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A Spectral Method for Network Cache Placement Based on Commute Time

Permanent Link: http://ufdc.ufl.edu/UFE0045571/00001

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Title: A Spectral Method for Network Cache Placement Based on Commute Time
Physical Description: 1 online resource (43 p.)
Language: english
Creator: Sinha, Priyanka
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2013

Subjects

Subjects / Keywords: cache -- commute -- expected -- placement -- time -- wireless
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Information caching in networks can be used to reduce latency and increase reliability in accessing information and also to reduce network traffic. In wireless networks, changing channel conditions may impact the availability of caches, and this should be taken into account when determining where in the networks caches will be placed. In this thesis, we investigate this problem and propose that expected commute time between a nodes and its corresponding cache is a good measure to optimize because it takes into account both the distances between the node and the cache and the number of paths between the node and the cache. We then develop an efficient way to place the caches using spectral clustering. The performance of cache placement based on expected commute time is compared to the performance of cache placement based on Euclidean distance The results show that for most of network topologies, the commute-time based clustering outperforms provides better access latency than distance-based clustering.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Priyanka Sinha.
Thesis: Thesis (M.S.)--University of Florida, 2013.
Local: Adviser: Shea, John Mark.

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Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2013
System ID: UFE0045571:00001

Permanent Link: http://ufdc.ufl.edu/UFE0045571/00001

Material Information

Title: A Spectral Method for Network Cache Placement Based on Commute Time
Physical Description: 1 online resource (43 p.)
Language: english
Creator: Sinha, Priyanka
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2013

Subjects

Subjects / Keywords: cache -- commute -- expected -- placement -- time -- wireless
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Information caching in networks can be used to reduce latency and increase reliability in accessing information and also to reduce network traffic. In wireless networks, changing channel conditions may impact the availability of caches, and this should be taken into account when determining where in the networks caches will be placed. In this thesis, we investigate this problem and propose that expected commute time between a nodes and its corresponding cache is a good measure to optimize because it takes into account both the distances between the node and the cache and the number of paths between the node and the cache. We then develop an efficient way to place the caches using spectral clustering. The performance of cache placement based on expected commute time is compared to the performance of cache placement based on Euclidean distance The results show that for most of network topologies, the commute-time based clustering outperforms provides better access latency than distance-based clustering.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Priyanka Sinha.
Thesis: Thesis (M.S.)--University of Florida, 2013.
Local: Adviser: Shea, John Mark.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2013
System ID: UFE0045571:00001


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ASPECTRALMETHODFORNETWORKCACHEPLACEMENTBASEDONCOMMUTETIMEByPRIYANKASINHAATHESISPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFMASTEROFSCIENCEUNIVERSITYOFFLORIDA2013

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c2013PriyankaSinha 2

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Tomyparents(Mr.PradipSinhaandMrs.RekhaSinha),andmyuncle(Mr.ShaktiChatterjee) 3

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ACKNOWLEDGMENTS ThisthesiswouldnothavebeenpossiblewithouttheguidanceandthehelpofDr.JohnM.Shea.Iwouldliketothankhimforhisencouragementandhisvaluableguidanceinthepreparationandcompletionofthiswork.Iwouldalsoliketothankmyfamilyandfriendsforalltheirinvaluablesupport. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 7 LISTOFFIGURES ..................................... 8 ABSTRACT ......................................... 9 CHAPTER 1INTRODUCTION ................................... 10 1.1ProblemOverview ............................... 10 1.2LiteratureReview ................................ 11 1.3SchemesthatAimtoImproveDataAccessEfciency ........... 12 1.3.1ImproveDataAccessEfciencywithSingleDataItem: ....... 12 1.3.2ImproveDataAccessEfciencywithMultipleDataItems: ..... 14 1.4SchemesthatAimtoImproveEnergyConsumption: ............ 16 1.5ContributionandOrganizationofthisThesis ................. 17 2SYSTEMMODELANDPROBLEMFORMULATION ............... 18 2.1SystemModel ................................. 18 2.1.1Topology ................................. 18 2.1.2LinkModel ................................ 19 2.2ProblemFormulation .............................. 20 2.2.1ExpectedCommuteTime ....................... 20 2.2.2UsingSpectralEmbeddingtoExpressCommuteTimeasEuclideanDistance ................................. 21 2.2.3OptimalityCriterion ........................... 23 3CLUSTERINGALGORITHM ............................ 24 3.1SelectionofAlgorithm ............................. 24 3.2PartitioningAroundMedoids(PAM)Algorithm ................ 25 3.3PAMforCacheSelection ........................... 26 3.4PAMParametersandPerformance ...................... 27 3.5MotivatingExample .............................. 28 4NETWORKSIMULATION .............................. 31 4.1Simulation .................................... 31 4.2Results ..................................... 33 5CONCLUSION .................................... 39 5

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REFERENCES ....................................... 40 BIOGRAPHICALSKETCH ................................ 43 6

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LISTOFTABLES Table page 4-1Simulationparameters ................................ 32 7

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LISTOFFIGURES Figure page 2-1TheGilbert-Elliotmodel ............................... 19 3-1Minimumaveragecommutetimeovermultipleruns. ............... 27 3-2AveragecommutetimebetweenverticesandmedoidsasafunctionofnumberofiterationsinthePAMclusteringalgorithm. .................... 28 3-3Clustersformedbydistance-basedPAMclustering. ............... 29 3-4Clustersformedbycommute-timebasedPAMclustering. ............ 29 4-1Averageaccesslatencyvspgbforpbg=0.8androutingfrequency=0.01. ... 33 4-2Averageaccesslatencyvspgbforpbg=0.6androutingfrequency=0.01. ... 34 4-3Averageaccesslatencyvspgbforpbg=0.2androutingfrequency=0.01. ... 35 4-4Averageaccesslatencyvspgbforpbg=0.8androutingfrequency=0.02. ... 36 4-5Averageaccesslatencyvspgbforpbg=0.8androutingfrequency=0.05. ... 37 8

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AbstractofThesisPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofMasterofScienceASPECTRALMETHODFORNETWORKCACHEPLACEMENTBASEDONCOMMUTETIMEByPriyankaSinhaMay2013Chair:JohnM.SheaMajor:ElectricalandComputerEngineeringInformationcachinginnetworkscanbeusedtoreducelatencyandincreasereliabilityinaccessinginformationandalsotoreducenetworktrafc.Inwirelessnetworks,changingchannelconditionsmayimpacttheavailabilityofcaches,andthisshouldbetakenintoaccountwhendeterminingwhereinthenetworkscacheswillbeplaced.Inthisthesis,weinvestigatethisproblemandproposethatexpectedcommutetimebetweenanodesanditscorrespondingcacheisagoodmeasuretooptimizebecauseittakesintoaccountboththedistancesbetweenthenodeandthecacheandthenumberofpathsbetweenthenodeandthecache.Wethendevelopanefcientwaytoplacethecachesusingspectralclustering.TheperformanceofcacheplacementbasedonexpectedcommutetimeiscomparedtotheperformanceofcacheplacementbasedonEuclideandistanceTheresultsshowthatformostofnetworktopologies,thecommute-timebasedclusteringoutperformsprovidesbetteraccesslatencythandistance-basedclustering. 9

