交通分配预测

Week11ByL.Wu,FacultyofCivilEng.,NFU1Section5TrafficAssignment第五节交通分配预测UserEquilibrium&SystemOptimization用户均衡分配与系统优化分配Week11ByL.Wu,FacultyofCivilEng.,NFU2ThefourstepsTrafficGenerationTrafficDistributionTrafficModalSplitTrafficAssignmentWhether?Where?Whichmode?Whichroad?Week11ByL.Wu,FacultyofCivilEng.,NFU3Thefoursteps(cont’d)Tripgeneration:Determinethenumberoftripsoriginatingandterminatingindifferentzonesofthestudyarea.Output:tripproduction&attraction.Tripdistribution:Describetheallocationoftripsfromapointoforigintothedestinationzones.Output:ODmatrix.Week11ByL.Wu,FacultyofCivilEng.,NFU4Thefoursteps(cont’d)Modechoice(Modalsplit):Determinetheportionofthetotalnumberoftripsmadebetweenanoriginanddestinationusingdifferenttransportmodes.Output:modeusagerate（方式划分率）.Routechoice(Trafficassignment):AllocateODtripstoroutesinthetransportationnetworktoestimatetheresultingvolume,traveltimeandspeed,etc.Output:trafficflowonthesectionsandpattern(路段上的交通流量以及交通方式).Week11ByL.Wu,FacultyofCivilEng.,NFU5ElementsofTrafficAssignmentGraphrepresentationofthenetworkcentroids,links,nodes,connectorsLinkperformancefunction(s)PrinciplesofroutechoiceWeek11ByL.Wu,FacultyofCivilEng.,NFU6LinkPerformanceFunctions路阻函数Amathematicalformularepresentingthetravelimpedance,levelofserviceofthelinkAsknownaslinkcostfunctionTraveltimeisthemeasureusedmostoften.(有时候会考虑距离和固定费用：linkdistance+fixedcosts)CrucialtotrafficassignmentWeek11ByL.Wu,FacultyofCivilEng.,NFU7LinkPerformanceFunctions路阻函数Expected‘nice’propertiesAconvexfunction－凸函数Positive,nonlinear,strictlyincreasingfunctionsoflinkflow－是流量的正的，非线性严格递增的函数ThemostfamousoneistheBPR(BureauofPublicRoads)functionWeek11ByL.Wu,FacultyofCivilEng.,NFU8LinkPerformanceFunctions路阻函数BPRfunctionWeek11ByL.Wu,FacultyofCivilEng.,NFU9LinkPerformanceFunctions路阻函数Week11ByL.Wu,FacultyofCivilEng.,NFU10LinkPerformanceFunctions路阻函数AdditionalNotes…Whyconvex?Foraminimizationprogram,aconvexobjectivefunctionisthesufficient(secondorder)conditionfortheoptimalsolutiontoexist(assumingthattheconstraintsetisaconvexset).TheHessianmatrixofaconvexfunctionisnotedasPositiveDefinite(P.D.).Week11ByL.Wu,FacultyofCivilEng.,NFU11PrinciplesTrafficAssignment交通分配原理Thefinalstepinthemodelingprocess.Vehicletripsfromonezonetoanotherareassignedtospecifictravelroutesbetweenzones.Thisassignmentisdoneonthebasisofminimumgeneralizedcost(最小的通用费用)oftravelbetweeneachO-Dpairofzones－但并不表示路径唯一！