分析教案文件

2014IEEE17thInternationalConferenceonInligentTransportationSystems(ITSC)October8-11,2014.Qingdao,

UsingExitTimePredictionstoOptimizeSelfAutomatedParkingLots

RafaelNunes,LuisMoreira-MatiasandMichelFerreira

Privatecarcommutingisheavilydependentonthesubsidisationthatexistsintheformofavailableparking.However,thepublicfundingofsuchparkinghasbeenchanginerthelastyears,withasubstantialincreaseofmeter-chargedparkingareasinmanycities.Tohelptoincreasethesustainabilityofcartransportation,anovelconceptofaself-automatedparkinglothasbeenrecentlyproposed,whichleveragesonacollaborativemobilityofparkedcarstoachievethegoalofparkiniceasmanycarsinthesamearea,ascomparedtoaconventionalparkinglot.Thisconcept,knownasself-automatedparkinglots,canbeimprovedifareasonablepredictionoftheexittimeofeachcarthatenterstheparkinglotisusedtotrytooptimizeitsinitialcement,inordertoreducethemobilitynecessarytoextractblockedcars.Inthispaperweshowthattheexittimepredictioncanbedonewitharelativelysmallerror,andthatthispredictioncanbeusedtoreducethecollaborativemobilityinaself-automatedparkinglot.

Introduction

Parkingisamajorproblemofcartransportation,withimportantimplicationsintrafficcongestionandurbanland-scape.Ithasbeenshownthatparkingrepresents75%ofthevariablecostsofautocommuting[1],supportedbyamajorpublicsubsidisationofthespacedevotedtocarparking,wheretheuserdoesnotpayinmorethan95%oftheoccasions[2].

Thesustainabilityofcartransportationisnowadaysfacingseveralchallenges.Thenumberofcarsinmanycitieshasreachedalevelwheretheroadinfrastructureisunabletoavoidsystematictrafficcongestions.Inaddition,thehighcostoffossilfuelsandpollutantemissionlevelsarecreatingsignificantchallengesforthesustainabilityofprivatecarcommutinginmajorcities.Tollsandprohibitionofcircu-lationinoneortwoweekdaysforagivenvehiclearealreadyinceinsomeofourcities.Technologyistryingtomitigatethesechallengesfacedbycartransportation.Zero-emissionselectricpropulsionandconnectednavigationaretwoexamplesofthatcanhelpmakingcartransportationmoresustainable.

Technologyhasbeenfocusinghoweverinmovingcars,disregardingtheparkedperiodofthesecars,whichrepresents

ManuscriptsubmittedJune22,2014.

ManuscriptreviewedAugust19,2014.

RafaelNunesiswiththeFaculdadedeEngenharia,U.Porto,4200-465Porto-Portugal(:rafael.nunes[at]dcc.fc.up.pt).

LuisMoreira-MatiasiswiththeInstitutode unicac¸o˜es,4200-465Porto,PortugalandwithFaculdadedeEngenharia,U.Porto,4200-465Porto

-Portugal(phone:00351-91- ;:luis.matias[at]fe.up.pt).MichelFerreiraiswiththeInstitutode unicac¸o˜es,U.Porto,4169-

007Porto-Portugal(:michel[at]dcc.fc.up.pt).

ThisworkwassupportedbytheprojectI-CITY-”ICTforFutureMobility”,aspartofGrantNORTE-07-0124-FEDER-000064.