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CHAPTER1INTRODUCTION 1.1ProblemOverviewIncommunicationsnetworks,informationmaybecachedatlocationsthroughoutthenetworktoreducethecostinaccessingthatinformation.Forinstance,bycachingtheinformationclosetothenodesaccessingit,theinformationcangenerallybeaccessedatlowerlatency,higherspeed,andwithhigherreliability.IntheInternet,thisapproachhasspawnedthecreationofcontentdeliverycompanies,suchasAkamai.Cachingisalsoimportantinmilitarynetworks,andespeciallyindistributedwirelessnetworksinwhichcommunicationsoverlongroutesarepronetofailure.Inthisthesis,wefocusonthecaseofcacheplacementinwirelessadhocnetworks,andthediscussionwillbebasedonthisscenario.However,mostoftheideasandtechniquesareapplicabletootherwirelessandwiredcommunicationsnetworkswithminimalmodication.Animportantconsiderationiswheretoplacecachesinthenetwork.Thecachesshouldbedistributedthroughoutthenetworksothattheinformationiseasilyaccessiblebytheothernodesinthenetwork.Here,easilyaccessiblemayincludevariouscriteria,suchasshortpathsfromanodetothenearestcache.Givensuchapath,additionalcriteriacouldbethatithavehighreliability,highcapacity,orlowercongestion.Reliabilitycanbefurtherenhancedifthecacheisaccessibleviamultiplepossibleroutes.Inthisthesis,weproposetousetechniquesfromspectralgraphtheorytooptimizetheplacementofcachesinadistributedwirelessnetwork,withdynamiclinkstates.Informationiscachedatasetofnodesthatminimizestheexpectedcommutetimetonearbynodesthatmayaccessthecaches.Aswediscussfurtherbelow,expectedcommutetimebetweentwonodesisameasurethatnotonlydecreasesbothwhenthelengthofanypathconnectingthetwonodesdecreasesbutalsodecreaseswhenthenumberofpathsconnectingtwonodesincreases.Inaddition,byusingaspectralembeddingofthenodeadjacencyinformationintoahigh-dimensionalEuclidean 10

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space,theexpectedcommutetimeamongnodesinagraphcanbecalculatedusingEuclideandistance.Thislatterapproachallowsforcachestobeplacedusingsimplerepresentative-basedclusteringalgorithmsandalsoallowsformoreefcient,approximateoptimizationoftheexpectedcommutetimebyembeddingthenodesofthegraphinalower-dimensionalEuclideanspace.Resultsarepresentedtodemonstratetheeffectivenessofthealgorithms. 1.2LiteratureReviewSincewirelessnetworkshavelimitedcommunicationbandwidth,datacachingmaybeausefulapproachtoimprovetheefciencyofthedataaccess.Anumberofrecentandpastworkshavetackledtheproblemofcacheplacementinwirelessnetworks,andtheycanbebroadlycategorizedbasedonthefollowingcriteria: 1. Optimizationobjective: (a) Improvethedataaccessefciency (b) Improvetheenergyconsumption (c) Improvetherateofutilizationandcache-hitratio 2. Numberofdataitemsinnetwork: (a) Cacheplacementinanetworkwithsingledataitem (b) Cacheplacementinanetworkwithmultipledataitems:Theclassofproblemswithmultipledataitems,canagainbeclassiedonbasisofthesizeofdata: i. Uniform-sizedataitems ii. Nonuniform-sizedataitems 3. Optimizationapproach:Optimalcacheplacementforanetworkwithageneralgraphtopologyandasingletypeofdataitemisgenerallyformulatedasoneoftwodifferentgraph-theoryproblems: (a) Inthefacilitylocationproblem,thegoalistominimizethesumofthetotalcosts(cachesetupcost+accesscost)incurredduetocachingateachnodeinacertaincacheplacement,withoutanyconstraint,and (b) Inthek-medianproblem,thegoalistominimizethetotalaccesscostwithamaximumofkcachenodes. 11

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Cacheplacementproblemscanbefurtherclassiedintermsofthecomplexityofthealgorithmthatsolvesthem.Forinstance,boththefacilitylocationandk-medianproblemsareNP-hard,meaninganalgorithmforsolvingitcanbetranslatedintooneforsolvinganyNP-problem(nondeterministicpolynomialtimeproblem).TherearecertainworksthatareformulatedasAPX-hardproblems(approximableproblemsthatdoesnothaveapolynomialtimeapproximationscheme)like[ 1 ].Butinordertobeabletondasolutiontothesecacheplacementproblems,wemustovercomethehardnessorthenonapproxamibility.SeveralNP-hardorAPX-hardproblemshavebeensolvedusingconstant-factorapproximationalgorithms(polynomial-timeapproximationalgorithmswithapproximationratioboundedbyaconstant)aftercircumventingthehardnessorthenonapproximability.Example:[ 1 ]overcomesanonapproximabilityproblembychoosingtomaximizethereductionintotalaccesscostinsteadofminimizingthetotalaccesscost.SeveralworksovercomethehardnessofaNP-hardproblembyconsideringtreenetworksinsteadofgeneralgraphtopologies,[ 2 ],[ 3 ],[ 4 ],[ 5 ]. 4. Centralizedvs.distributed:Adistributedalgorithmhastheadvantageofbeingimplementableinanetworkwithdynamictrafcoveracentralizedone. 5. Memoryconstraint:Someoftheexistingworkstakeintoconsiderationthatthenodesinthenetworkmayhavelimitedmemoryandhenceposetheproblemwithamemoryconstraint[ 6 ].Inotherwork,memoryisnotconsideredaconstraint.Sincetheseclassicationcriteriaareoverlapping,weusetherstcriterion(optimizationobjective)asourprimarycriterionindescribingtheexistingliteratureoncacheplacementinwirelessnetworks. 1.3SchemesthatAimtoImproveDataAccessEfciency 1.3.1ImproveDataAccessEfciencywithSingleDataItem:In[ 7 ],thecacheplacementproblemisposedasatrade-offbetweenover-headcostduetocacheplacementandaccesslatency.ApolynomialtimealgorithmisdesignedtoapproximatelysolvetheNP-hardproblemofminimizingtheweightedsum 12

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ofoverheadcostandaccesslatency.Thealgorithmcanbeimplementedinadistributedandasynchronousfashion.In[ 8 ],ahybridcache-placementschemeisdevelopedthatcarriesoutanoptimaltradeoffbetweenthedisseminationandaccessoverheadcostandtheaccesslatency.Theproposedschemeusesaroutingnavigationalgraphthatguresoutthepotentialrelationshipamongthenodesintheroutingpaths,usingthecurrentdataaccesspatterns,andaclusteringstrategytopartitionthemultihopwirelessnetworktopicksuitablenodesforcacheplacementfromasetofnodesrelatedtotheusers'application.Thisapproachhelpsthecacheplacementschemebeadaptivetochangesindataaccesspatternswhileminimizingthenumberofcachenodes.Theschemeresultsinasmalleroverheadcostthanoodingandachievesasignicantimprovementwhenthenumberofnodesislarge.In[ 1 ]anevolutionaryapproachhasbeenproposedforndinganoptimalwebproxycacheplacementthatminimizestheaverageresponsetimeforaccessingthewebcontent.Whencomparedtothetraditionalapproacheslikedynamicprogrammingandpacketlevelsimulation,theevolutionaryapproachissaidtohavesimilarresultsaspacket-levelsimulationforsimplenetworks,whilebeingcomputationallyfaster.Theevolutionaryalgorithmhandleslargescalenetworksequallywellasthedynamicprogrammingapproach.Optimizingthecacheplacementtotradeoffbetweenthetotaltrafccostandaverageaccessdelayinwirelessmulti-hopadhocnetworksisconsideredin[ 2 ].SincedynamicnetworktopologiesareconsideredtheapproachiscalledDynamicCachePlacement(DCP).Unlikeotherdataaccessefciencyoptimizationproblems,DCPtakestheimpactofcontentionsinthewirelessnetworksintoaccount:hopcounts,whichareoftenusedtomeasurethetotalcostofcaching,resultindifferentperformancesdependingonthecontention/trafcloadsonthepaths.Threekindoftrafcowsareconsideredinthecachingsystem:AccessFlow:traversalofnodesfordataaccess,ReplyFlow(RF):Traversalofnodesforreplyingtodatarequestsfromcachenodes,andUpdateFlow:traversalofnodesforupdatingcache 13

