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Calibration of Vissim for BRT Systems in Beijing Using GPS Data 239 Calibration of Vissim for Bus Rapid Transit Systems in Beijing Using GPS Data Liu Yu, Beijing Jiaotong University Lei Yu, Texas Southern University and Beijing Jiaotong University Xumei Chen, Beijing Jiaotong University Tao Wan, Beijing Jiaotong University Jifu Guo, Beijing Transportation Research Center Abstract Bus Rapid Transit systems have grown in popularity in recent years. With the rapid development of computer technologies, using microscopic simulation models to study various strategies on planning, implementation and operation of BRT systems has become a hot research area in the field of public transportation. To make the simulation models accurately replicate field traffic conditions, model calibration is crucial. is paper presents an approach for calibrating the microscopic traffic simulation model VISSIM using GPS data for application to Beijing BRT systems. e Sum of Squared Error (SSE) of the collected versus simulated vehicle speeds at the cross-sections along the test route is specified as the evaluation index. A Genetic Algorithm is adopted as the optimization tool to minimize the SSE. Taking the Beijing North-South Central Axis BRT Corridor as a case study, it shows that the proposed approach is a practical and effective method for the model calibration.

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Calibration of Vissim for BRT Systems in Beijing Using GPS Data

239

Calibration of Vissim for Bus Rapid Transit Systems in

Beijing Using GPS Data

Liu Yu, Beijing Jiaotong University Lei Yu, Texas Southern University and Beijing Jiaotong University

Xumei Chen, Beijing Jiaotong University Tao Wan, Beijing Jiaotong University

Jifu Guo, Beijing Transportation Research Center

Abstract

Bus Rapid Transit systems have grown in popularity in recent years. With the rapid development of computer technologies, using microscopic simulation models to study various strategies on planning, implementation and operation of BRT systems has become a hot research area in the field of public transportation. To make the simulation models accurately replicate field traffic conditions, model calibration is crucial. This paper presents an approach for calibrating the microscopic traffic simulation model VISSIM using GPS data for application to Beijing BRT systems. The Sum of Squared Error (SSE) of the collected versus simulated vehicle speeds at the cross-sections along the test route is specified as the evaluation index. A Genetic Algorithm is adopted as the optimization tool to minimize the SSE. Taking the Beijing North-South Central Axis BRT Corridor as a case study, it shows that the proposed approach is a practical and effective method for the model calibration.

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IntroductionBusRapidTransit(BRT)systemshavegrowninpopularityinrecentyears.Withtherapiddevelopmentofcomputertechnologies,usingmicroscopicsimulationmodels to studyvarious strategiesonplanning, implementationandoperationofBRTsystemshasbecomeahotresearchareainthefieldofpublictransporta-tion, particularly in cases where field experiments are difficult or expensive toconduct.

There are plenty of available microscopic simulation models used worldwide,suchasVISSIM,CORSIM,PARAMICS,etc.Insuchmodels,thereareanumberofparametersdescribingthetrafficflowcharacteristics,drivingbehavior,andtrafficsystemoperations,whichhavesignificanteffectsonsimulationresults.Althoughthese models provide a set of default values for each parameter and users canconductasimulationwithoutcalibratingthem,thedefaultvaluesmaynotalwaysbe representative of the traffic situation under study. For example, the drivingbehaviorofBRTvehiclesontheexclusive lanesmaybedifferentfromthoseonurbanstreetsorfreewaysbecauseBRThassomeuniquetrafficcharacteristics(e.g.,dispatchingaccordingtoschedule,stoppingatbusstopsforservingpaSSEngers,etc.).EvenBRTsystemsindifferentcountriesordifferentcitiesmayhavediffer-entcharacteristics.ForasimulationstudyofBRTsystems,adequatecalibrationbasedonobservedtrafficconditionscanresultinaccurateandreliablesimulationresults, which can help transit operators make more appropriate decisions forBRTplanningandimplementation.So,whenusingasimulationmodelfordiffer-entgeographicandtrafficconditions,themostimportantanddifficultstepisthecalibrationandvalidationofthemodel.Thecalibrationistheprocessbywhichthevaluesofasimulationmodelinputparametersarerefinedandadjustedsothatthemodelaccuratelyreplicatesfield-measuredandobservedtrafficconditions.