95%ofthevehicleexistence.Recently,asimpleproposalthatleveragesontechnologysuchaselectricpropulsionorwirelessvehicularconnectivityhasaddressedtheissueofcarparking,arguingthatthroughacollaborativeapproachtotheparkingofcars,theareapercarcouldbereducedtonearlyhalf,whencomparedtotheareapercarinaconventionalparkinglot.Thisapproach,knownasself-automatedparkinglots[3],worksasfollows.Anelectricvehicle(EV)isleftattheentranceofaparkinglotbyitsdriver.ThisEVisequippedwithvehicularcommunicationsthatestablishaprotocolwithaParkingLotController(PLC).TheEVisalsobasedonDrive-by-Wire(DbW)technology,wherein-vehicleElectronicControlUnits(ECUs)managesignalssentbytheaccelerationandbrakingpedal,andsteeringwheel.TheVehicle-to-Infrastructure(V2I)communicationprotocolallowsthePLCtocontrolthemobilityoftheEVintheparkinglot.ThePLCremoydrivestheEVtoitsparkingspace,usingin-vehiclepositioningsensors(e.g.rotationperwheel),magnet-basedpositioning,orsomeothertypeofpositioningsystem(e.g.camera-based).Alternativelytoafully-automatedsystem,ascenarioofhuman-basede-operateddrivingcouldalsobeused[4].Inthisconceptofself-automatedparkinglotsthecarsareparkedinaverycompactway,withoutspacedevotedtoaccesswaysoreveninter-vehiclespacethatallowsopeningdoors.Asanewvehicleenterstheparkinglot,thePLCsendswirelessmessagestomovethevehiclesintheparkinglottocreatespaceto modatetheenteringvehicle.Ifablockedcarwantstoleavetheparkinglot,thePLCalsosendsmessagestomovetheothervehicles,inordertocreateanexitpath.In

[3]itwasshownthatthisconceptcouldreducetheareapervehicletonearlyhalf,aswellasreducetheoverallmobilityofcarsintheparkinglot,whencomparedtoaconventionalparkinglot.However,intheoriginalpaper,afirst-fitstrategywasusedtoinitiallyparkeachvehicle.Clearly,theinitialcementcanbeimprovedifsomeknowledgeabouttheexpectedexittimeofeachcarisused.Thebasicideaisthatacarshouldnotbeblockedbyanothercarthatwillleavetheparkinglotlater.Ifthecarsintheparkinglotarecedusinganorderthatreflectstheirexpectedexittimes,thentheoverallmobilityintheparkinglottocreateexitpathscanbereduced.

Inthispaperweuseanentireyearofentriesandexitsinaparkinglot,whereeachvehicleusesauniqueidentifier,tobeabletoderiveitpectedexittime,usingthisinformationtoimprovetheoriginalcementofthecarinordertoreducemanoeuvringmobility.Ourgoalisnottoobtainapreciseexittimeforeachvehicle,butratheratime-intervalthatcanbe

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usedinconjunctionwiththeparkinglotlayout(e.g.numberoflanes)toreducetheprobabilityofhavingtomoveparkedvehiclestocreatedexitpathsforblockedvehicles.

Theremainderofthispaperisorganisedasfollows:inthenextsectionwepresentsomeconsiderationsregardingparkinglotdesign,andfurtherdescribeouroptimisationgoalbasedonatypicallayoutforaself-automatedparkinglot.Wethenpresentourmethodologytopredictanexittimeintervalforeachvehicle,andhowthisintervalisusedtoselecttheoriginallanetoparkeachvehicle.Wethenpresentourdatasetsetusedascasestudyandpresentexperimentalresultsinthenextsection,includingadiscussionoftheseresults.Finally,weendwithsomeconclusions.

ParkingLotDesign

Thegeometricdesignoftheparkinglotisanimportantissueinaself-automatedparkinglot.Inconventionalparkinglotsthereareanumberofconsiderationsthathavetobetakenintoaccountwhendesigningthem.Forinstance,widthofparkingspacesandaccessways,one-wayortwo-wayuseoftheaccessways,entryangleintheparkingbays(90◦,60◦,45◦),pedestrianpaths,visibilitytofindanavailableparkingspace,etc.Inaself-automatedparkinglot,manyoftheseconsiderationsdonotapply.ManoeuvringisdoneautonomouslybythecarfollowingtheinstructionsofthePLC,pedestrianaccessisnotallowed,andtheassignedparkingspaceisdeterminedbythePLC.Themaindesignissueisdefiningageometriclayoutthat isesparkingspace,leveragingonminimalbufferareastomakethenecessarymanoeuvresthatallowtheexitfromanyparkingspaceunderalloccupancyconfigurations.Thisgeometricdesignisultimaydeterminedbytheshapeofthespaceoftheparkinglot.Theparkinglotarchitecturealsodefinesthetrajectoriesandassociatedmanoeuvrestoenndexiteachparkingspace.