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content.DCPaimstoselectcandidatenodesforcacheplacementsoastoreducetheaccesstrafcowsandincreasetheupdatetrafcowstothebestofthepossibilitiesandselectcachenodeswithfewercontentionsfromthecandidates.In[ 9 ]aneffectiveandlowcostcacheplacementschemeformobileP2Pnetworksisproposed,alongwithaschemetoupdatethecacheplacementasthenetworkevolves.Bothschemesareimplementableinadecentralizedmanner.In[ 10 ],aheuristiccache-distributionalgorithmisdevelopedthataimsatimprovingdocumentdownloadlatencybyimprovingtheovernetworklatency.Thisschemeestimatesthetrafcateachcacheofamesh-networkandbasedonthetrafc,eachcacheisassignedasuitablepercentageofthetotalstoragecapacityofthenetwork.Refs.[ 11 ]and[ 12 ]designoptimaldynamicprogrammingpolynomialalgorithmsforsolvingk-medianproblemsinundirectedanddirectedtrees,respectively.Inotherworks,[ 13 ]considerstheplacementofktransparentcaches,[ 14 ]considersacostmodelinvolvingreads,writes,andstorage,and[ 15 ]presentadistributedalgorithmforsensornetworkstoreducethetotalpowerexpended. 1.3.2ImproveDataAccessEfciencywithMultipleDataItems:Optimizingcacheplacementinadhocnetworkwithmultipletypesofdataitemsisthefocusof[ 16 ],inwhichthreedifferentalgorithmsareproposed.Intherst,eachnodecachestheitemsmostfrequentlyaccessedbyit.Thesecondapproacheliminatesreplicationsamongneighboringnodesintroducedbytherstapproach.Thethirdapproachrequirescreationofstablegroupstogatherneighborhoodinformationanddeterminecachingplacements.Theapproachin[ 16 ]isextendedin[ 17 ]and[ 18 ]bygeneralizingtheaboveapproachesforpush-basedsystemsandupdates,respectively.Here,[ 17 ]improvesusesapush-basedapproachtoshortentheaverageresponsetimefordataaccess,and[ 18 ]triestoimprovedataaccessibilityforsystemsinwhichthedataitemsareupdatedperiodically. 14

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Severalotherreferencesalsoconsidercacheplacementwithmultipledatatype.Ref.[ 19 ]suggeststransparentreplicaplacementintreenetworkstominimizetotaldatatransfercost.Tosupportdataaccessinamultipledataitemenvironment,[ 3 ]devisesthreesimpledistributedcachingtechniques:CacheData(cachesdataitemsthatarepassingby),CachePath(cachesthepathtothenearestcacheofthepassing-bydataitem),andHybridCache(whichcachesthedataitemifitssizeissmallenoughorthepathtothedataotherwise).TheyuseLRU(leastrecentlyused)policyforcachereplacement.Ref.[ 20 ],proposesa20.5-approximationnon-distributed(wheredistributedimplementationisnotpossible)algorithmforanon-APXoptimalcacheplacementwithuniform-sizemultipledataitems,asnopolynomial-timesolutionexistsforthenonuniform-sizedataitems.However,theirapproach(asnotedbythemselves)isnotamenabletoanefcientdistributedimplementation.Ref.[ 6 ]isasimilarworkthatminimizesthetotaldataaccesscostinadhocnetworkswithmultipleuniform-size(generalizabletonon-uniformsizedataitems)dataitemsandnodeswithlimitedmemorycapacity.Acentralizedtractablealgorithmwithaprovableperformanceboundisdeveloped.Thealgorithmisalsosuitabletoanaturaldistributedimplementation.Namely,acentralized4-approximationalgorithm(2-approximationforuniform-sizedataitems),andalocalizeddistributedalgorithm,basedontheapproximationalgorithmandcapableofhandlingmobilityofnodesanddynamictrafcconditionshavebeendevised.In[ 21 ],adatacachingalgorithmisproposedforadhocnetworkswithmultipledataitemsandwhosenodesexchangeinformationitemsinapeer-to-peermanner.Ateachnode,uponreceivingrequestedinformation,itdeterminesthecachedroptimeoftheinformationorwhichcontenttoreplaceforthenewlyarrivedinformation.Anearoptimalcacheplacementisproposedtomaximizereductioninoverallaccesscostwhilemeetingthelimitedmemoryconstraint,whichinturnleadstobetterbandwidthusageandenergysavings.Thealgorithmsproposedinthispaperarebothanalyticallytractablewithaprovableperformanceboundinacentralizedsettingandarealsoamenabletoa 15

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naturaldistributedimplementation.In[ 22 ]aneffectiveandlowcostcacheplacementstrategy,combinedwithanupdatescheme,hasbeenproposedwhichissuitablefordecentralizedimplementationinamobilepeer-to-peernetwork.Thispaperalsocomparesitsplacementandupdateschemewithvariousplacement-onlyschemeslikeGlobalBenetBasedCachePlacement(GBCP),LocalBenetBasedCachePlacement(LBCP)andClusterBasedCachePlacement(CBCP),andRandomPlacement(RAND)andestablishesthatacombinationofplacementandupdatedoesbetterthantheotherthreeplacementschemesintermsofaveragehopcountrequiredtotransmitasegmentofdata. 1.4SchemesthatAimtoImproveEnergyConsumption:In[ 4 ],cache-placementalgorithmsaredevelopedtominimizetheoverallaccesscostwithanupdatecostconstraint,thusreducingenergyconsumptionandtakingcareofresourceefciency.Dynamicprogrammingisusedtosolvetheoptimalcache-placementproblemfortreetopologies,andapolynomialtimealgorithmisdevelopedtoapproximatelysolvetheNP-hardcacheplacementproblemforgeneralgraphtopologies.Distributedimplementationsofthesealgorithmsarealsodeveloped.In[ 5 ]acachingschemethatoptimallytrades-offbetweenenergyconsumptionandaccesslatencyinwirelessadhocnetworkisdeveloped.Theproblemisaspecialcaseoftheconnectedfacilitylocationproblem,whichisknowntobeNP-hard.Apolynomialtimealgorithmforthesamehasbeendeveloped,whichprovidesasub-optimalsolutioninarbitrarynetworktopologies.Thisalgorithmcanbeimplementedinadistributedandasynchronousmanner.Inthecaseofatreetopology,thealgorithmgivesoptimalsolution.Anenergy-conservingcachingschemeforwirelesssensornetworksisdevelopedin[ 23 ].FindingthelocationsofthenodesforcachingdatatominimizecommunicationcostcorrespondstondingthenodesofaweightedMinimumSteinertreewhoseedgeweightsdependontheedge'sEuclideanlengthanditsdatatrafcrate.This 16