TheaimofthispaperistoproposeanapproachfortheautomaticcalibrationofthedrivingbehaviorparametersofVISSIMusingGPSdataforapplicationtoBei-jingBRTsystems.AGeneticAlgorithm(GA)isusedforfindingthebestcombina-tionofVISSIMdrivingbehaviorparameters,andaparticularcomputersimulationprogramnamedAUTOSIMisdesignedtoruntheVISSIMsimulationautomati-callyandconsecutively.ThevalidityoftheproposedapproachwasdemonstratedviaacasestudyfortheBeijingNorth-SouthCentralAxisBRTCorridor.TheresultsshowthatitisapracticalandefficientapproachforthecalibrationofVISSIM.

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Review of Calibration Methodologies Theproblemofmodelcalibrationisverycomplexbecauseoftheabsenceofaclearanalyticalformulationformodeluserstofollow.Inrecentyears,moreandmoretransportationresearchershaverealizedtheimportanceofmodelcalibrationandmadegreateffortstodevelopvariousmethodologiestocalibratetrafficsimula-tionmodels.

In earlier studies, manual changes were used for calibrating model parameters(Daigleetal.1998),whichwas foundnotefficientandpractical.FellendorfandVortisch(2001)calibratedthecarfollowingbehaviorofVISSIMwithmeasurementonthelevelofsinglevehicles,i.e.,dataaboutheadways,perceptionthresholds,anddrivingcharacteristics.However,itisdifficultformodeluserstocollectsomeofsuchdatainthefield.Merritt(2003)proposedamethodologyforthecalibrationandvalidationofCORSIMusingempiricaldata.Hefoundthatextensivefielddataneedtobecollectedtoimproveaccuracyofthemodelcalibration.

With the recent applications of ITS technologies and computational resources,therearemoreopportunitiestocalibratesimulationmodelsbasedonoptimiza-tiontheoriesandalgorithms.Ben-Akivaetal.(2004)presentedaframeworkforthe calibration of microscopic traffic simulation models using aggregate data.TheyadoptedasystematicsearchapproachbasedonBox’sComplexalgorithmforcalibration,whichdidnotrequirecalculationsofderivativesoftheobjectivefunction.Nevertheless,theirstudyfoundthatefficientalgorithmsarestillrequiredtoperformthecalibrationstep.Someotheralgorithms,suchassequentialsimplexalgorithm (Kim 2003) and simulated annealing algorithm (Wieland 2004), alsohavebeenstudiedbyseveralresearches.

Inrecentyears,microscopictrafficsimulationmodelshavebeenwidelyusedasanimportanttoolfortheanalysisanddesignoftransportationsystemsinChina.However, many users conduct simulations simply with the default parametersprovidedbythemodelwithoutcalibratingthem.ThestudyonthecalibrationoftrafficsimulationmodelsinChinaisalsoscarce.SunandYang(2004)proposedaprocedureformicroscopicsimulationmodelcalibrationinChina.TheydesignedtheexperimentbyusingLatinSquarealgorithmandcalibratedfourofthedrivingbehaviorparametersofVISSIM,includingwaitingtimebeforediffusion,minimumheadway, observed vehicles, and average standstill distance. However, it takesmuchtimetofinishallthesimulationexperimentsandthesefourparameterscan-notrepresentthewholesetofdrivingbehaviorparametersofVISSIM.

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Proposed Calibration ApproachIdentification of Calibration Parameters in VISSIMVISSIMisamicroscopic,time-stepandbehavior-basedsimulationmodeldevel-opedtomodelurbantrafficandpublictransitoperations.Itprovidessignificantenhancements in terms of driver behavior, multi-modal transit operations,interfacewithplanning/forecastingmodels,and3-Dsimulation.VISSIMcontainsa psycho-physical car-following model for longitudinal vehicle movement anda rule-based algorithm for lateral movements. Ten calibration parameters areselectedinVISSIM,including:

• Waiting Time before Diffusion—Itdefinesthemaximumamountoftimeavehiclecanwaitattheemergencystoppositionwaitingforagaptochangelanesinordertostayonitsroute.Whenthistimeisreachedthevehicleistakenoutofthenetwork(diffusion)andawarningmessagewillbewrittentotheerrorfiledenotingthetimeandlocationoftheremoval.

