2MCMBM.docx

2MCMBM.docx

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2MCMBM

Summary

TheQuickPasssystemallowsthetouriststodoubleusetheoriginalwaitingtimeandoffersthemmoretimeforotheractivitiesinthepark.However,therestillexitsomeproblemsinthecurrentQPsystem.Inthispaper,weanalyzetheexistingQPsystem,proposebetterQPschemes,andtesttheirvalidity.

AfterthecarefulanalysisofthecommonpursuitoftouristsandCEOs,weconcludethattheprincipleobjectiveofaQPsystemistoincreasetheaveragefreetimeoftourists.Thisincrementisdirectlyreflectedinthedecreaseofthelengthofawaitingline.Empirically,weassumethatthelengthofaregularlinehasanoptimalvalue.WealsosetalimittothelengthofthelineforQPholders.

WhenformulatingQPschemes,themostimportantfactoristhereturntimedesignatedtoeachtourist.First,weproposeScheme1,asimplifiedversionoftherealQPsystem,inwhichthereturntimeisdeterminedbythecurrentlengthoftheregularline.Weusetheresultofthisschemeasthebaselineofanalyzingthelaterschemes.ThenwetakeintoaccountthenumberofQPholdersinthevirtuallineandcreateScheme2.ThisisaFIFOsystemandthuscanavoidtheproblemoftheinstabilityoftheassignedreturntime.InScheme3,wepredictthearrivalpatternofthedayunderdiscussionusingthehistoricaldataandcomeupwithanalgorithmthatguaranteesthereturningQPholderstoavoidthepeaktimeoftourists’arrival.Scheme3cansuccessfullyimprovetheperformanceofthesystem.BasedonScheme3,wefurtherrecordthereturntimeofeachQPholderinthevirtuallineandintroduceScheme4.WestaggerthereturntimeofQPholdersandthuscontrolthelengthofthelineforreturningQPholderswithinadesirablelevel.Finally,weformulateScheme5fromanewperspective.Thisnewschemewillmakesurethateachdesignatedreturntimemaximizesthefreetimeincrementofthesystem!

Astheextensionofthismodel,wealsoproposeasystemwithpartialpriorityforQPholders.WebrieflycomparethenewsystemwiththeoriginalQPsystemwithabsolutepriorityandrecommendthesituationsofintroducingthispartialprioritystrategy.

Totesttheaboveschemes,weestablishaconsideratesimulationprogram,takingintoaccountmanycomplexfactorsintherealworldsituation.Thenwehavethepowerfulweapontotestourproposedschemes.Basedontheresultsofsimulation,wecometosomeusefulconclusionsandstrongrecommendationsfortheCEOs:

Thetwocriteriaofevaluatingaschemearethefreetimeincrementandtheregularlinelength.Thetwoquantitiesfollowalinearrelationshipapproximately.

AftertheimplementationofQPsystems,thelengthofregularlinereducesbyabout20%.

Tomaintainthelengthofregularlinewithinaproperrange,anappropriatenumberofQPticketsshouldbeissued.

Itisimportanttoaccumulateandupdatethehistoricaldata.

TheQuickPassStrategy

1AnalysisoftheProblem

Nowadays,theemergenceof"QuickPass"systemhasreducedthepeople’stimewaitinginlineandthushasbeenwidelyusedinmanyareas.Especiallyinamusementparks,thesystemhelpthetouristsgetridofthehorriblylongwaitinglineandofferthemmoretimeforotherrecreationalactivities.Itseemstobeawin-winstrategy.WehaveaccumulatedlotsofcommentspraisingtheintroducingofthissystembothfromtouristsandCEOsoftheparks.However,doestheQuickPassreallyhavethegreatpowertoenhancethesatisfactionoftouristsononehandandontheother,tobringmoreprofitstothebusinessmen?

Actually,wehavefoundsome“necessaryevils”fromtheQuickPasssystem（wewillcallitQPforshort）,whichweshouldpayspecialattentionto:

●AlongreturntimedesignatedbyQuickPass（say,6-8hours）willblockatouristfromgettinganyfurtherQPfortherestoftheday!

●AtouristmaynotgetaQPfromabigattractionlateinaday.

●Thereturntimemaybecomeunstablesometimes.Forinstance,atouristmayfinditunfairtobeassignedtoreturn4hourslaterwhenheobservesthatjustashortlateronthesameride,theQuickPasswasgivenforanhourorsolater.

●PerhapsthemostdissatisfactorysituationisthattheQPholdersreturntotheridehappilyonlytofindthattheystillhavetowaitinalinenearlyaslongastheregularlines.

Accordingtothosedrawbacks（maybemore）,itisclearthatthere’sstillgreatneedtoimprovethecurrentsystem.Ourtaskisanalyzingtheproblemsintheoldsystem,proposingourbetterstrategiesandthentestingthevalidityofourschemes.Moreover,wewillcomeupwithsomekeycriteriatoevaluatetheQPschemesbasedonourmodel.