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treeiscalledaSteinerDataCachingTree(SDCT).ExpressionsdeterminingtheexactlocationofaSteinerpointforasetofthreenodesbasedontheirlocationarederivedalongwiththeirdatarefreshraterequirements.Basedonthese(optimality)results,adynamic,distributed,energy-conservingapplication-layerservicefordatacachingandasynchronousmulticastispresented.Areviewofthevariousdatacachingtechniquesinwirelesssensornetworks(WSNs)ispresentedin[ 24 ].In[ 15 ],adistributedapplication-layerserviceforcacheplacementandasynchronousmulticastinwirelesssensornetworkshasbeenproposedforplacingreplicasofrequesteddataitemsandupdatingtheminsuchamannersoastominimizethefrequencyofcommunication,whichresultsinreducedcommunicationoverheadandhencereducedpowerconsumption. 1.5ContributionandOrganizationofthisThesisTheexistingworkoncacheplacementfocusesonnetworksinwhichthelinksarereliable.Inwirelessmeshandadhocnetworks,dependingonthecommunicationfrequenciesandmobilityrates,thelinksmayoftenexperienceoutagesbecauseofmultipathfading.Thus,inthisthesiswefocusonthedesignofacacheplacementstrategytoimproveperformanceinthepresenceoflinkfailures.Therestofthisdocumentisorganizedasfollows.In chapter2 ,thesystemmodelispresented,andtheproposedmetricforoptimizingcacheplacementispresented.In chapter3 ,wedescribehowspectralclusteringalgorithmscanbeusedtoapproximatetheoptimalcacheplacements.In chapter4 ,wedescribeanetworksimulationthatwasusedtocompareperformanceoftheproposedcacheplacementalgorithmwithareferencealgorithm,andperformanceresultsarepresentedtoshowtheadvantagesofthecacheplacementalgorithmwepropose.Finally,in chapter5 ,conclusionsaredrawnandpossibleextensionstothisworkarediscussed. 17

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CHAPTER2SYSTEMMODELANDPROBLEMFORMULATION 2.1SystemModelWeconsiderawirelessnetworkwithstatictopologybuttime-varyingcommunicationlinks.Thisscenariocanmodelaslowlymovingadhocnetworkovershorttimeframesandissufcienttodemonstratewhethertheproposedcache-placementtechniquescanimproveperformanceinthepresenceoflinkqualityuctuations.Forthepurposesofthisstudy,atanygiventime,communicationoveralinkbetweentworadiosiseitherpossible(thelinkisup)ornotpossible(thelinkisdown).Linksareassumedtotransitionbetweenupanddownaccordingtoarandomprocess.Thus,wecancharacterizethenetworkintermsofitstopologyandthelinkmodel. 2.1.1TopologyConsiderrstthefullnetworktopology,whichconsistsofthesetofcommunicators(nodes)alongthesetoflinkswhenalllinksareup.ThefullnetworktopologycanberepresentedbyasimpleweightedgraphG=(V,E),whereVisthesetofvertices(representingthedataornodesinthenetwork)andEisthesetofedgesconnectingtheverticesinV.Forconvenience,letN=jVjbethenumberofvertices,ornodes,inthenetwork.WeassumethatGisaconnectedgraph,whichmeansthatthereisapathfromanyvertextoanyothervertex.Ifanedgeexistsbetweentwoverticesviandvj,thenthoseverticeshaveanonzerosimilarityorafnitymeasure,aij0whichistheweightassignedtothatedge.Largerweightsindicatethatcommunicationiseasierbetweenthenodes,intermsofanappropriatemeasure,suchasthroughputorreliability.TheweightscanbecollectedintoaweightedadjacencymatrixA=[aij],i,j=1,2,...,N.Herewij=0ifviandvjdonotshareanedgeorifi=j.Thedegreeofvertexvi2Visdi=PNj=1aij.LetDbethediagonalmatrixwithDii=di.Animportantmatrixthatwewillutilizelateristhe(unnormalized)LaplacianmatrixforG,whichisL=D)]TJ /F8 11.955 Tf 11.96 0 Td[(A. 18

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2.1.2LinkModelAspreviouslymentioned,atanygiventime,agivencommunicationlinkmayeitherbeupordown.Forconvenience,wedividetimeintoslotsandcharacterizethestateofeachedgeGineachslot.Weassumethatthestatesfordifferentlinksareindependent,whichmaynotnecessarilybetrueinsituationssuchasshadowing;howeverthiswillbetrueifthelinkqualityiscausedbyfadinginarichmultipathenvironment.Formostsituationsthatcauselinkqualitytouctuate,suchasfadingorshadowing,thelinkqualitywillnotbeindependentfromslottoslot.Tomodelthedependencebetweenslots,inthisthesis,weusetheGilbert-Elliotchannelmodel,whichisbasedonatwo-statediscrete-timeMarkovchain.Thetwostatesarethegoodstateandthebadstate,wherethelinkisupwhentheMarkovchainisinthegoodstateandthelinkisdownwhentheMarkovchainisinthebadstate.AstatediagramfortheGilbert-Elliotchannelisshownin Figure2-1 Figure2-1. TheGilbert-Elliotmodel Letpgbdenotetheconditionalprobabilitythatthenextstateisthebadstategiventhatthecurrentstateisthegoodstate.Similarly,letpbgdenotetheconditionalprobabilitythatthenextstateisthegoodstategiventhatthecurrentstateisthebadstate.TheGilbert-Elliotmodelcanbecompletelycharacterizedbyspecifyingtheprobabilitiesoftransitioningtotheoppositestate.(Thetworemainingstatetransitionprobabilitiesaregivenbypbb=1)]TJ /F3 11.955 Tf 12.55 0 Td[(pbgandpgg=1)]TJ /F3 11.955 Tf 12.55 0 Td[(pgb).Theexpectednumberofslotsforwhichaparticularlinkstaysinagivenstateisknownasthestatesojourntime,whichinturndependsonthetransitionprobabilitiesgiventhatthechannelisinthat 19

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particularstate.ThestatesojourntimesforthegoodandbadstateareTg=1=pgbandTb=1=pbg,respectively. 2.2ProblemFormulationWeconsidertheproblemofhowtoplaceKcachesamongtheNnodesinthenetworktominimizethelatencyfortheNnodestoaccessthecacheddata.LetCVbethesubsetofnodesatwhichdatawillbecached.Weconsidercacheplacementundertheassumptionthateachnodewillaccessasinglecacheforwhichithasthesmallestcosttoaccess.Inawirelessnetwork,evenifthelinksarereliable,thetimetofulllcacherequestsmaybeextremelydifculttocharacterizebecauseofcontentionissuesandqueuingdelays.Thus,weconsiderinsteadminimizingacostfunctionthatencodesfeaturesthatimpactlatency.Forexample,ifthelinksarereliable,stable,andmulti-pathroutingisnotused,thecostmaybethenumberofedgesthatmustbetraversedorthesumofacostfunctioncomputedfromtheweightsontheedges(suchasw)]TJ /F10 7.97 Tf 6.59 0 Td[(1ij).However,innetworkswithtime-varyinglinkquality,suchmeasuresmayresultinpoorperformancebecausetheydependonasingleroutefromthenodestothecaches,andtheseroutesmaybreakbecauseofchangesinlinkquality.Thus,itisdesirabletouseadistancemeasurethatincorporatespathlength,linksweights,andinformationaboutmultipleroutesbetweenthenodes.Onesuchmeasureisexpectedcommutetime. 2.2.1ExpectedCommuteTimeExpectedcommutetimeisdenedintermsofarandomwalkonthegraphG.Everyvertexinthegraphisassociatedwithastateinadiscrete-timehomogeneousMarkovchain.Lets(t)bethestateoftheMarkovChainattimet.Thenweletthetransitionprobabilitiesbetweenstatesbeproportionaltotheweightsoftheedgesemergingfromthestates.Thus,thesingle-steptransitionprobabilityfromstateitostatejisgivenbyP[s(t+1)=jjs(t)=i]=aij=di=pij.Sincethegraphisconnectedandtheedgesarenotdirected,theMarkovchainisirreducible. 20

