交通分配预测.ppt
Section 5 Traffic Assignment第五节 交通分配预测User Equilibrium&System Optimization用户均衡分配与系统优化分配Week 111By L.Wu,Faculty of Civil Eng.,NFUThe four stepsnTraffic Generation nTraffic DistributionnTraffic Modal SplitnTraffic AssignmentWhether?Where?Which mode?Which road?Week 112By L.Wu,Faculty of Civil Eng.,NFUThe four steps(contd)nTrip generation:nDetermine the number of trips originating and terminating in different zones of the study area.nOutput:trip production&attraction.nTrip distribution:nDescribe the allocation of trips from a point of origin to the destination zones.nOutput:OD matrix.Week 113By L.Wu,Faculty of Civil Eng.,NFUThe four steps(contd)nMode choice(Modal split):nDetermine the portion of the total number of trips made between an origin and destination using different transport modes.nOutput:mode usage rate（方式划分率）.nRoute choice(Traffic assignment):nAllocate OD trips to routes in the transportation network to estimate the resulting volume,travel time and speed,etc.nOutput:traffic flow on the sections and pattern(路段上的交通流量以及交通方式).Week 114By L.Wu,Faculty of Civil Eng.,NFUElements of Traffic AssignmentnGraph representation of the networkncentroids,links,nodes,connectorsnLink performance function(s)nPrinciples of route choiceWeek 115By L.Wu,Faculty of Civil Eng.,NFULink Performance Functions路阻函数nA mathematical formula representing the travel impedance,level of service of the linknAs known as link cost functionnTravel time is the measure used most often.(有时候会考虑距离和固定费用：link distance+fixed costs)nCrucial to traffic assignmentWeek 116By L.Wu,Faculty of Civil Eng.,NFULink Performance Functions路阻函数nExpected nice propertiesnA convex function 凸函数nPositive,nonlinear,strictly increasing functions of link flow 是流量的正的，非线性严格递增的函数nThe most famous one is the BPR(Bureau of Public Roads)functionWeek 117By L.Wu,Faculty of Civil Eng.,NFULink Performance Functions路阻函数BPR functionWeek 118By L.Wu,Faculty of Civil Eng.,NFULink Performance Functions路阻函数Week 119By L.Wu,Faculty of Civil Eng.,NFULink Performance Functions路阻函数nAdditional NotesnWhy convex?nFor a minimization program,a convex objective function is the sufficient(secondorder)condition for the optimal solution to exist(assuming that the constraint set is a convex set).nThe Hessian matrix of a convex function is noted as Positive Definite(P.D.).Week 1110By L.Wu,Faculty of Civil Eng.,NFUPrinciples Traffic Assignment交通分配原理nThe final step in the modeling process.nVehicle trips from one zone to another are assigned to specific travel routes between zones.nThis assignment is done on the basis of minimum generalized cost(最小的通用费用)of travel between each O-D pair of zones 但并不表示路径唯一！