交通分配预测

Section5TrafficAssignment

第五节交通分配预测UserEquilibrium&SystemOptimization用户均衡分配与系统优化分配Week111ByL.Wu,FacultyofCivilEng.,NFUThefourstepsTrafficGenerationTrafficDistributionTrafficModalSplitTrafficAssignmentWhether?Where?Whichmode?Whichroad?Week112ByL.Wu,FacultyofCivilEng.,NFUThefoursteps(cont’d)Tripgeneration:Determinethenumberoftripsoriginatingandterminatingindifferentzonesofthestudyarea.Output:tripproduction&attraction.Tripdistribution:Describetheallocationoftripsfromapointoforigintothedestinationzones.Output:ODmatrix.Week113ByL.Wu,FacultyofCivilEng.,NFUThefoursteps(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).Week114ByL.Wu,FacultyofCivilEng.,NFUElementsofTrafficAssignmentGraphrepresentationofthenetworkcentroids,links,nodes,connectorsLinkperformancefunction(s)PrinciplesofroutechoiceWeek115ByL.Wu,FacultyofCivilEng.,NFULinkPerformanceFunctions

路阻函数Amathematicalformularepresentingthetravelimpedance,levelofserviceofthelinkAsknownaslinkcostfunctionTraveltimeisthemeasureusedmostoften.(有时候会考虑距离和固定费用：linkdistance+fixedcosts)CrucialtotrafficassignmentWeek116ByL.Wu,FacultyofCivilEng.,NFULinkPerformanceFunctions

路阻函数Expected‘nice’propertiesAconvexfunction－凸函数Positive,nonlinear,strictlyincreasingfunctionsoflinkflow－是流量的正的，非线性严格递增的函数ThemostfamousoneistheBPR(BureauofPublicRoads)functionWeek117ByL.Wu,FacultyofCivilEng.,NFULinkPerformanceFunctions

路阻函数BPRfunctionWeek118ByL.Wu,FacultyofCivilEng.,NFULinkPerformanceFunctions

路阻函数Week119ByL.Wu,FacultyofCivilEng.,NFULinkPerformanceFunctions

路阻函数AdditionalNotes…Whyconvex?Foraminimizationprogram,aconvexobjectivefunctionisthesufficient(secondorder)conditionfortheoptimalsolutiontoexist(assumingthattheconstraintsetisaconvexset).TheHessianmatrixofaconvexfunctionisnotedasPositiveDefinite(P.D.).Week1110ByL.Wu,FacultyofCivilEng.,NFUPrinciplesTrafficAssignment

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!Week1111ByL.Wu,FacultyofCivilEng.,NFUTrafficAssignmentWeek1112ByL.Wu,FacultyofCivilEng.,NFUWeek1113ByL.Wu,FacultyofCivilEng.,NFUWeek1114ByL.Wu,FacultyofCivilEng.,NFU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：EquilibriummodelsUserEquilibriumSystemOptimizationWeek1115ByL.Wu,FacultyofCivilEng.,NFUShortestPathMethod

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。Week1116ByL.Wu,FacultyofCivilEng.,NFUShortestPathMethod(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。Week1117ByL.Wu,FacultyofCivilEng.,NFUShortestPathMethod(cont’d)

最短路分配法最短路交通分配法的步骤确定路段行驶时间。确定各OD点之间的最短路径。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。累计得出各路段的交通量。Week1118ByL.Wu,FacultyofCivilEng.,NFUShortestPathMethod(cont’d)