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Considerthetimetorstreachsomestatekfromstatei,Tik.Formally,Tij=minft0js(t)=jands(0)=ig.Theexpected(oraverage)rst-passagetimefromstateitostatejism(jji)=E[Tij].Detailsofthecalculationofm(jji)aregivenin[ 25 ].Notethatm(jji)isnotnecessarilyequaltom(ijj),sincetheydepend,respectively,ontheprobabilitiesofleavingstateiandleavingstatej,whichareingeneraldifferent.Thus,m(jji)isnotadistancemeasure.However,considertheexpectedcommutetime,n(i,j)=m(jji)+m(ijj), (2)whichistheexpectedtimeforarandomwalkertorstreachstatejandthentorstreturntostatei.Thenn(i,j)isavaliddistancemeasure[ 25 ].Theexpectedcommutetimen(i,j)hastheusefulpropertythatitdecreaseswhenanyofthepathsbetweeniandjareshortenedorifadditionalpathsareaddedbetweeniandj.ThiscanbeshowntrueviaanisomorphismwithelectricalresistivenetworksandapplicationofRayleigh'sMonotonicityLaw[ 25 26 ].Thesepropertiesmaketheexpectedcommutetimeagoodcandidateforadistancemeasuretouseinselectingcachelocationsinacommunicationsnetworkbecausetheyencodenotonlythedistancebetweenthenodesandthecachesbutalsotherobustnessofthecachetolinkfailuresbecauselowerexpectedcommutetimebetweennodesisalsoassociatedwithmultiplepathsconnectingthenodes. 2.2.2UsingSpectralEmbeddingtoExpressCommuteTimeasEuclideanDis-tanceExpectedcommutetimehasanotherpropertythatmakesitagoodcandidateasadistancemeasure.ItcanbecomputedusingEuclideandistancebyanappropriateembeddingoftheverticesofthegraphintoahigh-dimensionalEuclideanspace.Thedetailsofthisapproacharegivenin[ 25 ]andsummarizedhereforclarity.LetLydenotetheMoore-PenroseinverseofL.NotefurtherthatLyisthediscreteGreen'sfunctionforL(withnoboundaryconditions)[ 27 ].LycanbewrittenintermsoftheLaplacianmatrix 21

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L,asLy=L)]TJ /F8 11.955 Tf 13.15 8.09 Td[(eeT n)]TJ /F10 7.97 Tf 6.59 0 Td[(1+eeT n, (2)wherenisthenumberofverticesofGande=[1,1,...,1]T.LetVGbethevolumeofthegraph,VG=nXi=1di. (2)Thentheexpectedcommutetimebetweennodesiandjisn(i,j)=VG(ei)]TJ /F8 11.955 Tf 11.96 0 Td[(ej)TLy(ei)]TJ /F8 11.955 Tf 11.95 0 Td[(ej), (2)whereeiistheunitvectoroflengthnwithzerosinallpositionsexceptfortheithposition,whichisone.InsteadofcomputingthecommutetimeusingLyand( 2 ),weinsteadproposetoembedtheverticesofGaspointsinaEuclideanspacewherethecommutetimecanbecomputedusingEuclideandistance.SinceLyisareal-symmetricmatrix,ishasaspectralfactorizationoftheformLy=UpUT.HerepisadiagonalmatrixwiththeeigenvaluesofLyonthediagonal,andUisamatrixwhosecolumnsaretheeigenvectorsofLy.Then( 2 )canberewrittenasn(i,j)=VG(xi)]TJ /F8 11.955 Tf 11.95 0 Td[(xj)T(xi)]TJ /F8 11.955 Tf 11.95 0 Td[(xj)=VGkxi)]TJ /F8 11.955 Tf 11.96 0 Td[(xjk2, (2)wherexi=p1=2UTei.Thus,thecoordinatesofalloftheembeddedverticesisgivenbythecolumnsofthematrixXgivenbyX=p1=2UT (2)Asnotedin[ 25 ],itisnotnecessarytocomputeLytocomputethespectralembeddinggivenby( 2 ).LetfyigbetheeigenvaluesofLy,andfigbetheeigenvalues 22

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ofL.ThenLandLyhavethesameeigenvectors,andyi=1=i(exceptfortheeigenvalue0,whichissharedbybothmatrices).Thus,theprojectionin( 2 )canbecarriedoutdirectlyfromtheeigenvaluesandeigenvectorsofL. 2.2.3OptimalityCriterionWewishtochooseasubsetCVsuchthattheexpectedcommutetimefromthenodesVtothecachesCisinminimizedaccordingtosomecostcriterion.Aspreviouslymentioned,weassumethateachnodeisassignedtoaccessonecache.Thus,thenetworkispartitionedbasedonwhichcachesthenodesareassignedto.LetC(Vi)bethecachetowhichvertexiisassigned,andletV(Cj)denotethesetofverticesassignedtocacheCj.Below,weassumethatspecifyingfC(Vi)gforallVi2VimplicitlyspeciesC.Wecalltheoptimizationcriterionforselectionofwhichnodeswillactascachesandforassignmentofnodestocachestheminimumaveragecommutetime(MACT):MACT=argminfC(Vig1 jVjXC2CXV2V(C)n(V,C) (2)Notethattheterm1=jVjisaconstantthatcanbeomittedinthecomputations.Theallocationofcachescanbesolvedefcientlyviaclustering,asdetailedinthenextchapter. 23

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CHAPTER3CLUSTERINGALGORITHM 3.1SelectionofAlgorithmAsmentionedin[ 28 ]clusteringalgorithmscanbebroadlydividedintotwoclasses:basedonhierarchicalmethodsandbasedonpartitioningmethods.Hierarchicalalgorithmsagaincanbeoftwomaintypes:agglomerativeanddivisive.Inagglomerativealgorithms,everyobjectformsaseparatecluster,andinconsecutivestepsclustersaremerged,untilthedesirednumberofclustersisachieved.Incontrast,divisiveclusteringstartsbyassigningallobjectstoasinglecluster,andsplittingoneclusterineachsubsequentstep.Thesplittingstopsafterdesirednumberofclustershavebeenachieved.Inthisworkwechoosetoworkwithpartitioningalgorithmsbecauseofaninherentdisadvantageofhierarchicalmethodstheirinabilitytoundoamergingorsplittingoftwoclusters,eveniftheirregroupingresultsinasmalleraveragedissimilarityinthenewcluster.Thispropertytypicallyresultsininferiorclusteringperformance.Ontheotherhand,apartitioningalgorithmtriestondoutthebestclusteringbyputtingthemostsimilarobjectstogetherinacluster.TherearevarioustypesofpartitioningalgorithmslikeK-means,K-medians,K-medoids,andfuzzyanalysis.WechosetoworkwithK-medoidalgorithmsbecauseunlikeK-meansproblems,K-medoidsclusteringproblemschooseasetofKobjectsfromthegivensetofobjectstobetherepresentativeoftheclustersandassociateseachoftherestoftheobjectstooneofthechosenKrepresentatives.InadditionK-medoidalgorithmsareknowntohandlelargedatasetsmoreefcientlyandneedsnomodicationfortranslationororthogonaltransformationofdatapoints.PartitioningAroundMedoids(PAM)isoneofthebestknownK-medoidalgorithms.AlthoughPAMhasaveryhighcomputationalcomplexity,weselectedPAMforourpurposeasitprovidesuswithveryhighqualityclusteringresultsandneedslittlemodicationfor 24

