Comparison of parametric and nonparametric models 参数与非参数模型的比较Word文件下载.docx

Comparison of parametric and nonparametric models 参数与非参数模型的比较Word文件下载.docx

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cDepartmentofSystemsEngineering,OlssonHall,UniversityofVirginia,Charlottesville,VA22903-2442,USA

Received12July1999;

accepted5July2001

Abstract

Singlepointshort-termtrafficflowforecastingwillplayakeyroleinsupportingdemandforecastsneeded

byoperationalnetworkmodels.Seasonalautoregressiveintegratedmovingaverage（ARIMA）,aclassic

parametricmodelingapproachtotimeseries,andnonparametricregressionmodelshavebeenproposedas

wellsuitedforapplicationtosinglepointshort-termtrafficflowforecasting.Pastresearchhasshownsea-

sonalARIMAmodelstodeliverresultsthatarestatisticallysuperiortobasicimplementationsofnon-

parametricregression.However,theadvantagesassociatedwithadata-drivennonparametricforecasting

approachmotivatefurtherinvestigationofrefinednonparametricforecastingmethods.Followingthismo-

tivation,thisresearcheffortseekstoexaminethetheoreticalfoundationofnonparametricregressionandto

answerthequestionofwhethernonparametricregressionbasedonheuristicallyimprovedforecastgener-

ationmethodsapproachthesingleintervaltrafficflowpredictionperformanceofseasonalARIMAmodels.

2002ElsevierScienceLtd.Allrightsreserved.

Keywords:

Trafficforecasting;

Nonparametricregression;

ARIMAmodels;

Motorwayflows;

Short-termtrafficprediction;

Statisticalforecasting

1.Introduction

Asintelligenttransportationsystems（ITS）areimplementedwidelythroughouttheworld,

managersoftransportationsystemshaveaccesstolargeamountsof‘‘real-time’’statusdata.

Whilethisdataiskey,ithasbeenrecognizedbyresearchersandpractitionersalikethatthefull

*Correspondingauthor.Tel.:

+1-434-243-8585;

fax:

+1-434-982-2951.

E-mailaddress:

briansmith@virginia.edu（B.L.Smith）.

0968-090X/02/$-seefrontmatter2002ElsevierScienceLtd.Allrightsreserved.

PII:

S0968-090X（02）00009-8

304B.L.Smithetal./TransportationResearchPartC10（2002）303-321

benefitsofITScannotberealizedwithoutanabilitytoanticipatetrafficconditionsintheshort-

term（lessthanonehourintothefuture）.Thedevelopmentoftrafficconditionforecastingmodels

willprovidethisability,andsupportproactivetransportationmanagementandcomprehensive

travellerinformationservices.Whatdistinguishestrafficconditionforecastingfromthemore

traditionalforecastsoftransportationplanningisthelengthofthepredictionhorizon.While

planningmodelsusesocioeconomicdataandtrendstoforecastoveraperiodofyears,traffic

conditionforecastingmodelspredictconditionswithinthehourusingdatafromroadwaysensors.

Withoutapredictivecapability,ITSwillprovideservicesinareactivemanner.Inotherwords,

therewillbealagbetweenthecollectionofdataandtheimplementationoftrafficcontrolstrat-

egies.Therefore,thesystemwillbecontrolledbasedonoldinformation.Inordertocontrolthesysteminaproactivemanner,ITSmusthaveapredictivecapability.‘‘Theabilitytomakeandcontinuouslyupdatepredictionsoftrafficflowsandlinktimesforseveralminutesintothefutureusingreal-timedataisamajorrequirementforprovidingdynamictrafficcontrol’’（Cheslowetal.,1992）.Furthermore,trafficconditionforecastingisimportantintravellerinformationsystems.Thisis

illustratedinthestatement,‘‘therationalebehindusingpredictiveinformation（forrouteguidance）

isthattraveller’sdecisionsareaffectedbyfuturetrafficconditionsexpectedtobeineffectwhentheyreachdownstreamsectionsofthenetwork’’（Kaysietal.,1993）.Infact,currenttravellerinfor-

mationactivitiesarebeinghamperedbythelackofacapabilitytopredictfuturetrafficconditions.

1.1.Transportationconditionforecasting

Predictingfuturetrafficconditionsisageneralconcept.Infact,thereareawidevarietyofneedsforconditionforecastsdependingonparticularapplications.Forexample,forecastsoftrafficflow,speed,traveltime,andqueuelengtharerequiredforspecifictransportationmanagementapplications.Furthermore,itiscertainlytruethatfuturetrafficconditionswillbedependentontransportationmanagementstrategiesemployed,andthattrafficflowcanbetracked,givenasufficientnumberandplacementofsensors,asitprogressesthroughanetwork.Forthesereasons,anidealapproachtotrafficconditionforecastingisanetwork-basedmodelthatsimulatesthesystemasitrespondstotransportationmanagementstrategies.Inotherwords,amodelthattakesadvantageofspatialinformationandtrafficflowdynamics.

