5) (cid:5)(cid:20)(cid:9)
ity forthebiasedsamplingalgorithm. Figure6(b)plotsthe theobjectivefunctionisintegral,andthereisanupperboundonits
(cid:9)(cid:27)(cid:14)(cid:17)(cid:16)(cid:15)(cid:18)
percentageofconflict-freeusers(expectedvalue)forat for value(=totalnumberofclients),thealgorithmwillconverge.
(cid:9) (cid:14)(cid:17)(cid:16)(cid:15)(cid:18)
(cid:6) (cid:2) (cid:22) (cid:5) (cid:13) and (cid:13)(cid:6)(cid:24) . Theoptimalvaluesfor(cid:9) canbeprecomputed
andstored(cid:6) inatableindexedby (cid:23)(cid:6)(cid:25)(cid:24)(cid:27)(cid:26)(cid:29)(cid:28) (cid:5) !(cid:31)(cid:30). Thetablewouldhave 5.4 ImplementationIssues
(cid:22) (cid:13) entriesallforpracticalvaluesof(cid:6) and! . Wehavediscussedtwoalgorithms–CFAssign-RaCandCFAssign-
(cid:6) (cid:6)
BiS. Bothalgorithms operateon a conflict-freecoloringformula-
BasedonEquation1weobservethefollowingimportantproperties tion (cid:10) (cid:12) . APs can find out the range and interference sets of
ofCFAssign-BiS: (cid:2) (cid:5)(cid:27)(cid:21)
theirclientsbyrequestingthelattertoconductasite-reportasspec-
ifiedinIEEE802.11Kdrafts[11].Inasite-report,aclientscansall
FairnessandResiliencetoMobility channels and reportsall theAPs withinits rangeon thedifferent
Let bethemaximumsizeofanyrangesetforthewireless channels.Suchscanscanberequestedperiodicallyordynamically
(cid:8) (cid:24)(cid:27)(cid:26) (cid:28)
network (cid:10) (cid:5) (cid:14) (cid:12) . Each client has the same and equal minimum based on mobility. A scan for IEEE 802.11b can be completed
(cid:2)
probabilityofassociatingtoaconflict-freeAPasgivenbythequan- inaround150ms[12], whichisnegligibleoverthedurationofa
tity(cid:0) (cid:10) ! (cid:12) .ThisfollowsfromthefactthatEquation1 channelre-assignment.
(cid:8) (cid:24)(cid:27)(cid:26)(cid:29)(cid:28) (cid:5) (cid:5)(cid:13)(cid:9)(cid:27)(cid:14)(cid:26)(cid:16)(cid:27)(cid:18)
isnotalteredbydifferencesintheexactrangesetsbetweenanytwo
clients. Notethatthemaximumsizeofanyrangeset, ,isa TheCFAssign-BiSalgorithmoperatesobliviousoftheexactmem-
(cid:8) (cid:24)(cid:27)(cid:26) (cid:28)
functionoftheplacementofAPs,andhenceitdoesnotdistinguish bershipoftherangeandinterferencesets. Inthisalgorithm,each
between clients. Also, since is a property of the wireless AP just requires an estimate of the largest range/interference set
(cid:8) (cid:24)(cid:27)(cid:26) (cid:28)
network,theperformanceoftheCFAssign-BiSalgorithmwithre- size. An AP can construct a good ‘local’ estimate of the largest
specttoconflict-freedomandfairnessisunaffectedbyanymodel setsizebyaggregatingthisinformationfromitsownclientsalone.
ofmobilityfollowedbytheclients.Morespecifically,regardlessof SinceanAP’schannelassignmenthasaneffectonclientswithin
howmanyclientsaremobileandhowfasttheymove,eachclient its range only, i.e., a ’local’ effect, we expect a local estimateof
hasthesameminimumprobabilityoffindingaconflict-freeAP. thelargestsetsizetoperformequallywell. Inourevaluationsde-
scribed in the next section, each AP uses this local estimate ap-
Theseresultscanbeextendedtriviallytoincorporateinterference proach (requiring no coordination between APs) when using the
setsaswell,andwepresentthedetailedproofsinatechnicalreport. CFAssign-BiSalgorithm. However,asimpledistributedalgorithm
Geometric:InthismodelweassumethatRFsignalsattenuateisotrop-
Percentage of Conflict Free Users 000000000 .........01123456789 3 4 5 6 7CC F8FAAs ss9sigig n1n-0R-Ba 1iCS1 12 13 14 Percentage of Conflict Free Users 000000000 .........01123456789 3 4 5 6 7CC F8FAAs ss9sigig n1n-0R-Ba 1iCS1 12 13 14 irTtcltcrohaihaarwnenceldludrsiyoemnlimasftaotrier.scrrisfecfbriEeoooutrarnmtredicanoirhnncanasegdAmofi,iuPftaixossnets.hrdditaaWohondrnensaemaneaTggnwiwtesrednoasi.etin-ihoRrnsEanmtahtaeeyicrrigdasfhhGesntirgwciorenloennoitsuecenrsneroaeftdfdetrasriatPulehnosrnsegofocecptnehoshaoapbogdisoonsaelettasohintnohgicnniiuiosennnstmdmhi,tfereooooopdnradlemelerenelellwdday[ae5ibornta]yheftt.
Number of Channels Number of Channels networkcoverage. Themeansizeoftherangesetsofclientswere
4and8forthelowandhighinterferencetopologiesrespectively.