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handlingEuclideancriteria,andinthisthesisouraimistoachievethebestpossibleclusteringquality.Alternatively,theCLARANSalgorithmcanbeused,withlowercomplexity.CLARANSistheacronymforAClusteringAlgorithmbasedonRandomizedSearch).Thegeneralproblemofclusteringcanbeviewedastheproblemofsearchingagraphwhereeverynoderepresentsasolutioni.e.asetofkmedoids.Twonodesarecalledneighborsiftheirsetdiffersbyonlyoneobject.Thereforeeachnodehasn(n-k)numberofneighbors,wherekisthenumberofclusters.Thuseachnodecanbeassignedcostdenedasthetotaldissimilaritybetweeneveryobjectandmedoidsofitsclusters.ThusPAMisthesearchforaminimumonthisgraph,andateachstepalltheneighborsofthecurrentnodeischecked,andthecurrentnodereplacedwiththeneighborthathastheminimumnegativecost.WhereasPAMchecksallthenodes,CLARANSdrawsasampleofneighborsdynamically.ThisisthekeydifferencebetweenPAMandCLARANS.CLARANSismoreefcientandscalablethanPAMis. 3.2PartitioningAroundMedoids(PAM)AlgorithmPAMwasdevelopedbyKaufmanandRousseeuwandisdocumentedin[ 29 ,Ch.2].TheobjectiveofPAMistominimizetheaveragedissimilaritybetweenanobjectanditsmedoid.ThealgorithmstartsinaBUILDphaseinwhichmedoidsareselected,andthenexecutesaSWAPphaseinwhichalternatenodesareevaluatedasmedoids. 1. BUILDphase:InthisphasePAMselectsKobjectsrandomlyfromthegivensetofNobjectsandcallsthemthemedoidpoints.Nexteachof(N)]TJ /F3 11.955 Tf 12.34 0 Td[(K)objectsareassignedtooneoftheclustersrepresentedbythosekmedoidsonbasisoftheobjectssimilaritytothosemedoidobjects.IfapointPihasminimumdissimilaritywithamedoidpointPm,comparedtoallothermedoids,thenPiisassignedtotheclusterbelongingtoPm.ThustheinitialclustersareformedintheBUILDstage. 2. SWAPphase:HerewerstcomputetheoverallreductioninaveragedissimilaritybyreplacingeachmedoidOmbyeachofthenon-medoidobjectsOm0inthecluster.Thereplacementthatprovidesthemaximumreductioninoverallaveragedissimilarityisthenimplementedbyactuallymakingthereplacement.Inthisprocesswealsoconsiderthetransferofanon-medoidobjectOifromoneexistingclustertotheclusterbelongingtothesecondnearestmedoidOm2dependingon 25

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changesthatareinictedbyreplacingamedoidwithanon-medoidpoint.Therecanbefoursuchsituations: (a) OiisinitiallyassignedtotheclusterbelongingtothemedoidpointOm.NowifOmisreplacedbyOm0whichismoredissimilartoOiascomparedtothenearestmedoidpointOm2,thenthepointOiwouldmovetotheclusterrepresentedbyOm2.Thisimpliesthisreplacementincreasesaveragedissimilarity,i.e.thecostofsuchreplacementispositiveandcanbegivenbyCosti=dissimilarity(Oi,Om2))]TJ /F3 11.955 Tf 11.95 0 Td[(dissimilarity(Oi,Om). (b) OiisapartoftheclusterrepresentedbyOmandOm2ismoredissimilartoOithanthenon-medoidOm0,soOistaysinthesameclusterwhichisnowrepresentedbyOm0.Thecostassociatedmightbenegativeorpositiveandisgivenbycosti=dissimilarity(Oi,Om0)dissimilarity(Oi,Om). (c) OiisapartofaclusterrepresentedbyOm2andnotOm.NowOmisreplacedbyOm0,whileOiismoresimilartoitscurrentmedoidOm2thantoOm0.SoOistaysinthesamecluster,andthecostassociatedisthiscosti=0. (d) OiisapartofaclusterrepresentedbyOm2andnotOm.ThistimeOiislesssimilartoitscurrentmedoidOm2thanOm0,sowhenOmisreplacedbyOm0,OimovesfromtheclusterrepresentedbyOm2totheclusterrepresentedbyOm0.Costassociatedisnegativeandisgivenascosti=dissimilarity(Oi,Om0))]TJ /F3 11.955 Tf 11.96 0 Td[(dissimilarity(Oi,Om2).Thetotalcost(CT)ofreplacinganexistingmedoidOmbyanon-medoidOm0iscomputedbysummingthecostscalculatedaboveoverallthenon-medoids,i.e.CT(Om,Om0)=Picosti.Thepairof(Om,Om0).thatprovidesanegativeminimumtotalcostisselected. 3.3PAMforCacheSelectionInthisworkweusePAMtoselectasubsetofthecommunicatorstoserveascaches.WeusePAMtopartitionthenodesintoKclustersforwhichthemedoidswillbeassignedthecaches.PAMisappliedtondthecacheassignmentsfortwodifferentapproaches.Intherst,thedissimilaritybetweentwoverticesismeasuredbytheEuclideandistancebetweentheverticesofagraphinaR2subspace.Inthesecond,thedissimilaritybetweentwoverticesisgivenbytheexpectedcommutetimebetweenthosevertices.TherstapproachisthemosttraditionalformofPAM.ThesecondapproachcanalsobedirectlyimplementedusingthePAMalgorithmusing( 2 ),whichshowsthat 26

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Figure3-1. Minimumaveragecommutetimeovermultipleruns. expectedcommutetimecanbecomputedusingEuclideandistancebyusingaspectralembeddingoftheverticesofthegraphintoahigh-dimensionalspace.Wenotethatadirectspectralembeddingdoesrequirethatthegraphtopologybefullyconnected,andweonlyconsiderthisscenariointhiswork. 3.4PAMParametersandPerformanceSincePAMdependsonarandomizedsearch,resultsmayvaryeachtimethealgorithmisrun.Therefore,inordertondthebestresult,theclusteringalgorithmisrunforseveraltimesforeachtopology,andtheclusteringcorrespondingtotheminimumaveragecostischosen. Figure3-1 isaplotthatshowshowtheaveragecostobtainedforacommute-timebasedPAMina100-nodetopologywith5clustersvarywithmultipleruns. 27

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Figure3-2. AveragecommutetimebetweenverticesandmedoidsasafunctionofnumberofiterationsinthePAMclusteringalgorithm. Theresultsin Figure3-2 showtheaveragecommutetimebetweenthenon-medoidnodesandthemedoids(wherethecacheswillbeplaced)asafunctionofthenumberofiterationsinthePAMalgorithm.Asexpected,theplotismonotonicallydecreasing,howevertheperformancesaturatesafter6iterations. 3.5MotivatingExampleWeuseanexampleofasmall,simplenetworktodemonstratethedifferencebetweentheresultsobtainedbythedistance-basedclusteringandcommute-timebasedclusteringalgorithms.Atotalof18nodesarepartitionedinto2clusters. Figure3-3 showstheclusterassignmentandcacheassignmentforthedistance-basedclusteringalgorithm,and Figure3-4 showstheclusterassignmentandcacheassignmentforthecommute-timebasedclusteringalgorithm.Solidlinesbetweenverticesindicatethattheverticesshareacommunicationlink.Redandbluenodecolorsdifferentiatethetwoclusters,andthecirclednodesarethemedoidsoftheclusters,wherethecacheswillbeplaced.ConsidertheresultswhenPAMisappliedtothistopologywiththedistance-basedmetric,whichisshownin Figure3-3 .Theresultsmatchwithintuition.Thenetworkis 28