• Minimum Headway (front/rear)—defines the minimum distance to thevehicleinfrontthatmustbeavailableforalanechangeinstandstillcondi-tion.

• Maximum Deceleration—thefastestavehiclecanslowdownorstop.

• -1 per Distance—usedtoreducethemaximumdecelerationwithincreasingdistancetotheemergencystopposition.

• Accepted Deceleration—thevalueofitissmallerthanmaximumdecelera-tionbutbiggerthanminimumdeceleration,andthevehiclecanslowdownsafelywithoutanydangerouswithaccepteddeceleration.

• Maximum Look Ahead Distance—themaximumdistancethatavehiclecanseeforwardinordertoreacttoothervehicleseitherinfrontortothesideofit(withinthesamelink).Thisvaluerelatestohuman’sphysicalobservationability.

• Average Standstill Distance—definestheaveragedesireddistancebetweenstoppedcarsandalsobetweencarsandstoplines(signalheads,priorityrules,etc.)

• Additive Part of Desired Safety Distance—thisparameterandthenextone(i.e.Multiple Part of Desired Safety Distance)containedwiththecarfollowingmodeldeterminethesaturationflowrateforVISSIM.ThesaturationflowratedefinesthenumberofvehiclesthatcanfreeflowthroughaVISSIMmodelduringonehour.

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• Multiple Part of Desired Safety Distance—describedabove.

• Distance of Standing at 50 km/h—thesafetydistancebetweentwoparallelcarsatboththeconditionofstopandmoving.

As the parameters mentioned above directly affect the vehicle interaction andthuscancausesubstantialdifferences insimulationresults,calibrationof theseparametersbecomeveryimportant.Tothisend,ascientificapproachisneededtocalibratetheseparameters.

Selection of an Optimization AlgorithmForcalibrationofatrafficsimulationmodel,thedifficultyistoselectthebestcom-binationoftheparametersbeingcalibrated.However,alloftheseparametersneedtobecalibratedsimultaneously,andeachmayhaveadifferentvaluerange,whichmakethecalibrationprocessverycomplicatedandtimeconsuming.So,toidentifythebestparametersetforthemodel,anoptimizationalgorithmisrequired.

AGeneticAlgorithm(GA)isasearchtechniqueusedincomputersciencetofindapproximatesolutionstooptimizationandsearchproblems.Itisaparticularclassofevolutionaryalgorithmsthatusetechniquesinspiredbyevolutionarybiology,such as inheritance, mutation, natural selection, and recombination (or cross-over).Itmodelseachpossibleparametersetasaseparatechromosome,andeachchromosomeisevaluatedbyafitnessfunctionthatrepresentshowwellitfitsagivenproblem(Kim2001).GAisconsideredrobustbecauseitperformsasearchfrommultiplepointsinsteadofstartingthesearchatasinglepoint.So,usingtheGAapproachcanconsiderablyreducethenumberofsearchstepsneededandtheamountoftimerequiredtocompletethesearchwhenthesearchspaceislargeandcomplex.

Index of Simulation Accuracy Toevaluatethequalityofthesimulationinthecalibration,anevaluationindexneedstobedefined.Therearevariousindexesthatcanbeused,suchastrafficvol-umes,averagetraveltime,averagetravelspeed,queuelengths,etc.ThispaperusestheSumofSquaredError(SSE)betweenthevehiclespeedscollectedandthosesimulatedatpre-definedcross-sectionsata20-meterintervalalongthetestroute,whichiscalculatedbythefollowingequation:

(1)

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where:

i cross-sectionnumberata20-meterintervalalongtheroutewherethespeediscollected

n numberofcross-sections

vcivehiclespeedcollectedatcross-sectionibyGPS,and

vsi

vehiclespeedsimulatedatcross-sectionibyVISSIM

Thespeeds of vehicles in the simulation network are a good reflection of driv-ing behavior parameters, provided the traffic volumes are known. Further, theinstantaneousspeeddatacaneasilybecollectedbyusingGPS.Therefore,usingthespeedtoevaluatetheaccuracyofmodelcalibrated isnotonlyappropriatebutalsopractical.