TheparkinglothasaV2IcommunicationdevicewhichallowsthecommunicationbetweenthevehiclesandthePLC.Intheory,thisinfrastructureequipmentcouldberecedbyavehicleintheparkinglot,whichcouldassumethefunctionofPLCwhileparkedthere,handinerthisfunctiontoanothercaruponexit,similarlytotheenvisionedfunctioningofaV2VVirtualTrafficLightprotocol[5].Note,however,thattheexistenceoftheactualinfrastructure,whichcouldbecomplementedwitha -cameraofferinganaerialoftheparkinglottoimprovethecontrollerperceptionofthelocationandorientationofvehicles,couldsimplifytheprotocolandimprovereliability.

Reducingandsimplifyingsuchtrajectoriesandmanoeu-vresisalsoanimportantdesignissue,astheyaffectthereliabilityofthesystemandallowfasterstorageandretrievalofcars.Notealsothattheparkinglotarchitecturecantakeadvantageofthefactthatthepassengerdoesnotentertheparkinglot,andthustheinter-vehicledistancesdonotneedtoallowforspacetoopendoors.Tooptimiseandsimplifymanoeuvres,theseself-automatedparkinglotswillrequirespecificminimumturningradiusvaluesforvehicles.

Fig.1.Anexamplelayoutforaself-automatedparkinglot.Theparkinglotcanneverbecompleyfull,asbufferareasarenecessarytobeabletoallowtheexitofeachvehicleunderallpossibleconfigurations.Inthisexample,aminimumof6emptyspararenecessary.

Onlyvehiclesthatmeettheturningradiusspecifiedbyeachparkinglotwillbeallowedtoenterit.

Thegeometriclayoutoftheparkinglotanditsbufferareascanassumeverydifferentconfigurationsfortheself-automatedfunctioning.Onepossibilityistohaveparallellaneswithminimalspacebetweenthem,asillustratedinFig.1.Inthistypeoflayout,thePLCstartsbyassigningalanetoavehicle.Thisinitialdecisioniscritical,asitshouldminimisetheneedtomoveavehiclefromonelanetoanother.NotethatiftheredvehicleinFig.1needstoleaveunderthecurrentconfiguration,thenthevehiclebehinditneedstobemovedtoanotherlane.Ifwecouldpredictthattheexitoftheredvehiclewouldhappenbeforetheexitofthevehiclebehindit,thenthislastvehiclewouldbebettercedinadifferentlane.Ourgoalinthispaperiactlytobeabletopredictanexit-intervalforeachvehicle,anddesignalaneselectionmethodologythatreducesthemobilityneededtocreateexitpaths.

Notethatparkinglotswillnotbeabletobecompleyfull,asbufferspaceneedstoexisttoallowtheexitofeachvehicleunderallpossibleconfigurations.Theminimumnumberofemptyspaces,configuringbufferareas,dependsontheparkinglotlayout.InthelayoutpresentedinFig.1,withalanedepthof7,weneedabufferareawithaminimumof6emptyspaces.

Methodology

Ourmethodologyconsistsonthefollowingfoursteps:itstartsby(A)dividingtheoriginaldatasetinksmallerones,containinguserswithsimilarparkinghabits;then,(B)datadrivenregressionisperformedoverthenewlycreatedsub-datasets.Thirdly,aparkingtimeintervalisgenerated(C)basedonsuchpredictionsandontheirpreviousresiduals(differencebetweenapredictedvalue(yˆ)anditsrealone,y).Finallytheselectedlane(D)willbetheonewhiinimizesthelikelihoodofperformingunnecessaryvehiclemovements

1.ThismethodologyissummarizedinFig.2andexinedindetailthroughoutthissection.

ProfileGeneration

i=1

LetX={X1,X2,...,Xn}bentimestampeddatarecordsontheparkinglotentriesdescribingtheentry/exitbehavioursofρdistinctusers.LetUi⊆Xdenotetherecordsofandindividualuseri(i.e.Uρ≡X)andΨidescribethesample-basedprobabilitydensityfunction(p.d.f.)ofitsparkingtimehabits.AclusteringprocessisfirstlymadeonXbasedon

i=1

S

theextractedΨi.TheresultingkclusterscanbedefinedasΠ={π1,π2,...,πk}.Theywillcomprisesub-datasetscontainingdatarecordsonusershavingsimilarprofiles(i.e.parkingtime-habits).Consequently,X≡kπi.