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Figure3-3. Clustersformedbydistance-basedPAMclustering. Figure3-4. Clustersformedbycommute-timebasedPAMclustering. partitioneddownthemiddleintotwoequal-sizedclusters,withthenodenearthemiddleofeachcluster(nodes0and9)assignedasthemedoids.Whenthesametopologyisclusteredusingcommute-timebasedPAMclusteringalgorithm,wegetdifferentresults.Althoughthetwoclustersarethesame,themedoidsoftheclustershavechangedtonodes5andnodes10,asshownin Figure3-4 .Themedoidschosenbythecommute-timebasedPAMcanbereachedbyeverynodeexceptfornodes0and9by 29

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twopaths,thusresultinginalowercommutetimeforthosenodes.Ifoneofthelinksontheringfails,thenwiththecommute-timebasedmedoidassignment,thenodeswillbeabletoreroutethecachingtrafcaroundthefailedlink,whereasthedistance-basedmedoidassignmenthasacriticaldependenceforallnodesonthelinksbetweenvertices0and9.Wenotethatexpectedcommutetimealsohastheadvantageofprovidingabettermedoidlocationbasedonnetworklinksevenintheabsenceoflinkfailures.Tomakearoughestimateofthenetworkperformanceunderthetwotypesofclustering,wecomputetheaveragehopcountbetweeneachcommunicator(vertex)anditscorrespondingcache(medoid).Sinceinbothcasethetwoclustersformedaresymmetric,theaveragehopcountisequaltothehopcountofanyoneoftheclusters.Lethcdistandhccomdenotethehopcountsunderdistance-basedclusteringandcommute-timebasedclustering,respectively.Then,itiseasytoseethathcdist=1=9(hc(9,10)+hc(9,11)+hc(9,17)+hc(9,12)+hc(9,16)+hc(9,13)+hc(9,15)+hc(9,14))=1/9(1+22+23+24+5)=2.67;hccom=1=9(hc(0,1)+hc(0,2)+hc(0,8)+hc(0,3)+hc(0,7)+hc(0,4)+hc(0,6)+hc(0,5))=1/9(4+23+22+21+1)=1.88;Soweseeaperformanceimprovementofapproximately30percentfromtheuseofcommute-timebasedclustering.Inthefollowingchapter,weuseanetworksimulationtoseeifthisimprovementandthepotentialrobustnesstolinkfailurestranslatesintoimprovementsincacheaccesslatencies. 30

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CHAPTER4NETWORKSIMULATION 4.1SimulationInthischapter,wereportonresultsofusingnetworksimulationtoevaluatetheperformanceoftheproposedclusteringalgorithmsinrandomconnectednetworkswithtime-varyinglinks.Weevaluatetheperformanceofthedistance-basedandcommute-timebasedcacheplacementalgorithmsbycomputingthetotaltimerequiredtocompleteaseriesofcacherequests,fromwhichwecomputetheaveragecacheaccesslatency.Thenetworksimulationusesaslottedprotocol.Eachtopologyissimulatedovermanyslots,andtheaccesslatenciesareaveragedovermanyrandomlygeneratedconnectedtopologies.Thesimulationmodelisaslottedsystem,andthefollowingactivitiestakeplaceineachoftheslots: 1. Allthenon-medoidnodesinthenetwork,generateacacherequestwithacertaincacherequestprobability(pcache).Anodethathasalreadygeneratedacacherequestbutdidnotcompletethedataaccessyetisnotallowedtogenerateanothercacherequest. 2. Nodesthathavegeneratedacacherequest,pushtherequestpackettotheirrespectivesendqueue.Eachnodeinthenetworkisassignedaninnitequeue,wherethepacketstotransmittedarestoredinFIFObasis. 3. Toemulatethefactthattheupdatefrequencyofroutingtablesistypicallymuchsmallerthanthepackettransmissiontime,theroutingtablesareupdatedbycalculatingtheminimum-hoppathbetweeneachpairofnodesduringeveryrthtransmissioninterval.Wecall1=rtheroutingupdatefrequency. 4. Eachnodewithanon-emptysendqueuewilltrytosendtherstpacketintheirsendqueuetothenext-hopforthatpacketwithtransmissionprobabilitypT. 5. Ifanodetransmitsinaninterval,thenitusesitsroutingtabletondapathbetweenitselfandthedestinationnode. 6. Ifthelinkbetweenthecurrentnodeandthenextnodeinthepathisup,thepacketissenttothenextnode,otherwisethepacketstaysinthesendqueueofthecurrentnode. 31

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7. Afteradatapacketreachestheintendednode,thedataaccessisassumedtobecompleted,andthecurrenttimestampisstoredasreceivetimefortheparticularnode. 8. Thedifferencebetweenthetransmittimeandreceivetimegivesthethedataaccesstimeforthenode. 9. Atthenendofeachslot,thelinkstateisupdatedaccordingtothestatetransitionprobabilitiesofthechannel. Table4-1. Simulationparameters ParameterValue pcache0.05ptrans0.6pbg0.8,0.6,0.2pgb0.05to0.5Numberofnodes100Numberofclusters5Routingfrequency0.01,0.02,0.05 Simulationswererunfordifferentvaluesofthestatetransitionprobabilities.Foreachsetofvalues,50randomlygeneratedtopologiesweresimulated.Foreachtopology,thesimulationwasrunfor10,000slots.Thedataaccesstimeswereaveragedforaparticulartopologywereaveragedtoproducetheaveragelatencyforthattopology,andtheoverallaveragelatencywasdeterminedbyaveragingtheseoverthe50differenttopologies.Theparametersofthesimulationarecollectedin 4-1 Differenttopologiesweregeneratedbyrandomlyvaryingtheconnectivitydistance,eldsizeandcoordinatesoftheverticesornodesinthenetworkononthey.Sinceweneedaconnectedgraph,aftergeneratingeachrandomtopology,acheckisperformedtomakesuretheproducedtopologyisaconnectedgraph.Ifnotwetrytoconvertitintoaconnectedgraphbyvaryingtheconnectivitydistance.Connectivitydistanceisthemaximumdistancebywhichtwonodesthatshareanedge,canbeapartby.Theparametereldsizedeterminesthemaximumrangeofthexandy-coordinatesinthetopology. 32

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4.2ResultsAsthepgbdecreases,andthereforechannelsremaindownforalongerperiodoftime.Wesimulateoursystemi.e.computetheaverageaccesslatencyforaxedvalueofpbgandplotitasafunctionofpgb.Asexplainedbythefollowinggures,foraxedpbg,asthepgbgoesuptheaccesslatencyincreasesandcommutetimebasedclusteringgivesaloweraccesslatencyascomparedtotheclusteringbasedondistance-basedclustering.Wealsoseethatforlowervalueofpbgalsoaccesslatencyincreases,althoughthecommutetimebasedclusteringprovidesuswithabetterperformance.Wealsovarytheroutingfrequencyasaparameter,andassuggestedbytheresults,astheroutingfrequencyincreasestheoverallaccesslatencydecreasesmaintainingasuperiorperformancebythecommutetimebasedclustering. Figure4-1. Averageaccesslatencyvspgbforpbg=0.8androutingfrequency=0.01. Theresultsin Figure4-1 showtheaverageaccesslatencyasafunctionoftheprobabilityoftransitioningfromthegoodstatetothebadstate,pbgforthetwodifferent 33

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clusteringalgorithmswithpgb=0.8,androutingfrequency=0.01.Theresultsshowthatthecommute-timebasedcacheplacementalgorithmprovidessignicantlybetterperformancethancacheplacementbasedonEuclideandistance.Forexampleatpbg=0.3,theaccesslatencyforcommute-timebasedcacheplacementis20,whereastheaccesslatencyfordistance-basedcacheplacementis130.Forthevaluesconsideredinthisgraph,commute-timecacheplacementproducesareductioninaverageaccesslatencyofatleast85%. Figure4-2. Averageaccesslatencyvspgbforpbg=0.6androutingfrequency=0.01. Theresultsin Figure4-2 showtheaverageaccesslatencyasafunctionoftheprobabilityoftransitioningfromthegoodstatetothebadstate,pbgforthetwodifferentclusteringalgorithmswithpgb=0.6,androutingfrequency=0.01.Theresultsshowthatthecommute-timebasedcacheplacementalgorithmprovidesignicantlybetterperformancethancacheplacementbasedonEuclideandistance.Forexampleatpbg=0.3,theaccesslatencyforcommute-timebasedcacheplacementis100, 34