ForVISSIM,SSEcanbeconsideredasafunctionof10drivingbehaviorparameters(Yuetal.2005):

SSE=f(x1 , x2 , x3 , x4 , x5 , x6 , x7 , x8 , x9 , x10) (2)

wherexirepresentsthevalueoftheithcalibratedparameter,andfisafunctionthatisdifficulttoexpressinananalyticalform.Itcannotbesolvedthroughanana-lyticalapproacheither.ThispaperestablishesasimulationproceduretoindirectlyexpresstherelationshipbetweenSSEandthe10parameters.

Calibration Approach Using GAThe objective of the calibration process is to minimize the SSE, in which theGAisusedastheoptimizationtool.Thecompleteoptimizationprocess,whichcombinesGAandVISSIMtofindtheoptimalvaluesforthe10drivingbehaviorparameters,consistsofthefollowingsteps:

Step 1. Define the Agent to Represent the ParametersFor GA, the terms agent andgene are used. The termgene is represented by abinarydigit0or1.Oneagent isdefinedasagroupofgenesusedtorepresentavalueofeachparameter.Furthermore,onegenerationisdefinedasthespecifiednumbersofagents.Thepopulation sizeisdefinedasthenumberofagentsincludedinonegeneration.

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Step 2. Determine the Number of Genes for Each ParameterForeachparameter,thenumberofgenesneededvaryaccordingtothedomainoftheparameterandtheincrementoftheparametervalue.Thefollowingequationisusedtodeterminethenumberofgenesnineededforeachparameter:

(3)

where:

InEquation(3),max(xi)andmin(xi)shouldfirstbeidentified.Thenaninitialvalueisassignedtoαibasedonthenumberofincrementsdesiredinthesearchprocessforthisparameter.Finally,niisdetermined.Afterniisdetermined,itcanbesubsti-tutedbackintoEquation(3)tocalculatethefinalprecisevalueofαi.Theresultsofthecalculationforallthe10drivingbehaviorparametersareillustratedinTable1.Thevaluesofmax(xi)andmin(xi)aregivenbyVISSIM.

Table 1. Number of Genes and Increment of Each Parameter

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Step 3. Build Agent and Create Initial GenerationTable1showsthatatotalof39genesareneededtorepresentthese10parameters.Thepopulationsize,whichisthenumberofagentsinonegeneration,isdefinedas,butnotlimitedto16inthispaper(thenumberisrandomlychosen,butasasample,itshouldbearelativelylargenumbersothatthebetterindividualcouldbefoundinaveryshorttime).Intheinitialgeneration,eachgeneoftheagentisassigned0or1randomly.

Step 4. Decode Each Agent to Parameter ValueEquations (4)and (5)areused todecode theagentA to theactualparametervaluexi.

(4)

(5)

i =1, 2, 3, ... , 10

where:

xi thevalueofithcalibratedparameter,

αi theincrementvalueofxi,

ni thenumberofgenesoftheagenttorepresentxi,

βi min(xi),listedinTable1,

A vectortorepresentagent,

B coefficientvector,and

α1 , α2 , α3 , ... , 0or1

=

=−

12..

2

) ,... , , ,(1

321

i

i

n

n

B

aaaaA

βα += BAx ii **

inα

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Step 5. AUTOSIMFitnessisusedtoevaluatethequalityoftheagent.Thehigherthefitness,thebet-tertheagent.Inotherwords,thesetof10drivingbehaviorparametersisbetterif thefitness resulted fromthe simulation ishigher. In theproposedapproach,SSEisusedasthefitnessfunction,wherethefitnessisthehighestwhenSSEistheminimum.Asmentionedearlier, f isa functionthatcannotbeexpressed inananalyticalform.Assuch,asimulationprocedurenamedAUTOSIMisdesignedtoexpresstherelationshipbetweenSSEandthe10parameters.Thisprocedureauto-maticallyrunsVISSIMwithdifferentvaluesoftheinputparametersandgeneratestheoutputsofSSE.TheflowchartoftheAUTOSIMprocedure,programmedwithVisualBasic6.0,isshowninFigure1.

