URBAN-TRANSPORTATION-NETWORKS

TEACHINGMATERIALSNOVEMBER2005EXTRACTOFURBANTRANSPORTATIONNETWORKS:EquilibriumAnalysiswithMathematicalProgrammingMethodsByYOSEFSHEFFIEquilibriumAnalysisforUrbanTransportationNetwork1CHAPTER1URBANTRANSPORTATIONNETWORKANALYSISTheamountoftraveltakingplaceatagivenmomentonanystreet,intersection,ortransitlineinanurbanareaistheresultofmanyindividuals’decisions.Travelerschooseifandwhentotakeatripfromsomepurpose,whichmodeoftransportationtouse(e.g.whethertodriveortakepublictransit),wheretogo,andwhichwaytogetthere.Thesedecisionsdepend,onpart,onhowcongestedthetransportationsystemisandwherethecongestedpointsare.Congestiononanypointofthetransportationsystem,however,dependsontheamountoftravelthroughthatpoint.Thisbookdescribeshowtheseinteractionsbetweencongestionandtraveldecisioncanbemodeledandsolvedsimultaneouslytoobtaintheflowpatternthroughouttheurbantransportationnetwork.Oneofthemajorproblemsfacingtransportationengineersandurbanplannersisthatofpredictingtheimpactofgiventransportationscenarios.Theanalyticpartofthisproblemcanbedealtwithintwomainstages.First,thescenarioisspecifiedmathematicallyasasetofinputsthatareusedtopredicttheflowpatternresultinginfromsuchascenario.Second,theflowpatternisusedtocalculateanarrayofmeasuresthatcharacterizethescenariounderstudy.Theinputstotheanalysistypicallyincludeadescriptionofthefollowing(eitherexistingorprojected):1.Thetransportationinfrastructureandservices,includingstreets,intersections,andtransitlines.2.Thetransportationoperatingandcontrolpolicies.3.Thedemandfortravel,includingtheactivityandland-usepatterns.Thefirststageoftheanalysisusestheseinputstocalculatetheflowthrougheachcomponentoftheurbannetwork.Flowismeasuredintermsofthenumberoftravelunits(vehicles,passengers,pedestrians)thattraverseagiventransportationfacilityinaunittime.Thispartoftheanalysisbuildsonfunctionalrelationshipsbetweenflowsandcongestionaswellasrelationshipsbetweencongestionandtraveldecisions.Thesecondstageoftheanalysisinvolvesthecalculationofanarrayofmeasuresofinterest,giventheflowpattern.Thesemayincludethefollowing:1.Levelofservicemeasures,suchastraveltimeandtravelcosts.Theseaffecttheusersofthetransportationsystemdirectly.2.Operatingcharacteristics,suchasrevenuesandprofits.Theseareofprimaryconcerntotheoperatorsofthesystem.3.Flowby-products,suchaspollutionandchangesinlandvalues.Theseaffecttheenvironmentinwhichatransportationsystemisoperated.EquilibriumAnalysisforUrbanTransportationNetwork24.Welfaremeasures,suchasaccessibilityandequity.Thesemayindirectlyaffectvariouspopulationgroups.Thefocusofthisbookisonthefirststageoftheanalysis,thatofdeterminingtheflowpattern,giventheinputs.Manyoftheaforementionedmeasurescanbecalculatedfromtheseflowsinastraightforwardmanner.Others(suchaspollutionlevelorequitymeasures)mayrequiresophisticatedmethodologiesandcomplexmodelswhicharenotwithinthescopeofthisbook.Theseanalysis,however,usetheflowpatternasamajorinput.Inaddition,acompleteanalysisofagivenscenariomayinvolveimportantconsiderationswhicharenotbasedontheflow,suchasconstructioncostsandpoliticalandinstitutionalfactors.Theperspectiveofthemodelingapproachpresentedinthistextisdescriptiveratherthannormative.Inotherwords,itdescribeshowindividualstravelthroughanurbannetworkgiventhecomponentsofthatsystem(whicharespecifiedasinputs).Itdoesnotattempttodeterminetheoptimalsystemconfiguration(interms,say,ofwhichprojectshouldbebuiltorwhatkindofcontrolpoliciesshouldbeutilized).Inmanycases,however,theanalysisismotivatedbytheneedtodecideonagiventransportationinvestment,regulation,orpolicyfromamongasetofalternativecoursesofaction.Inthiscase,eachofthealternativescenariosshouldbespecifiedmathematicallyasasetofinputstotheanalysis.Themodelsdescribedinthisbookarethenformulatedandsolvedforeachalternativescenarioinordertopredicttheflowpatternthatisused,inturn,itdevelopmentmanyofthemeasuresofinterest.Thefullsetofmeasuresassociatedwitheachalternativeisthenusedtocomparetheirrespectiveimpacts.Thesemeasuresare,typically,alsocomparedtothesetofmeasurescharacterizingabasecase(whichcanbethecurrentsystemoraprojectionofhowthecurrentsystemwilloperateunderthedo-nothingalternative).Thesecomparisonsserveasabasisforrecommendationregardingpreferredcourseofaction.Thisbookpresentsassumptions,models,andalgorithmsusedtocalculatetheflowpatternfromtheinputs.Thethrustofthebookistheinteractionofcongestionandtraveldecisionthatresultinthisflow.Sincecongestionincreaseswithflowandtripsarediscouragedbycongestion,thisinteractioncanbemodeledasaprocessofreachingequilibriumbetweencongestionandtraveldecision.Theremainderofthischapterintroducesandexplainsthenotionofequilibriuminthecontextofurbantransportationanalysis.Section1.1presentsthisequilibriumingeneralterms,andcontrastsitwiththemorefamiliareconomicequilibriumframework.Section1.2describesthemathematicalrepresentationoftheurbantransportationsystemasanetwork.Thenetworkrepresentationisafundamentalcharacteristicoftheequilibriumdiscussedinthistext.Section1.3givestheactualdefinitionofseveralequilibriabetweencongestionandtraveldecisions.Theseeq