ParkingTimePrediction

Toperformtheparkingtimeprediction,weproposetousedatadrivenregression.Inregression,thegoalistodetermineafunctionf(Z,θ),giventheinputindependentvariables,Z,andtherealvaluesofthedependentvariables,

lerepresentsthepointthatisgreaterthan25%ofthedata,whilethethirdlethepointthatisgreaterthan75%.Lete1,iande3,idenotethefirstandthirdlesoftheregressionresidualsproducedbyagivenmodelMπionthepreviouslytesteddatarecordsinπi.OurbaselineintervalIisgivenbythefollowingequation:

Ij,πi=[pj,πi−e1,πi,pj,πi+e3,πi] (2)

Letahitoccureverytimetherealparkingtimeiscontainedwithintheintervalestimated.Otherwise,weconsidertheoccurrenceofamiss.Ourgoalistoproduceintervalsinorderto izethenumberofhitsand,atthesametime,tominimizeitswidth.Todoso,weproposetoextendthebaselinedescribedineq.(2)byemployingaself-adaptivestrategy.Suchstrategyconsistsonmultiplyingthele-

basedintervalwidthbya0≤β≤2(startingonβ=1).Thisvalueisincrementallyupdatedwheneveranuserofπileaves

theparkinglot(i.e.eachtimeanewlyrealparkingtimeisknownonπi).Letαπidenotethenumberofconsecutivemisses/hitsofourintervalpredictionmethodinπi.Whenever

θ.Theoutputofthemodelisnotnecessarilyequaltothe

realvalue,duetonoiseinthedataand/orlimitednumber

απi

>αth,thevalueofβisincremented/decrementedbyτ.

ofentries.Consequently,aregressionmodelcommonlycomprisesanerrore.Thefunctionfcanbeexpressedasfollows:

Y≈f(Z,θ)+e (1)

LetM={Mπ1,Mπ2,...,Mπk}bethesetofkregressionmodelsandpj,πidenotetheparkingtimepredictionforagiventimestampeduserentrancewiththeprofileπi.Mresultsofapplyinganinductionmethodofinteresttothe

datasetsinΠ.Byngso,theauthorpecttoapproximatetherealvehiclesparkingtimegivenasetofdescribingvariables(i.e.:Z).

IncrementalIntervalGeneration

Givenapredictionfortheparkingtimeofanusertimes-tampedentrance(i.e.pj,πi),itispossibletoestimateanintervalforthisvaluebasedontheresidualsproducedbyitsregressionmodel.Hereby,weproposetodosobyemployingtheresiduals’les.Aleisapointtakenfromacumulativedistributionfunctionofavariable.Thefirst

1Wheneveragivenvehiclecexits,allitslane’svehiclesstandingbetweencandtheparkinglotexit,havetobemovedtoabufferzone.Suchmovementscouldbeavoidedbyanexit-orientedsortingofeachlane’svehicles.

αthandτaretwouser-definedparameterssettinghowreac-tivetheintervalpredictionmodelshouldbe.Consequently,itispossibletore-writetheeq.(2)intothefollowingone:

Ij,πi=[pj,πi−∆,pj,πi+∆],∆=(e3,πi−e1,πi)×β(3)

Everytimethatasequencemiss/hitorhit/missoccurs,therespectiveαvalueissetto0.Theβendsupbycontrollingtheintervalwidth:thedescribedalgorithmaimstoadaptitselftothecurrentscenariobynarrowingtheintervalswidthwheneveritisgettingmultiplehitsorbystretchingitselfontheoppositescenario.

ParkingLaneSelection

Inthispaper,theparkinglotisassumedtofollowarectangularlayoutwheretheentranceandtheexitarethesame.Itispossibletorepresentitasal×rmatrix,where

l,rsetsthenumberoflanesandthe umnumberof

vehiclesineachlane,respectively.Whenavehicleenterstheparkinglot,itisnecessarytoselectalaneκtoparkitin.Suchselectionshouldminimizethenumberofunnecessaryvehiclemovements(i.e.ϑκ).Consequently,eachlanehasanassociatedscoreWκ.Itcanbefacedasalikelihoodofthatselectionunnecessarymovementsgiventhei)currentintervalpredictionforthenewlyarriveduser(Ij,πi)andii)thevehiclesalreadyparkedinκ.Thelanewithlowestscoreispredictedtobetheonethatminimizesϑκ.