Figure 1. The Flowchart of AUTOSIM

Step 6. Evaluate the Fitness of Agents and Select the Best AgentWiththeAUTOSIM,theevaluationofeachagentinonegenerationcanbeper-formed.BeforetheAUTOSIMisentered,Equations(4)and(5)areusedtodecode

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theagenttoderivethevaluesoftheparameters.AfterallagentsinthecurrentgenerationhavegonethroughtheAUTOSIM,thefitnessofagents isevaluatedbasedonSSE,andthenthebestagentisselected.IftheSSEofthebestagentinthecurrentgenerationdoesnotsatisfyapre-definedcriterion,thefollowingstepistakentocreatethenextgenerationofagents.Otherwise,theprocessstops,andtheoptimalparametervaluesarederived.

Step 7. Select, Crossover and Mutate AgentInGA,select,crossoverandmutatearethreechiefoperatorsneededincreatingthenextgenerationofagents.Selectionisbasedontheprobability,andtheagentswithhigherfitnessvalueswillmost likelybe selected.Tocrossover, twoagentsinterchangepartoftheirgenestocreatetwonewagents.Oneagentismutatedtocreateanewagentbychangingoneofitsgenesfrom1to0orfrom0to1.

Step 8. Create a New GenerationThe search for the optimum values is an iterative process. After the operatorsofselection,crossoverandmutationarecarriedouttotheagentsoftheformergeneration,moreagentswillbeproducedtoformanewgenerationwhilekeepingthesamepopulationsize.

Step 9. Implementation of the approachThe MATLAB platform is used for programming to implement the GA-basedapproach.TheGeneticAlgorithmToolboxdevelopedbyUniversityofSheffieldalsoisused.Thistoolboxprovidesfunctionstoimplementtheoperatorsofselec-tion, crossover and mutation. The final program integrates the MATLAB, GAtoolbox,VisualBasic,andVISSIM.

Case Study for Beijing BRT SystemsBeijingisthecapitalandmostcongestedcityinChina,withthenumberofreg-istered motor vehicles exceeding 2 million (including 1.28 million cars). Trafficspeedonsomeurbanroadsaveraged12km/hin2003,comparedto20km/hin1996,and45km/hin1994.Morethan40percentofresidentsspentmorethanonehourgetting towork, and 87percentof road sectionsare constantly con-gested.Therefore,trafficcongestionwillbeamajorchallengeforBeijingforthe2008summerOlympicGames.DevelopingBRTis,ofcourse,oneofthefeasiblesolutionsforBeijing.

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Withtechnical support fromtheBeijingEnergyFoundation, theBeijingNorth-SouthCentralAxisBRTCorridorwaslaunchedinDecember2004asatestBRTcorridor,whichwasthefirstclosedBRTsystem(stationsrequiringfarecollectionbeforeboarding)inChinaandonlythesecondoutsideLatinAmerica.TheBeijingNorth-South Central Axis BRT Corridor is 15.8 kilometers long and paSSEs theQianmencommercialareaandfourringroads.ThisBRTCorridorwascompletedintwophases.PhaseIopenedforoperationonDecember25,2004,andstartsatQianmentowardMuxiyuan,with5stops,andis5kilometerslong.PhaseIIopenedonDecember30,2005,andgoesfromMuxiyuantoDemaozhuang,with11stops,andis11kilometerslong.

Test Site ThetestsiteinthispaperisthePhaseIoftheBeijingNorth-SouthCentralAxisBRTCorridor,whichis5kmlong,with2.5kmexclusivebuslanesand2.5kmmixeduseroadway,includingeightintersections.Theexclusivebuslanesareseparatedfromcarsatthecenteroftheroad,andthebusstopsare5mwideand40-60mlong.TheBRTbusesoperatingontheexclusivelanesare18meterslong,air-condi-tioned,withleft-opendoors,lowfloorsandacapacityof200passengers.TheBRTbusesrunfrom5:00amto10:30pm,withaheadwayof2-3minutesatpeakhourand4-5minutesatoff-peakhour.ThelayoutofthetestsiteisshowninFigure2.