(a)Randomtopologywith (b)Randomtopologywith
lowinterference highinterference
Random: In this model APs and clients were allowed to induce
interferencewith arbitraryother APs orclients. Each client(and
AP)wasallowedtoselectasubsetofAPs(andclients),uniformly
1 1
Percentage of Conflict Free Users 000000000......... 1234567890 CCFFAAssssigignLn-CR-BCaiCSS Percentage of Conflict Free Users 000000000......... 1234567890 CCFFAAssssigignLn-CR-BCaiCSS amawlbotmueoctroaidaoctuenihnlnodo,tnobowomesofhtef,wienwttrehhteeieeetnrthfhnse2ewoirzdehaieennniscctodeheafr.1nftteAh5dhreeetAmyhniPeceinneasttte,nrerrawarfonfnefiesrgtmr4eheenswi.tcshTsaeaeirshoesmiunesdsterseiiaascdnnatuatsgontueealsgsdiek.eGdebnFayettouohrrtasehtcseeeigoaaeacnpnohthlrmodoycwilselsiitttecirrhnnaiiec--lt
3 4 5 6 7 8 9 10 11 12 13 14 3 4 5 6 7 8 9 10 11 12 13 14 terferencetopologies,andameanof8wasusedtogenerateahigh
Number of Channels Number of Channels
interferencetopologies. Therelativelynon-homogeneousrandom
interferencemodelisanapproximationofcertainRFpropagation
(c) Geometric topology (d) Geometric topology
withlowinterference withhighinterference vagariesofindoorwirelessenvironments.
Figure7showsthesimulationplots. Eachplotshowstheaverage
Figure7:Figurecomparesperformanceofthethreealgorithms over 100 different CF formulations along with the 10th and 90th
overvarioustopologies. percentiles.Wediscussthesalientpointsofourresultsbelow:
1. Both CFAssign-BiS and CFAssign-RaC outperform LCCS:
tocomputethemaximumsetsizecanalsobeemployedtoimprove
Asexpected,LCCSdoesnotcapturealltypesofinterference
performance.
thatcanexistinanetworkandalsodoesnottakeaclient’s
perspectiveintoconsideration.Bothalgorithmsperformsig-
Channelre-assignmentcanbedoneeitherperiodicallyordynami-
nificantlybetterthanLCCSregardlessoftheamountofin-
callybasedonfeedback. Thefeedbackbasedtechniquetriggersa
terference and the model used for generating the datasets.
re-assignmentifthequalityofthecurrentassignmentasmeasured
Alsotheperformancegainincreasesasthenumberofchan-
byanobjectivefunctiondegradesrelativelybelowathreshold.We
nelsisincreasedthusexposingtheweaknessesofLCCSas
discusssuchextensionsinourmobilitysimulationsinsection7.
discussedearlierinsection2.
ChangingthechannelforanAP/clientisarelativelylow-costop- 2. CFAssign-RaCperformsbetterthanCFAssign-BiS:CFAssign-
eration ((cid:13) (cid:14)(cid:21)(cid:24) ms)whichcanbe implementedmostly asadriver RaC exploits the knowledge of range and interference sets
update. Theactualoperationofchangingthechannelcanbesyn- of all clients to perform the compaction step in a central-
chronizedwithanAP’sbeacon. TheIEEE802.11Kdraftspecifies izedmanner,andprovidesabetterchannelassignmentthan
MAClevelprimitivestoachievethisgoal. CFAssign-BiS.However,theapplicationdomainsofbothal-
gorithmsaredifferent.Thesimplicityanddecentralizedmode
ofoperationofCFAssign-BiSmakesitparticularlyapplica-
bletonetworkswithlimitedornocentralizedcontrolwhere
5.5 Topology-levelSimulations
CFAssign-RaCmaybedifficulttodeploy.
WestudytheperformanceoftheCFAssignalgorithmswithrespect
to the number of clients that are conflict-free, through extensive
topology-level simulations. Weevaluate them undervarious sce- MultipleCo-ExistingWirelessNetworks
narios,includingtwodifferentRFmodels,differentAPandclient Wenowexaminehowthesealgorithmsperforminasituationwhere
densities.Inparticular,weuseageometricmodelwheretheRFsig- multiplenetworksareforcedtocompeteforthesamespectrum.In
naldecaysinanisotropicmanner,andarandommodelwherethe ourscenario,wehavethreecompetingnetworkswith20APseach,
rangeandinterferencesetsofaclientareconstructedinarandom and equal client distribution (80 clients per network) sharing the
manner. TherandommodeldoesnotconformtoanyspecificRF samephysicalspace.Weconsiderthesamesetofalgorithmsasbe-
propagationmodel. Weusethistodemonstratetheindependence fore. TheLCCSandtheCFAssign-BiSalgorithmsoperateidenti-
fromthevalidityofanyparticularRFmodel. Forthenetworksize callyregardlessoftheextentofcooperationbetweenthecompeting
in both these models we used 50 APs and 200 clients that were networks.FortheCFAssign-RaCalgorithm,however,itispossible
distributedinathreedimensionalphysicalregionuniformlyatran- todefinedifferentdegreesofcooperationfortheCFAssign-RaCal-
dom. Each client is considered active, i.e., it will cause and ex- gorithm.
perienceinterferencewithotherclientsastheycommunicatewith
their respective APs. The degree of interference in these models 1) RaC-UpperBound: In this mode of cooperation the three net-
wasvariedusingdifferenttechniquesasdescribednext. worksemployperfectcooperation. Thechannelassignmentofall