EmptylaneshaveapredefinedscoreofW=1whilea

Users’p.d.f.

Clustering

Regression

Models

Numerical

Predictions

Estimation

Interval

fullonehaveW=∞.Lethbethelastvehicleinκ(i.e.

𝜋1

𝑀1

𝑃1

𝐸𝐼1

𝜋2

𝑀2

𝑃2

𝐸𝐼2

𝑋

Lane

Selection

𝑛

Regression

Training

Regression

Testing

Interval

EstimationModel

𝜋

𝑀𝑘

𝑃𝑘

𝐸𝐼𝑘

𝑘

j,πi

thevehiclemostrecentlyparked),IU betheupperlimit

andI

L

h,πb

bethelowerlimitoftheestimatedinterval(note

thatthevehicle’sjprofile,πi,maybe(ornot)thesame

h,πb

ofthevehicleh,πb).IfIU

L

<I

j,πi

,iti pectedthat

,

thevehiclejofprofileπiexitstheparkinglotfirstthanh

j,πi

(e.g.:Fig.3-c).Inthiscase,Wκ=∞.IfIU

L

<I

h,πb

Fig.2.Anillustrationonthedifferentstepsoftheproposedmethodology.

theniti pectedthatjandhcanleavetheparkinglotprovokingnounnecessarymovements(i.e.:ϑκ=0;e.g.:

EntriesExits

Fig.3.Ina),theupperlimitofIhislowerthanthelowerlimitofIj,sohipectedtoleavetheparkinglotfirstthanj.Inb)thereisanoverlapbetweenthetwointervals.Itswidthisusedtocomputethelane’sscore.Finally,c)istheoppositescenarioofa).

Fig.3-a).Consequently,thescoreisthenWκ=0onthiscase.Otherwise,Wκcanbecomputedasfollows

07h08h09h10h11h12h13h14h15h16h17h18h19h20h21h22h

0 500100015002000250030003500

Fig.4. BarplotchartrepresentinghistogramsfortheEntry/Exittimesbetween7amand10pm.

possibletoobservethatthemainentrytimesarebetween8amand10amandthemainexittimesbetween5pmand

IU−IL

(N−1)4

8pm.Thevehicle’itsfromtheparkinglotfollowsa

κ

W=j,πi h,πb+ κ

(4)

I

—I

r

U

h,πi

L

h,πb

bimodaldistribution,withthemodesatlunchtime(between

j,πi

i

whereNκstandsforthenumberofvehiclescurrentlyinκ.Thisapproachisinspiredonthetypicalp-valuestatisticaltestconsideringanullhypothesisbysettingtheextremedatapointasIUandIh,πasaroughapproximationontheparkingtimedistributionfunctionfortheparkedvehicleh.Thesecondtermofeq.(4)isanexponentialweightwhichaimstoexpressthepossiblecostofhavingunnecessaryvehiclemovementscausedbyassigningthenewlyarrivedvehiclejtothelaneκ.

CaseStudy

ThiscasestudyconsistsontheparkinglotoftheFacultyofScienceofUniversityofPorto,Portugal.Thedataof309usersduringtheyearof2013wasusedtovalidateourmethodology.Thisparkinglothasthecapacitytoholdupto100vehicles.Since96.4%ofthedataentriesareinweekdays,onlytheworkdaysareconsideredinthisstudy.

Eachdatarecordhasthefollowingfeatures:(i)anuserID,(ii,iii)twotimestampsfortheparkingentry/exit,(iv)typeofday(e.g.:Monday),(v)holiday/not-holidaybooleanand,finally,the(vi)department,(vii)and(viii)jobrole(e.g.FullProfessor).

Ideallyalldataentrieswouldhavetheirentryandexittimesproperlylabelled.However,itdoesnothappeninthiscasebecausetheparkingentrieitsarenotfullymonitored.Consequently,thereareentrieswithoutexitsandvice-versa.Totacklesuchissue,apreprocessingtasktopairtheentrieswiththeexitswasperformed.Alltheresultingdatarecordswithparkingtimesmallerthan10minutesorhigherthan16hourswereremoved.Forthesamereasons,wehavealsofilteredtheparkinglotusersbyusingthedatarecordsofthetop-75%,regardingtheirnumberofparkingentries.