Thisgeneralizedcostasdefinedearlierisalinearcombinationofthelinkjourneytimeandthelinkdistance+fixedcostssuchasparkingortolls.Whenwearedonewehaveanassignednetwork!Week11ByL.Wu,FacultyofCivilEng.,NFU12TrafficAssignmentWeek11ByL.Wu,FacultyofCivilEng.,NFU13Week11ByL.Wu,FacultyofCivilEng.,NFU14Week11ByL.Wu,FacultyofCivilEng.,NFU15交通分配模型分类交通分配模型通常分为非平衡模型：non-equilibriummodels最短路（全有全无）交通分配法－shortestpathmethod(alsocalledall-or-nothingmethod)容量限制法－minimumpathwithcapacityrestraintsmethod多路径概率交通分配法(probabilityofmulti-pathmethod)容量限制－多路径分配平衡模型：EquilibriummodelsUserEquilibriumSystemOptimizationWeek11ByL.Wu,FacultyofCivilEng.,NFU16ShortestPathMethod最短路分配法也叫全有全无分配法是一种静态的交通分配方法；取两点间的行驶时间为常数；在分配中，取路权（两交叉口间的出行时间）为常数，即假设车辆的路段行驶车速、交叉口延误不受路段、交叉口交通负荷的影响。每一OD点对应的OD量被全部分配在连接该OD点对的最短线路上，其他道路上分配不到交通量。所有的OD对的OD量按上述原则全部分配在路网上，累加各路段的交通量。Week11ByL.Wu,FacultyofCivilEng.,NFU17ShortestPathMethod(cont’d)最短路分配法该分配法进行交通分配时，不考虑路段通行能力的限制；也不考虑过多的交通量将影响行车速度；特点：计算简单；是其他分配方法的基础。缺点：交通量在路网上分配不均，出行的交通量全部集中在最短路上；且网络总费用值较大。总费用＝关键是求最短路：最常用的方法有Dijkstra算法。ahadcZa0Week11ByL.Wu,FacultyofCivilEng.,NFU18ShortestPathMethod(cont’d)最短路分配法最短路交通分配法的步骤1.确定路段行驶时间。2.确定各OD点之间的最短路径。3.各交通区之间的交通量全部放在路阻最小的路径上，其余的路径上的交通量为零。4.累计得出各路段的交通量。Week11ByL.Wu,FacultyofCivilEng.,NFU19ShortestPathMethod(cont’d)最短路分配法Example:用最短路法分配该OD矩阵ODABCDA0200200500B2000500100C2005000250D5001002500Week11ByL.Wu,FacultyofCivilEng.,NFU20ShortestPathMethod(cont’d)最短路分配法解:（1）确定路段行驶时间（已知的）（2）确定A、B、C、D四个交通区的最短路径。可用Dijkstra的方法求得：Week11ByL.Wu,FacultyofCivilEng.,NFU21ShortestPathMethod(cont’d)最短路分配法（3）分配OD量将各OD点对的OD量分配到与该OD点对相对应的最短路径上。A-BA-CA-DB-AB-CB-DC-AC-BC-DD-AD-BD-C双向交通量1-22002004001-420050020050014002-32002004002-503-650010050010012004-550050050050020004-720050020050014005-650050050050020005-806-950010050010012007-82502505008-9250250500OD量200200500200500100200500250500100250Week11ByL.Wu,FacultyofCivilEng.,NFU22容量限制分配法也是把交通量分配到最小路权的线路上；考虑了车速与交通量之间的关系，即考虑了交叉口、路段的通行能力限制，比较符合实际情况。容量限制分配法的关键是路权的确定。Week11ByL.Wu,FacultyofCivilEng.,NFU23容量限制分配法容量限制分配法的步骤1.用一般方法把交通表示为路网,以“零流量”路段行程时间开始；2.依次对每个起点分区计算通过路网的最短行程时间的通路；3.按全有全无分配模型,将OD点的交通模式加到路网；4.计算分配到每条路段上的交通量；5.在流量与行程时间的关系式中，用分配给路段的交通量计算路段行程时间，重新计算最短路；6.按全有全无分配模型将原来OD点的交通模式加到路网上,但要用由步骤5得出的新的最短路上；7.返回到步骤4，继续分配，直到分配的交通量和行程时间稳定为止。Week11ByL.Wu,FacultyofCivilEng.,NFU24容量限制分配法容量限制法进行分配时，需先将OD表中的每一个OD量分解成k部分，即分解成k个OD分表，然后分k次用最短路法分配，每次分配一个OD分表，并且每分配一次，路权修正一次，直到把k个OD分表全部分配在路网上。Week11ByL.Wu,FacultyofCivilEng.,NFU25容量限制分配法分配次数k与每次的OD分配率(%)AB40+202030+1010401020+4030+1030出行量T(A--B)=40+30+20+10容量限制分配法Week11ByL.Wu,FacultyofCivilEng.,NFU27多路径概率分配法出行者希望选择效用最大的路径出行－最短路因素但是路网有其复杂性和交通状况的随机性，出行