交通分配預測

Section5TrafficAssignment

第五節(jié)交通分配預測UserEquilibrium&SystemOptimization用戶均衡分配與系統(tǒng)優(yōu)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（方式劃分率）.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

路阻函數Amathematicalformularepresentingthetravelimpedance,levelofserviceofthelinkAsknownaslinkcostfunctionTraveltimeisthemeasureusedmostoften.(有時候會考慮距離和固定費用：linkdistance+fixedcosts)CrucialtotrafficassignmentWeek116ByL.Wu,FacultyofCivilEng.,NFULinkPerformanceFunctions

路阻函數Expected‘nice’propertiesAconvexfunction－凸函數Positive,nonlinear,strictlyincreasingfunctionsoflinkflow－是流量的正的，非線性嚴格遞增的函數ThemostfamousoneistheBPR(BureauofPublicRoads)functionWeek117ByL.Wu,FacultyofCivilEng.,NFULinkPerformanceFunctions

路阻函數BPRfunctionWeek118ByL.Wu,FacultyofCivilEng.,NFULinkPerformanceFunctions

路阻函數Week119ByL.Wu,FacultyofCivilEng.,NFULinkPerformanceFunctions

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

交通分配原理Thefinalstepinthemodelingprocess.Vehicletripsfromonezonetoanotherareassignedtospecifictravelroutesbetweenzones.Thisassignmentisdoneonthebasisofminimumgeneralizedcost(最小的通用費用)oftravelbetweeneachO-Dpairofzones－但并不表示路徑唯一！Thisgeneralizedcostasdefinedearlierisalinearcombinationofthelinkjourneytimeandthelinkdistance+fixedcostssuchasparkingortolls.Whenwearedonewehaveanassignednetwork!Week1111ByL.Wu,FacultyofCivilEng.,NFUTrafficAssignmentWeek1112ByL.Wu,FacultyofCivilEng.,NFUWeek1113ByL.Wu,FacultyofCivilEng.,NFUWeek1114ByL.Wu,FacultyofCivilEng.,NFU交通分配模型分類交通分配模型通常分為非平衡模型：non-equilibriummodels最短路（全有全無）交通分配法－shortestpathmethod(alsocalledall-or-nothingmethod)容量限制法－minimumpathwithcapacityrestraintsmethod多路徑概率交通分配法(probabilityofmulti-pathmethod)容量限制－多路徑分配平衡模型：EquilibriummodelsUserEquilibriumSystemOptimizationWeek1115ByL.Wu,FacultyofCivilEng.,NFUShortestPathMethod

最短路分配法也叫全有全無分配法是一種靜態(tài)的交通分配方法；取兩點間的行駛時間為常數；在分配中，取路權（兩交叉口間的出行時間）為常數，即假設車輛的路段行駛車速、交叉口延誤不受路段、交叉口交通負荷的影響。每一OD點對應的OD量被全部分配在連接該OD點對的最短線路上，其他道路上分配不到交通量。所有的OD對的OD量按上述原則全部分配在路網上，累加各路段的交通量。Week1116ByL.Wu,FacultyofCivilEng.,NFUShortestPathMethod(cont’d)

最短路分配法該分配法進行交通分配時，不考慮路段通行能力的限制；也不考慮過多的交通量將影響行車速度；特點：計算簡單；是其他分配方法的基礎。缺點：交通量在路網上分配不均，出行的交通量全部集中在最短路上；且網絡總費用值較大?？傎M用＝關鍵是求最短路：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驟確定路段行駛時間。確定各OD點之間的最短路徑。各交通區(qū)之間的交通量全部放在路阻最小的路徑上，其余的路徑上的交通量為零。累計得出各路段的交通量。Week1118ByL.Wu,FacultyofCivilEng.,NFUShortestPathMethod(cont’d)

最短路分配法Example:用最短路法分配該OD矩陣ODABCDA0200200500B2000500100C2005000250D5001002500Week1119ByL.Wu,FacultyofCivilEng.,NFUShortestPathMethod(cont’d)