Intheresultingdataset,theaverageparkingtimeis5hoursand25minutesandwithastandarddeviationof3hoursand8minutes.Fig.IVexhibitstwohistogramsrepresentingthehourlyfrequenciesontheentryandexittimes.Itis

12amand2pm)andatlateafternoon(between5pmand7pm).

ExperimentalResults

Inthissection,westartbydescribingtheexperimentalsetupusedinourexperimentsandtheevaluationmetricsusedtovalidateourmethodology.Then,wepresentsomeexperimentalresultsandabriefdiscussionontheirinsights.

ExperimentalSetup

Theinitialdatasetwasdividedinatrainingset(JanuarytoOctober)andatestset(November).AllexperimentswereconductedusingRSoftware[6].Thealgorithmsusedwerethek-NearestNeighbours(kNN)[7],theRandom s(RF)[8],theProjectionPursuitRegression(PPR)[9]andtheSupportVectorMachines(SVM)[10]fromtheRpackages[kknn],[randoms],[stats]and[e1071].

Regardingthefeatureselection,awell-knownstate-of-the-arttechniquewasused:PrincipalComponenty-sis(PCA)[11].Thetestedfeaturesweretypeofday,holiday/not-holidaybooleanvariableandtheuser’sde-partment,andjobrole.ForclusteringweusedtheExpectation- izationalgorithmwiththeRpackage[MClust].ThisalgorithmwaschosenduetobeingabletodeterminetheoptimalnumberofclustersautomaticallybasedonBayesianInformationCriterion[12].

Thelast2weeksofthetrainingsetwasusedformodelselection.Inthisstage,thefollowingparametersweretestedforeachalgorithm:forkNN,distance=[1..5],kMax=[2..15]andthekernels:rectangular,triangular,epanechnikov,gaussian,rankandoptimal,forRFmtry={3,4,5}andntrees={500,750,1000},forPPRnterms={2,3,4}

andmax.terms={5,6,7,8}andforSVMthekernels:

linear,radial,polynomialandsigmoid.Thebestpair(algo-rithm,parametersetting)wasselectedtoperformthenumer-icalpredictioninthetestset.

Finally,thereactivenessparametersontheintervalesti-mationmodel(τ,αth)weresetforthevalues0.1and3,respectively.

Toevaluateourmethodperformance,weconsideredabaselinenaivestrategy.Itconsistsondirectingthenewlyarrivedvehicletotheleftmostlaneκwithanemptyspace.Aseriesofsimulationswereconductedtocomparetheparkinglotbehaviorusingtheaforementionedlaneselectionstrategies(i.e.naiveandsmart).Multipleparkinglayoutswereconsideredonthisseriesofsimulations.Itaimedtodemonstratethatthestrategiesbehaviorisindependentontheparkinglayout.Theaveragedumnumberofparkedcarsonadailybasisontheconsidereddatasetis50.Consequently,everyparkedlayoutswithacapacitybetween50and80vehicles(i.e.:the1stle)containing,atleast,8lanes,wereconsideredonourexperiences.

Evaluation

Theroot-mean-squared-error(RMSE)andthemeanab-soluteerror(MAE)werethemetricsusedtoevaluatethepredictions.Theycanbedefinedasfollows:

TABLEI

Resultsfromthenumericprediction.

Group

#ofIndividuals

RMSE

MAE

Hit%

Interval

1

11

5124

3320

63

8942

2

9

4804

3255

66

3862

3

3

7047

5235

68

9584

4

6

4644

4047

78

9764

5

3482

6

1

376

340

72

3504

7

5

3968

3317

68

9196

8

7

7618

6101

58

11738

9

11

9106

7628

53

11900

10

6

8244

7403

55

12560

11

4

2609

2058

72

5255

12

10

7871

5436

67

9583

72

9558

54

11228

50

6258

16

10

6682

5356

70

10293

3158

W.Average

6601

5076

65

11188

TABLEII

Simulationresultswiththenumberofunnecessaryvehiclemovementsforbothstrategies.

RMSE=

t=1 ,MAE=t=1

sPg

(yˆt−yt)2 Pg |yˆt−yt|

Config.

Naive

Smart

Config.