Figure 2. Layout of the Test Site

Data CollectionForthepurposeofcalibration,trafficandGPSdataneedtobecollected.Trafficdata includethetrafficvolumesentering intothenetwork,theturningratioateach intersection,thesignaltimingofthesignalized intersections, theschedule

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oftheBRToperation,andtheBRTdwellingtimeateachbusstop.GPSdataareinstantaneousspeedofvehiclescollectedbyusingGPSequippedonthetestBRTvehicle or car. The vehicle equipped with GPS is driven along the test route inasimilarwaytothefloatingcarmethod. Inthis study,boththespeedsofBRTvehicleandcarwerecollected.Tenrepeatedcyclerunsofthetestwereconductedalongthesameroute.

SixsectionsforBRTandtwosectionsforcarweredefinedtoconductthedatacollection,asshowninFigure3andFigure4.

Figure 3. Six Sections for BRT along the North-South Central Axis BRT Corridor

Figure 4. Two Sections for Car around the North-South Central Axis Road

Table2describesthesectionsdefined.

TocalculatetheSSEofeachsection,thesimulatedspeedsofvehiclesshouldbeoutputbysettingupdetectorsalongthetestrouteinVISSIM.

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Table 2. Description of the Sections Defined

Model Calibration and Results BecauseofthedifferencebetweenBRTandgeneraltrafficinoperation,thevaluesofdrivingbehaviorparametersofBRTvehiclesmaybedifferent fromthoseonurban streets or freeways. Therefore, both the driving behavior parameters ofBRTvehiclesandcarsshouldbecalibrated.Tocarryoutthecalibrationprocess,the MATLAB platform is used for programming to implement the calibrationapproachandtheGeneticAlgorithmToolboxinMATLABisusedforperformingtheGAoperation.InthisMATLABplatform,theAUTOSIMprogrammentionedearliercanbecalledtoruntheVISSIMmodelautomatically.

Inthiscasestudy,acriterionisspecifiedonwhentheprogramshouldstop.Thestoppingcriterionisspecifiedaswheneither10consecutivegenerationshavethesameSSE,orthedifferencebetweenSSEsfromtwoconsecutiverunsislessthanorequalto1percent(notincludingtwoconsecutivegenerationswiththesameSSE).Table3illustratestheresultsfromthecalibration, inwhichthecriterionismetaftertheprogramrunsfor28generationsforBRTand25generationsforCars.

Tables4and5showpartoftheresultsofSSEfromtheprogramforBRTandcars.

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Table 3. The Values of Default and Optimal Parameters

Table 4. Simulation Results of SSE from 28 Iterations for BRT

Table 5. Simulation Results of SSE from 25 Iterations for Cars

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InTables4and5,generationnumber0meansthedefaultparametervalues.Forthefirstgeneration,theagentsarecreatedatrandom,sotheSSEofthebestagentinthisgenerationisgreaterthanthedefaultSSE.However,inthefollowinggen-erations,theSSEofthelattergenerationissmallerthan(orequalto)theformer.TakeBRTasanexample.Afterthecomputerprogramrunsfor5,10and28genera-tions,itsvaluesarereducedto3158,2448and1513,respectively.Thus,theSSEhasdecreasedalmost53.5percentwhentheparametersarechangedfromthedefaultvaluestotheoptimalones.TotheplanningofBRTprojectsinpracticalterms,thisvaluemeanspotentialbenefits,suchasoperatingcostsavings,improvedserviceplanningand levelofservice,becauseBRToperatorscanmakebetterdecisionsaccordingtothesimulationresultsprovidedbythemodelcalibrated,whichaccu-ratelyreplicatestheobservedtrafficconditions.

Tovisualizetheresults,thespeedssimulatedusingthedefaultparametervalues,collectedbyusingGPSsystemandoptimizedafterthecalibration,arecompared.Figure5showsanexampleofthespeedprofileforBRT,andFigure6isanexampleofthespeedprofileforcars.

Forcomparisonpurposes,theerrorsbetweenthesimulatedspeedsandthecol-lectedspeedsatcross-sectionsarecomputed.ForBRT,withthedefaultparametervalues,thepercentageofrelativeerrorsgreaterthan20percentofthetotalsampleis80.3 percent, compared with only 19.7 percent when the optimal parametervaluesareused.Furthermore,theoverallStandardDeviationwithdefaultvaluesis19.32,andonly5.55withoptimalvalues.Theresultsshowthattheaccuracyofthemodelaftercalibrationisimprovedconsiderably.