最短路分配法Example:用最短路法分配该OD矩阵ODABCDA0200200500B2000500100C2005000250D5001002500Week1119ByL.Wu,FacultyofCivilEng.,NFUShortestPathMethod(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：Week1120ByL.Wu,FacultyofCivilEng.,NFUShor扫test后Pat较hMe疫thod鼠(co拍nt’d益)最短路亦分配法（3）分配OD量将各OD点对的OD量分配暂到与该OD点对相对垮应的最短路栽径上。Week旨1121By钟L.罩Wu,出Fa境cul蚊ty硬of磁Civ门il伪Eng猪.,浴NFU容量限制培分配法也是把锣交通量嘉分配到朴最小路稿权的线嘴路上；考虑了车生速与交通户量之间的尺关系，即渗考虑了交滨叉口、路朗段的通行降能力限制群，比较符蛾合实际情地况。容量限近制分配瞧法的关统键是路奸权的确寄定。Week过1122By欠L.具Wu,先Fa论cul桥ty亲of茫Civ们il爪Eng愤.,咏NFU容量限糕制分配挤法容量限制穿分配法的炒步骤1.用一般方占法把交通段表示为路速网,以“零流量”路段行程搅时间开始培；2.依次对每燥个起点分坚区计算通查过路网的配最短行程烦时间的通缸路；3.按全有蝴全无分诵配模型,将OD点的交用通模式指加到路鸡网；4.计算分配盗到每条路枕段上的交粘通量；5.在流量视与行程暗时间的敲关系式欧中，用累分配给宰路段的攻交通量抖计算路圆段行程岗时间，史重新计畅算最短在路；6.按全有皂全无分扬配模型矮将原来OD点的交通档模式加到堡路网上,但要用由团步骤5得出的新度的最短路板上；7.返回到步凯骤4，继续群分配，强直到分绸配的交涛通量和叛行程时移间稳定匪为止。Wee况k1肌123ByL哨.Wu劈燕,Fa巾cult敞yof悉Civ府ilE箱ng.,河NFU容量限悬制分配之法容量限制陵法进行分标配时，需彼先将OD表中的认每一个OD量分解肺成k部分，即每分解成k个OD分表，纷然后分k次用最药短路法糠分配，撑每次分传配一个OD分表，扑并且每适分配一株次，路色权修正临一次，倒直到把k个OD分表全部聪分配在路粱网上。Week叨1124By在L.屠Wu,问Fa隐cul压ty撇of舱Civ母il架Eng磨.,距NFU容量限制颂分配法分配次数k与每次犯的OD分配率(%)Week雷1125By父L.督Wu,石Fa停cul部ty屡of染Civ磁il亮Eng溪.,窑NFUAB40+202030+1010401020+4030+1030出行量T(A-疼-B)架=40+30+20宪+10容量限馋制分配由法多路径考概率分礼配法出行者希拨望选择效许用最大的庭路径出行革－最短路州因素但是路轿网有其君复杂性齐和交通斧状况的婆随机性绳，出行赚者在选花择出行矮路线的脆时候往不往带有圈不确定坟性－随机因趴素考虑这两恳种因素的肥主次地位治，各出行械线路被选鞋用的概率谈可用Log喜it型的路泉径选择孟模型计将算。Wee昆k1破127By谋L.异Wu,锋Fa昌cul徒ty军of蝴Civ牌il悄Eng举.,威NFU多路径剃概率分挽配法Week辆1128ByL说.Wu芦,Fa繁cult蚂yof哲Civ臣ilE仓ng.,列NFU多路径概悬率分配法多路径箩概率分邀配法中伏的有效恶路段和疾有效出租行路径有效路段贩：定义有细效路段[i,j]为路段味终点j比路段什起点i更靠近出宏行终点s的路段。有效路慨径：由狼有效路妈段组成智的连接OD的路径避。每一OD量只在纤它相应主的有效李出行路源线上进薪行分配桃。Week兄1129By啄L.教Wu,由Fa仁cul带ty毒of垃Civ灰il门Eng窗.,捉NFU多路径支概率分持配法Exam谣ple:A区到D区的OD出行量怨为T(1才,9)恳=90追0ve动h/d尘,试用多啊路径概率分配伤法将OD分配到路嫁网上。Wee妙k1转130ByL六.Wu梨,Fa素cult叠yof酿Civ时ilE盯ng.,命NFU多路径咬概率分彼配法解:(壶1)计算各节财点至终点9的最短路菠权：(2)令i等于出行偶起点r，即从r开始进行顾分配；(3)判别与约节点i邻接的有协效路段，仙并计算有氧效路径长度短。判别条狂件：if，则它湾为有效路段，有效路小径长度：Week震1131ByL养.Wu射,Fa蜡cult层yof队Civ挖ilE掉ng.,由NFU多路径概穗率分配法起点1邻接的仙两条路泪段[1,2斤]、[1,若4]都是有寇效路段爸，则(4)计算Logi队t型的分子(5)计算Log售it型的分母Wee姑k1昆132By识L.堪Wu,凶Fa薯cul释ty吵of先Civ艇il纳Eng患.,皱NFU多路径概机率分配法(6)计算有效译路段的分荷配率：Wee席k1驶133ByL表.Wu望,Fa拾cult洗yof挣Civ话ilE誉ng.,建NF