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whereastheaccesslatencyfordistance-basedcacheplacementis550.Forthevaluesconsideredinthisgraph,commute-timecacheplacementproducesareductioninaverageaccesslatencyofatleast80%.Ifwecomparethisresultwiththatof Figure4-1 ,wewouldseethatduetoanincreaseinthesojourntimeinthebadstate,i.e.duetoanincreaseinpgb,theperformanceofboththealgorithmshavedegradedascomparedtothatin Figure4-1 ,althoughthecommute-timebasedalgorithminthiscasealsoperformsbetterthanthedistancebasedalgorithm. Figure4-3. Averageaccesslatencyvspgbforpbg=0.2androutingfrequency=0.01. Theresultsin Figure4-3 showtheaverageaccesslatencyasafunctionoftheprobabilityoftransitioningfromthegoodstatetothebadstate,pbgforthetwodifferentclusteringalgorithmswithpgb=0.2,androutingfrequency=0.01.Theresultsshowthatthecommute-timebasedcacheplacementalgorithmprovidesignicantlybetterperformancethancacheplacementbasedonEuclideandistance.Forexampleatpbg=0.3,theaccesslatencyforcommute-timebasedcacheplacementis200, 35

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whereastheaccesslatencyfordistance-basedcacheplacementis800.Forthevaluesconsideredinthisgraph,commute-timecacheplacementproducesareductioninaverageaccesslatencyofatleast75%.Ifwecomparethisresultwiththatof Figure4-1 and Figure4-2 ,wewouldseethatduetoanincreaseinthesojourntimeinthebadstate,i.e.duetoanincreaseinpgb,theperformanceofboththealgorithmshavedegradedascomparedtothatin Figure4-1 and Figure4-2 ,althoughthecommute-timebasedalgorithminthiscasealsoperformsbetterthanthedistancebasedalgorithm. Figure4-4. Averageaccesslatencyvspgbforpbg=0.8androutingfrequency=0.02. Theresultsin Figure4-4 showtheaverageaccesslatencyasafunctionoftheprobabilityoftransitioningfromthegoodstatetothebadstate,pbgforthetwodifferentclusteringalgorithmswithpgb=0.8,androutingfrequency=0.02.Theresultsshowthatthecommute-timebasedcacheplacementalgorithmprovidesignicantlybetterperformancethancacheplacementbasedonEuclideandistance.Forexampleatpbg=0.3,theaccesslatencyforcommute-timebasedcacheplacementis100, 36

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whereastheaccesslatencyfordistance-basedcacheplacementis225.Forthevaluesconsideredinthisgraph,commute-timecacheplacementproducesareductioninaverageaccesslatencyofatleast55%.Ifwecomparethisresultwiththatof Figure4-1 ,wecanseethatanincreaseinroutingfrequencyhasimprovedtheperformanceofthenetworkforboththealgorithm.Theperformancegapbetweenthetwoalgorithmhasreducedwiththeincreaseintheroutingfrequency,althoughthecommute-timebasedalgorithmcontinuestomaintainabetterperformanceattheincreasedroutingfrequencyaswell. Figure4-5. Averageaccesslatencyvspgbforpbg=0.8androutingfrequency=0.05. Theresultsin Figure4-5 showtheaverageaccesslatencyasafunctionoftheprobabilityoftransitioningfromthegoodstatetothebadstate,pbgforthetwodifferentclusteringalgorithmswithpgb=0.8,androutingfrequency=0.05.Theresultsshowthatthecommute-timebasedcacheplacementalgorithmprovidesignicantlybetterperformancethancacheplacementbasedonEuclideandistance.Forexampleatpbg= 37

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0.3,theaccesslatencyforcommute-timebasedcacheplacementis25,whereastheaccesslatencyfordistance-basedcacheplacementis160.Forthevaluesconsideredinthisgraph,commute-timecacheplacementproducesareductioninaverageaccesslatencyofatleast84%.Ifwecomparethisresultwiththatof Figure4-1 ,wecanseethatanincreaseinroutingfrequencyhasimprovedtheperformanceofthenetworkforboththealgorithm.Theperformancegapbetweenthetwoalgorithmhasreducedwiththeincreaseintheroutingfrequency,althoughthecommute-timebasedalgorithmcontinuestomaintainabetterperformanceattheincreasedroutingfrequencyaswell.Bycomparingtheresultof Figure4-4 with Figure4-5 ,wecanseethatwithafurtherincreaseinroutingfrequencyfrom0.02to0.05,theperformanceofbothalgorithms,haveimprovedfurtherascomparedtothatin Figure4-4 38

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CHAPTER5CONCLUSIONInthisthesis,weproposeacacheplacementschemetoreducedataaccesslatencyinadhocnetworkswithunreliablelinks.Inparticular,wehavedevelopedaclusteringalgorithmthatpartitionsthenetworkonthebasisofexpectedcommutetime.Sincecommutetimebetweenapairofnodesdecreaseswithdecreaseinthedistancebetweenthetwopointsandwithanincreaseinthenumberofpathsconnectingthem,thecommute-time-basedclusteringalgorithmprovidesuswithcluster-representativesthathasbetterconnectivity,thusminimizingtheprobabilitythatanodecannotreachitsdesignatedcache.Wehavecomparedthenetworkperformanceusingtheproposedalgorithmtotheperformanceofthesamenetworkwithclustersassignedusingalocation-basedalgorithm.Theresultsshowthatthedataaccesslatencyforcommute-timebasedcacheplacementismuchlowertothatofthelocation-basedalgorithm.Potentialfutureextensionstothisworkincludeinvestigatingothertheoptimalitycriteriabasedonexpectedcommutetime.Forexample,possibleothercriteriainclude: 1. Minimummax-sumcommutetime(MMSCT):Heplsbalancenumberofnodesassignedtocaches.MMSCT=argminfC(VigmaxC2CXV2V(C)n(V,C) (5) 2. Min-Maxcommutetime(MMCT):Optiimizeswors-casecommutetime.MMCT=argminfC(VigmaxV2Vn(V,C(V)) (5)ThePAMalgorithmhashighcomplexityandisnoteasilymodiedtohandlenon-Euclideancriteria,suchasMMSCTandMMCT.ThustooptimizeMMSCTandMMCT,onecanutilizerandomizedsearch,similartotheCLARANSalgorithm[ 28 ].Anotherareaforfutureworkistodevelopdecentralizedversionsofthesealgorithms,especiallyforupdatingcachelocationsinmobilenetworks. 39

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BIOGRAPHICALSKETCH PriyankaSinhawasbornin1987,inRampurhat,India.Shereceivedherbachelor'sdegreeinelectricalengineeringwithrst-class-distinctionfromNationalInstituteofTechnology,Durgapur,India,in2010,andhermaster'sdegreeinelectricalandcomputerengineeringfromtheUniversityofFlorida,Gainesville,USA,inMay2013.WhilepursuinghergraduatedegreesattheUniversityofFlorida,sheworkedonhermaster'sThesisunderthesupervisionofherthesiscommitteeChair,JohnM.Shea.Herresearchinterestsarewirelesscommunicationsandnetworks. 43