University of Florida Digital Collections Home
UFDC Home myUFDC Home  |   Help 
<%BANNER%>

A Spectral Method for Network Cache Placement Based on Commute Time

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

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


This item has the following downloads:


Full Text

PAGE 1

ASPECTRALMETHODFORNETWORKCACHEPLACEMENTBASEDONCOMMUTETIMEByPRIYANKASINHAATHESISPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFMASTEROFSCIENCEUNIVERSITYOFFLORIDA2013

PAGE 2

c2013PriyankaSinha 2

PAGE 3

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

PAGE 4

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

PAGE 5

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

PAGE 6

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

PAGE 7

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

PAGE 8

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

PAGE 9

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

PAGE 10

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

PAGE 11

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

PAGE 12

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

PAGE 13

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

PAGE 14

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

PAGE 15

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

PAGE 16

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

PAGE 17

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

PAGE 18

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

PAGE 19

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

PAGE 20

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

PAGE 21

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

PAGE 22

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

PAGE 23

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

PAGE 24

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

PAGE 25

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

PAGE 26

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

PAGE 27

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

PAGE 28

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

PAGE 29

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

PAGE 30

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

PAGE 31

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

PAGE 32

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

PAGE 33

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

PAGE 34

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

PAGE 35

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

PAGE 36

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

PAGE 37

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

PAGE 38

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

PAGE 39

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

PAGE 40

REFERENCES [1] G.Houtzager,C.Jacob,andC.Williamson.Anevolutionaryapproachtooptimalwebproxycacheplacement.2006IEEECongressonEvolutionaryComputation,pages1522,2006. [2] X.Fan,J.Cao,andW.Wu.Contention-awaredatacachinginwirelessmultihopadhocnetworks.MobileAdhocandSensorSystems,2009.MASS'09.IEEE6thInternationalConferenceon12-15Oct.2009,pages1,2009. [3] L.YinandG.Cao.Supportingcooperativecachinginadhocnetworks.IEEETrans.MobileComputing,5:77,2006. [4] B.TangandH.Gupta.Cacheplacementinsensornetworksunderanupdatecostconstraint.JournalofDiscreteAlgorithms5,7:289,2007. [5] P.Nuggehalli,V.Srinivasan,andC.-F.Chiasserini.Energy-efcientcachingstrategiesinadhocwirelessnetworks.MobiHoc'03,pages25,2003. [6] B.Tang,H.Gupta,andS.Das.Benet-baseddatacachinginadhocnetworks.IEEETRANSACTIONSONMOBILECOMPUTING,7:289,2008. [7] P.Nuggehalli,V.Srinivasan,C.-F.Chiasserini,andR.R.Rao.Efcientcacheplacementinmulti-hopwirelessnetworks.IEEE/ACMTRANSACTIONSONNETWORKING,14:1045,2006. [8] Y.XinandF.Dan.Ahybridcacheplacementschemeformulti-hopwirelessservicenetwork.WuhanUniversityandSpringer-VerlagBerlinHeidelberg,15:308,1987. [9] F.Ye,Q.Li,andEChen.Contention-awaredatacachinginwirelessmultihopadhocnetworks.MobileAdhocandSensorSystems,2009.MASS'09.IEEE6thInternationalConferenceon12-15Oct.2009,pages1,2009. [10] A.Tamir.AnO(pn2)algorithmforp-medianandrelatedproblemsontreegraphs.OperationsResearchLetters,19,1996. [11] A.Tamir.AnO(pn2)algorithmforp-medianandrelatedproblemsontreegraphs.OperationsResearchLetters,19,1996. [12] A.Vigneron,L.Gao,M.J.Golin,G.F.Italiano,andB.Li.Analgorithmforndingak-medianinadirectedtree.InformationProcessingLetters,74,1996. [13] P.Krishnan,D.Raz,andY.Shavitt.Thecachelocationproblem.IEEE/ACMTrans.Networking,8,2000. [14] K.Kalpakis,K.Dasgupta,andO.Wolfson.Steiner-optimaldatareplicationintreenetworkswithstoragecosts.Proc.Int'lSymp.DatabaseEng.andApplications(IDEAS'01),2001. 40

PAGE 41

[15] S.Bhattacharya,H.Kim,S.Prabh,andT.Abdelzaher.Energy-conservingdataplacementandasynchronousmulticastinwirelesssensornetworks.Proc.ACMInt'lConf.MobileSystems,Applications,andServices(MobiSys'03),2003. [16] T.Hara.Effectivereplicaallocationinadhocnetworksforimprovingdataaccessibility.Proc.IEEEINFOCOM'01,2001. [17] T.Hara.Cooperativecachingbymobileclientsinpush-basedinformationsystems.Proc.ACMInt'lConf.InformationandKnowledgeManagement(CIKM'02),2002. [18] T.Hara.Replicaallocationinadhocnetworkswithperiodicdataupdate.Proc.Int'lConf.MobileDataManagement(MDM'02),2002. [19] J.Xu,B.Li,andD.L.Lee.Placementproblemsfortransparentdatareplicationproxyservices.IEEEJ.SelectedAreasinComm,20,2002. [20] I.BaevandR.Rajaraman.Approximationalgorithmsfordataplacementinarbitrarynetworks.Proc.ACM-SIAMSymp.DiscreteAlgorithms(SODA'01),2001. [21] C.SrinivasandS.Khan.Datacachingplacementbasedoninformationdensityinwirelessadhocnetwork.InternationalJournalofEngineeringResearchandApplications(IJERA)ISSN:2248-9622www.ijera.com,2:120,2012. [22] F.Ye,Q.Li,andE.Chen.Benetbasedcachedataplacementandupdateformobilepeertopeernetworks.Ubi-mediaComputing(U-Media)20103rdIEEEInternationalConferenceon5-6July2010,pages50,2010. [23] K.S.PrabhandT.F.Abdelzaher.Energy-conservingdatacacheplacementinsensornetworks.ACMTransactionsonSensorNetworks,1:178,2003. [24] S.Pant,N.Chauhan,andP.Kumar.Effectivecachebasedpoliciesinwirelesssensornetworks:Asurvey.InternationalJournalofComputerApplications(0975-8887),pages17,2010. [25] F.Fouss,A.Pirotte,J.-M.Renders,andM.Saerens.Anovelwayofcomputingdissimilaritiesbetweennodesofagraph,withapplicationtocollaborativeltering.InProc.15thEuropeanConf.onMachineLearning(ECML2004),WorkshoponStatisticalApproachesforWebMining(SAWM),pages26,2004. [26] P.G.DoyleandJ.L.Snell.RandomWalksandElectricalNetworks.CarusMathematicalMonographs.MathematicalAssnofAmerica,1984.Updatedversionavailableonlineat http://math.dartmouth.edu/~doyle/docs/walks/walks.pdf asofJuly2012. [27] FanChungandS.-T.Yau.Discretegreen'sfunctions.J.CombinatorialTheory,SeriesA,91(12):191,2000.URL http://www.sciencedirect.com/science/article/pii/S0097316500930942 41

PAGE 42

[28] R.T.NgandJ.Han.Clarans:amethodforclusteringobjectsforspatialdatamining.IEEETrans.Knowl.DataEng.,14(5):1003,Sep./Oct.2002. [29] L.KaufmanandP.J.Rousseeuw.FindingGroupsinData:AnIntroductiontoClusterAnalysis.Wiley,NewYork,1990. 42

PAGE 43

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