nThis generalized cost as defined earlier is a linear combination of the link journey time and the link distance+fixed costs such as parking or tolls.nWhen we are done we have an assigned network!Week 1111By L.Wu,Faculty of Civil Eng.,NFUTraffic AssignmentWeek 1112By L.Wu,Faculty of Civil Eng.,NFUWeek 1113By L.Wu,Faculty of Civil Eng.,NFUWeek 1114By L.Wu,Faculty of Civil Eng.,NFU交通分配模型分类n交通分配模型通常分为n非平衡模型：non-equilibrium modelsn最短路（全有全无）交通分配法 shortest path method(also called all-or-nothing method)n容量限制法minimum path with capacity restraints methodn多路径概率交通分配法(probability of multi-path method)n容量限制多路径分配n平衡模型：Equilibrium modelsnUser EquilibriumnSystem OptimizationWeek 1115By L.Wu,Faculty of Civil Eng.,NFUShortest Path Method最短路分配法n也叫全有全无分配法n是一种静态的交通分配方法；n取两点间的行驶时间为常数；n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。n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。Week 1116By L.Wu,Faculty of Civil Eng.,NFUShortest Path Method(contd)最短路分配法n该分配法进行交通分配时，不考虑路段通行能力的限制；n也不考虑过多的交通量将影响行车速度；n特点：计算简单；是其他分配方法的基础。n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n关键是求最短路：最常用的方法有Dijkstra算法。Week 1117By L.Wu,Faculty of Civil Eng.,NFUShortest Path Method(contd)最短路分配法n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。Week 1118By L.Wu,Faculty of Civil Eng.,NFUShortest Path Method(contd)最短路分配法Example:用最短路法分配该OD矩阵 ODABCDA0200200500B2000500100C2005000250D5001002500Week 1119By L.Wu,Faculty of Civil Eng.,NFUShortest Path Method(contd)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：Week 1120By L.Wu,Faculty of Civil Eng.,NFUShortest Path Method(contd)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。Week 1121By L.Wu,Faculty of Civil Eng.,NFU容量限制分配法n也是把交通量分配到最小路权的线路上；n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。n容量限制分配法的关键是路权的确定。Week 1122By L.Wu,Faculty of Civil Eng.,NFU容量限制分配法n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。Week 1123By L.Wu,Faculty of Civil Eng.,NFU容量限制分配法n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。Week 1124By L.Wu,Faculty of Civil Eng.,NFU容量限制分配法分配次数分配次数k与每次的与每次的OD分配率分配率(%)Week 1125By L.Wu,Faculty of Civil Eng.,NFUAB40+202030+1010401020+4030+1030出行量出行量T(A-B)=40+30+20+10容量限制分配法多路径概率分配法n出行者希望选择效用最大的路径出行最短路因素n但是路网有其复杂性和交通状况的随机性，出行者在选择出行路线的时候往往带有不确定性随机因素n考虑这两种因素的主次地位，各出行线路被选用的概率可用Logit型的路径选择模型计算。Week 1127By L.Wu,Faculty of Civil Eng.,NFU多路径概率分配法Week 1128By L.Wu,Faculty of Civil Eng.,NFU多路径概率分配法n多路径概率分配法中的有效路段和有效出行路径n有效路段：定义有效路段i,j为路段终点j比路段起点i更靠近出行终点s的路段。n有效路径：由有效路段组成的连接OD的路径。n每一OD量只在它相应的有效出行路线上进行分配。Week 1129By L.Wu,Faculty of Civil Eng.,NFU多路径概率分配法Example:A区到D区的OD出行量为T(1,9)=900veh/d,试用多路径概率分配法将OD分配到路网上。Week 1130By L.Wu,Faculty of Civil Eng.,NFU多路径概率分配法解:(1)计算各节点至终点9的最短路权：(2)令i等于出行起点r，即从r开始进行分配；(3)判别与节点i邻接的有效路段，并计算有效路径长度。判别条件：if ，则它为有效路段，有效路径长度：Week 1131By L.Wu,Faculty of Civil Eng.,NFU多路径概率分配法起点1邻接的两条路段1,2、1,4都是有效路段，则(4)计算Logit型的分子(5)计算Logit型的分母Week 1132By L.Wu,Faculty of Civil Eng.,NFU多路径概率分配法(6)计算有效路段的分配率：Week 1133By L.Wu,Faculty of Civil Eng.,NFU多路径概率分配法(7)计算有效路段i,j的分配交通量Q(i,j)(8)将2点和4点分别作为i，返回到(3)，并一直继续到i=s点的时候为止Week 1134By L.Wu,Faculty of Civil Eng.,NFU多路径概率分配法Week 1135By L.Wu,Faculty of Civil Eng.,NFU容量限制多路径分配法n容量限制多路径分配法n思路类似于容量限制分配方法；n将OD表分若干次进行分配；n每分配一次，修改路权一次，然后再进行一次多路径概率分配。如此循环，直至全部OD量分配完毕。Week 1136By L.Wu,Faculty of Civil Eng.,NFU