Naive

Smart

10x05

1665

1379

05x10

7799

7540

11x05

1482

1205

05x11

7817

7615

12x05

1255

1074

05x12

7817

7633

13x05

1074

914

05x13

7817

7633

14x05

937

813

05x14

7817

7633

15x05

811

771

05x15

7817

7633

09x06

2234

2032

06x09

5596

5423

10x06

1819

1583

06x10

5596

5444

11x06

1510

1282

06x11

5596

5453

12x06

1255

1139

06x12

5596

5453

13x06

1074

930

06x13

5596

5453

08x07

2808

2520

07x08

3818

3545

09x07

2248

2116

07x09

3818

3545

10x07

1819

1616

07x10

3818

3551

11x07

1510

1303

07x11

3818

3551

07x08

3818

3545

08x07

2808

2520

09x08

2248

2116

08x09

2808

2535

10x08

1819

1617

08x10

2808

2535

08x08

2808

2535

g g

(5)

whereyˆisthepredictedvalue,ytherealoneandgisthenumberofsamples.

Theparkingtimeestimationintervalisevaluatedintwoforms,apercentageofhitsandaratiobetweenthehitsand

itswidth.Ifforasamplesthereisahit,thenhits

otherwisehits=0.Theratiocanbedefinedas:

=1,

X

ratio= gs=1

hits

1

×

δI×g

(6)

whereδIisthewidthoftheestimationintervalandgisthenumberofconsideredsamples.

Theevaluationcriteriaemployedinthesimulationwasthetotalnumberofunnecessaryvehiclemovementsdbyagivenstrategy(i.e.,UM).Letusconsideraexitingvehiclec,parkedinalaneκwithgvehicles,inpositioni.TheunnecessarynumberofmovementsUMcausedforctoexittheparkinglotcanbecomputedas:

simulationineverytestedconfigurations,withthenumberofunnecessaryvehiclemovements,µforbothstrategies.The

X

UM= g−ij (7)

j=1

Letusconsideralanewithg=5vehicleswherethevehicleonthepositioni=2isrequestedtoexitasanexemplificationforthecalculusofMU.Inthiscase,MU=3+2+1=6.

Results

Theobtainedresultsarethreefold:(1)thePCAresultshave mendedtoremovetheuser’sandtheholidayfeaturefromtheoriginalset.(2)TableIexhibitstheresultsofthenumericalpredictionusingtheremainingfeaturesetforeachprofileπi,bypointingthenumberofuserscontainedineachgroupandthe(RMSE,MAE)obtainedineachoneofthem.(3)TableIIshowstheresultsfromtheparking

intervalsgeneratedhad65%hitsandaageintervalwidthof≈11000seconds.Thesmartstrategy esthenaiveoneinalltheconsideredconfigurations.

Discussion

TableIexhibitsalargevariationonRMSE/MAEproducedbythemodelsofthedifferentgroups.Thegroupssizeisalsodifferentfromgrouptogroup.Thesegroupscanbefacedasprofileswhichdescribethetypicalparkingbehavioroftheuserswithin.Itispossibletoobservethatsomegroupscontainonlyoneuser(i.e.5,6,17)whichindicatesthattheyhaveacompleydifferentprofilethantheremainingones.Sofar,suchprofilesareonlybasedoneachuser’sparkingtime(namely,byusingtheEuclideanDistanceovertheirp.d.f.).However,someuserscanexperiencelarge

variationsontheirparkingtimedependingonsomesubsetsoffeaturevalues(i.e.toentertheparkinglotatmorningoratafternoon).ThisfactcanpartiallyexintheabovementionedRMSE/MAEvariability.

Theaveragedhitspercentage(65%)anditslargewidthuncoverthestochasticityoftheparkingtimevariablegiventhecurrentfeatureset.Infact,itisreasonabletoadmitthatwemayneedotherfeaturestoimproveourpredictionmodelsuchasweatherorevent-basedones(e.g.asunnydayoraspecialsoccermatayreduce/increasetheparkingtime).However,wecannotsustaintheseinsightsonthepresentresults.

Thenaivestrategyisclearlybenefitedbyconfigurationswithmorelanes,wheretheUMcanbenaturallyminimizedbyunderusingthetotallane’scapacitybyfillingfirsttheemptyones.Infact,thisstrategyisalreadyfocuse