Beforeestablishingourmathmodel,itisimportanttogetadeeperunderstandingofthe“QuickPass”System.ThekeywordinaQuickPassSystemis“virtualline”.Thisconceptderivesfromaverysimpleidea,thatis,tousesomecertainformtorecordthepositionofapeopleinaline,toestimatethetimefromnowonuntilhegetstheserviceandtoassignareturntimeforthepeople.Thesystemthenallowsthepeopleto“idle”duringtheperiodofhisoriginalwaitingtime,doingwhateverhewants,solongashereturnstoaccepttheserviceatthedesignatedtime.Disneylandisoneofthefirstamusementparkswhoadoptthiskindofsystem,namely,FastPass,andthecompanyhasachievedsomesuccess.Inthepast,touristsvisitingDisneylandcomplainironicallythatthe“mostfrequentactivity”issimplytowaitinaline!

Althoughitmaybealittleexaggerating,thelongwaitinglineisindeedtheNO.1headacheofbothtouristsandtheCEO.Obviously,itiscausedbythecontradictionbetweentheever-increasingtouristsandthelimitedcapacityofsomehotattractions.Longwaitinglineswillnotonlycauselargeamountsofcomplaintsfromtouristsbutalsothelackoftimeforthemtogoshoppingordininginthepark,whichisagainstthehopeoftheCEO?

（Sincetouristsdonotbuyextraticketsaftertheyenterthepark,theprofitgainfromshoppingcentersorrestaurantsistheonlypossiblesourceforprofitincrement.）Therefore,DisneylandintroducestheFastPasssystemtoskillfullyallocatetourists’timeandmakespossiblethedoubleuseoftheirtime.

NowwehavegotsomeideaofthereasonforintroducingtheQuickPasssystem.ButwestillwouldliketofurtherexploretheexpectedbenefitsoftheQPsystemfromtwodifferentperspectives:

theenjoymentrelatedconsiderationoftouristsandtheprofitrelatedconsiderationsofCEOs.

●Tourists

1.Toplayinasmanyattractionsaspossible

Ofcourseitisthesincerehopeofeverytouristsandtoday’sQPsystemfacilitatetherealizationofthishope.Ourschemeswillfurtherimprovetheenjoymentoftourists.

2.Toreducethewaitingtime

QPsystemwillgivetouristsmoretimeforotheractivities,includingplayinginmoreattractions.Therefore,thisfactorincorporatesthefirstone.

●CEOs

1.Tostretchtheaveragefreetimeforeachtourist

The“averagefreetimeofatourist”isdefinedastheaveragevalueofatourist’stotaltimeusedintheparkminusthetimeusedtowaitinlinesandactuallyplayinattractions.TheincreaseofthistimemeansthatthelikelihoodforthetouriststogoshoppingordiningintheparkmaybecomelargerandsodoesthelikelihoodfortheCEOstoearnmoreprofitgains（althoughwecannotexactlycontrolthebehavioroftourists）.Ontheotherhand,touristsalsoprefertohavemorefreetimeforplayingorshoppingratherthanpassivelywaitinanendlessline.

Weputemphasisontheincreaseofaveragefreetimeforallthetourists,includingQPholdersandtouristsintheregularline.Obviously,QPsystemcanincreasethefreetimeofthoseQPholders,butatthesametimesomeoftheQPstrategiesmayalsostretchthewaitingtimeofthoseintheregularlines.SincetotheCEOsthetwogroupsoftouristshaveequalstatus,weshouldtakeintoaccounttheinterestsofbothgroups.SomeofourQPschemescanincreasethefreetimeforbothQPholdersandregulartourists.

2.Tomaintainawaitinglinewithappropriatelengthinfrontofeachattraction

Thisstatementmayseemalittleconfusingatthefirstsight,butaccordingtothecommentsfrommanyCEOSofamusementparks,theyhopethatthereisawaitinglineinfrontofeachattractionbecauseitisasymbolofattractivenessofthisattraction.Obviously,theQPrulestrytoreducethewaitingline.ButthegoalofourQPsystemistomaintainawaitinglinewithappropriatelengthinsteadofeliminatingtheline.

Fromtheaboveanalysis,wefindthatthepursuitsofCEOandtouristsarequitesimilar:

morefreetimefortourists.WithregardtothesecondhopeofCEO,althoughitisobviouslynotthehopeoftourists,mosttouristsarewillingtoacceptalinewithanappropriatelength,especiallyinathemepark.

2Assumptions

●Atouristonlybuysonetickettoenteranamusementparkandnoextramoneyforplayinginanyattraction.Butgoingshoppingordiningintheparkisextracost.

●TouristscanfreelychoosewhetherornottorequestaQPticket.

●EverytouristisallowedtohaveonlyoneQPticketatatime.

●Thelengthofreturntimewindowisaconstantvalue.

●Acertainpercentage（1-m%）ofQPholderswillreturntotheattractionatthedesignatedtime.

●OverdueQPticketisinvalid.

●Thereisnobreakdownofanattractionandstaffsoftheattractionarealwaysworkingduringbusinesshours.Therefore,thecapacityofanattractionremainsconstantduringaday.

3TermsandDefinition

Name

Definition

ri

thearrivetimeoftouristi

qi

thelengthofregularlinewhentouristiarrives

vi

thelengthofvirtualline（thenumberofthepreviousvalidQPholders）whentouristiarrives

Ti

ther