Model Validation Todeterminethatthemodelcalibratedaccuratelyrepresentstherealsystem,theTianqiaoIntersectionisusedtodothemodelvalidation.Themeasuredvolumesof the South Approaches of this intersection, the simulated volumes using thedefaultparameters,andthesimulatedvolumesusingthecalibratedparametersare compared (shown in Figure7). From this figure, it is found that the modelcalibratedmatchesthefieldobservationswithinasmallerrorrange,inwhichthemaximumrelativeerrorisonly2.5percent.However,themaximumerrorofthemodelwithdefaultparameterscanreachto27.4percent.

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Figure 5. Comparison of BRT Vehicle Speed Profile for Section 1

Figure 6. Comparison of Car Speed Profile for Section II

Figure 7. Comparison of Volumes with Default versus Optimal values

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Conclusions and RecommendationsThis paper presented an approach for calibrating the microscopic simulationmodelVISSIMforBeijingBRTsystemsusingGPSdata.TheSSEofthecollectedversussimulatedvehiclespeedsatthecross-sectionswasdefinedastheevaluationindex.TheobjectiveofthecalibrationistosearchforthebestcombinationoftheparametersthatminimizetheSSE,andaGeneticAlgorithmisadoptedasanopti-mizationtooltoimplementthesearchprocess.Fortheefficiencyimprovementofcalibration,acomputerprogramisdevelopedtointegratetheMATLAB,VisualBasic,andVISSIM.ThevalidityoftheproposedapproachwasdemonstratedviaacasestudyfortheBeijingNorth-SouthCentralAxisBRTCorridor.BoththefieldinstantaneousspeedsofBRTvehicleandcarsalongthetestroutewerecollectedbyusingGPSforcalibration.ThecasestudyshowsthattheproposedapproachisapracticalandeffectivemethodforcalibratingtheVISSIMmodel.

SincethisstudyusedonlyoneMeasureofEffectiveness(MOE),i.e.,SSE,formodelcalibration,theperformanceofotherMOEsisuncertain.Furtherresearchisrec-ommendedtoincludemoreMOEs(e.g.,delayorqueue)inthecalibrationprocess.Furthermore,withanincreasedtrendofsimulationapplicationforstudyonBRTsystems,othertypesofBRT(e.g.,allarterialorallexclusiveright-of-way)shouldbeconsideredtoverifytheperformanceoftheproposedapproach.Doingsowillprovidemoreinsightonthefeasibilityoftheproposedapproach.

Acknowledgements

Thispaperwaspreparedbasedonaproject(Y0604002040691)fundedbyBeijingMunicipalScience&TechnologyCommissiontitled“BRTPlanning,OperationalandOrganizationalCoordinationTechniques,”theprojectsof“TalentBuilding”FoundationofBeijing JiaotongUniversity (YSJ04001),andNationalNaturalSci-enceFoundationofChina(50208002).

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About the Authors

Liu Yu([email protected])isaPh.D.candidateatSchoolofTrafficandTrans-portation, Beijing Jiaotong University in Beijing, China. Her research interestsinvolveBusRapidTransitdevelopment,transportationsimulation,andIntelligentTransportationSystems.

Lei Yu([email protected])isProfessorandChairmanofDepartmentofTransporta-tionStudies,TexasSouthernUniversity.HeisalsoChangjiangScholarofBeijingJiaotongUniversityandhasmanaged50researchprojectsandhaspublishedover100scientificpapers.

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Xumei Chen ([email protected]) is an associate professor of Schoolof Traffic and Transportation, Beijing Jiaotong University in Beijing, China. HerresearchinterestsinvolveITStechnologies,networkplanningofurbanrailtransit,andindustrypolicyoftransportation.

Tao Wan([email protected])isagraduateresearchassistantatSchoolofTrafficandTransportation,BeijingJiaotongUniversityinBeijing,China.Hisresearchinterestsinvolvevehicleexhaustemissiontesting,BusRapidTransitdevelopment,andtransportationmodelling.

Jifu Guo ([email protected]) is the Deputy Director of Beijing TransportationResearchCentre(BTRC).Hismainresearchareastrafficforecasting,metro/highwayplanning,trafficimpactanalysis,andtrafficenvironmentanalysis.