However,everynetworkmusthaveboundarypoints,locationsthatserveasentry‘‘nodes’’to

thenetworkthatdonothavetheadvantageofupstreamdetectorstouseinpredictingtheirstate.

Infact,anydynamictrafficnetworkmodels,suchascommonlyusedsimulationmodels（for

example,CORSIM）,are‘‘driven’’bythetrafficflowrate（usuallyinvehiclesperhour）atthese

boundarypoints.Inessence,theboundarypointsdefinetheshort-termdemandfortravelthrough

thenetwork.Forthisreason,animportantsubsetoftrafficconditionforecastingistheabilityto

predictfuturetrafficflowatalocation（aboundarypoint）,givenonlydatadescribingpast

conditionsatthispoint.Theresearchdescribedinthispaperaddressesthisspecificchallengeof

singlepointtrafficflowprediction.

Basedonthisdefinitionoftheproblem,onewillnotethatsinglepointtrafficflowpredictioncan

bedescribedasatimeseriesproblem.Givenaseriesofpastflowreadingsmeasuredinregular

intervals,amodelisdesiredtopredicttheflowatthenextinterval.Thus,weconsiderthedemand

fortravel（measuredbyflow）atapointtobeadynamicsystem,whichbydefinitionconsistsoftwo

parts:

astate,ortheessentialinformationdescribingthesystem,andadynamic,whichistherule

B.L.Smithetal./TransportationResearchPartC10（2002）303-321305

thatgovernshowthestatechangesovertime（MulhernandCaprara,1994）.Adynamicsystem

evolvestowardsanattractor,whichisthesetofvaluestowhichthesystemeventuallysettles

（Thearling,1995）.Dynamicsystemsareoftencomplexduetochaoticattractors,whichhavea

boundedpaththatisfullydetermined,yetneverrecurs（MulhernandCaprara,1994）.Thepresence

ofchaoticattractorstendstocloudthedistinctionbetweendeterministicandstochasticbehavior,

andmakestheselectionofanidealmodelingapproachdifficult.Aconsiderableamountofresearch

hasaddresseddynamicsystemmodelinginareassuchasfluidturbulence（Takens,1981）,disease

cases（SugiharaandMay,1990）,andmarketing（MulhernandCaprara,1994）.Inaddition,this

areahasseenalargelevelofinterestinthetransportationresearchcommunityoflate.

Whenevaluatingdynamicsystemsmodelsfortrafficflowforecasting,itiscertainlyimportanttoconsidertheaccuracyofthemodel.However,itisequallyimportanttoconsidertheenvironmentinwhichthemodelwillbedeveloped,used,andmaintained.Intelligenttransportationsystemsdeployedinmetropolitanregionsincludethousandsoftrafficdetectors.Forexample,intheHamptonRoadsregionofVirginia,amoderate-sizedmetropolitanarea,thestatedepartmentoftransportationisintheprocessofinstallingover1200sensorstationsonthefreewaysalone.Inaddition,thedepartment,likemostothers,facesseverepersonnelshortages.Asaresult,modelsthatrequiresignificantexpertiseandtimetocalibrateandmaintain,onasite-by-sitebasis,aresimplyinfeasibleforuseinthisenvironment.Therefore,onemustexplicitlyconsidertherequirementsfordynamicsystemmodelcalibrationandmaintenance.

1.2.Modelingapproaches

Predictingtrafficflowatapointdecomposesintoatime-seriesmodelingprobleminwhichoneattemptstopredictthevalueofavariablebasedonaseriesofpastsamplesofthevariableatregularintervals.Timeseriesmodelshavebeenstudiedinmanydisciplines,includingtransportation.Inparticular,transportationresearchershavedevelopedtimeseriestrafficpredictionmodelsusingtechniquessuchasautoregressiveintegratedmovingaverage（ARIMA）,nonparametricregression,neuralnetworks,andheuristics.AcompletereviewoftransportationapplicationsinthisareacanbefoundinSmith（1995）andWilliams（1999）.

RecentresearchbyWilliams（1999）hasappliedtraditionalparametricBox-Jenkinstimeseries

modelstothedynamicsystemofsinglepointtrafficflowforecasting.Thisworkhasaddressed

mostoftheparametricmodelconcernsfortrafficconditiondatabyestablishingatheoretical

foundationforusingseasonalARIMAforecastmodels（seeSection3.3）.ARIMAforecasting

isfoundedinstochasticsystemtheory.ARIMAprocessesarenondeterministicwithlinearstate

transitionsandcanbeperiodicwiththeperiodicityaccountedforthroughseasonaldifferencing.

Thereare,however,somesignificantconcernswiththeabilitytofitandmaintainseasonalARIMAmodelsona‘‘production’’basisinITSsystems,giventhelevelofexpertiseandamountoftimerequiredtodoso.Forexample,theresearchersrec