最短路分配法解:（1）確定路段行駛時間（已知的）（2）確定A、B、C、D四個交通區(qū)的最短路徑。可用Dijkstra的方法求得：Week1120ByL.Wu,FacultyofCivilEng.,NFUShor掃test后Pat較hMe疫thod鼠(co拍nt’d益)最短路亦分配法（3）分配OD量將各OD點對的OD量分配暫到與該OD點對相對垮應的最短路栽徑上。Week旨1121By鐘L.罩Wu,出Fa境cul蚊ty硬of磁Civ門il偽Eng豬.,浴NFU容量限制培分配法也是把鑼交通量嘉分配到樸最小路稿權的線嘴路上；考慮了車生速與交通戶量之間的尺關系，即滲考慮了交濱叉口、路朗段的通行降能力限制群，比較符蛾合實際情地況。容量限近制分配瞧法的關統(tǒng)鍵是路奸權的確寄定。Week過1122By欠L.具Wu,先Fa論cul橋ty親of茫Civ們il爪Eng憤.,詠NFU容量限糕制分配擠法容量限制穿分配法的炒步驟1.用一般方占法把交通段表示為路速網,以“零流量”路段行程攪時間開始培；2.依次對每燥個起點分堅區(qū)計算通查過路網的配最短行程煩時間的通缸路；3.按全有蝴全無分誦配模型,將OD點的交用通模式指加到路雞網；4.計算分配盜到每條路枕段上的交粘通量；5.在流量視與行程暗時間的敲關系式歐中，用累分配給宰路段的攻交通量抖計算路圓段行程崗時間，史重新計暢算最短在路；6.按全有皂全無分揚配模型矮將原來OD點的交通檔模式加到堡路網上,但要用由團步驟5得出的新度的最短路板上；7.返回到步凱驟4，繼續(xù)群分配，強直到分綢配的交濤通量和叛行程時移間穩(wěn)定匪為止。Wee況k1肌123ByL哨.Wu劈燕,Fa巾cult敞yof悉Civ府ilE箱ng.,河NFU容量限懸制分配之法容量限制陵法進行分標配時，需彼先將OD表中的認每一個OD量分解肺成k部分，即每分解成k個OD分表，紛然后分k次用最藥短路法糠分配，撐每次分傳配一個OD分表，撲并且每適分配一株次，路色權修正臨一次，倒直到把k個OD分表全部聰分配在路粱網上。Week叨1124By在L.屠Wu,問Fa隱cul壓ty撇of艙Civ母il架Eng磨.,距NFU容量限制頌分配法分配次數k與每次犯的OD分配率(%)Week雷1125By父L.督Wu,石Fa停cul部ty屢of染Civ磁il亮Eng溪.,窯NFUAB40+202030+1010401020+4030+1030出行量T(A-疼-B)架=40+30+20憲+10容量限饞制分配由法多路徑考概率分禮配法出行者希撥望選擇效許用最大的庭路徑出行革－最短路州因素但是路轎網有其君復雜性齊和交通斧狀況的婆隨機性繩，出行賺者在選花擇出行矮路線的脆時候往不往帶有圈不確定墳性－隨機因趴素考慮這兩懇種因素的肥主次地位治，各出行械線路被選鞋用的概率談可用Log喜it型的路泉徑選擇孟模型計將算。Wee昆k1破127By謀L.異Wu,鋒Fa昌cul徒ty軍of蝴Civ牌il悄Eng舉.,威NFU多路徑剃概率分挽配法Week輛1128ByL說.Wu蘆,Fa繁cult螞yof哲Civ臣ilE倉ng.,列NFU多路徑概懸率分配法多路徑籮概率分邀配法中伏的有效惡路段和疾有效出租行路徑有效路段販：定義有細效路段[i,j]為路段味終點j比路段什起點i更靠近出宏行終點s的路段。有效路慨徑：由狼有效路媽段組成智的連接OD的路徑避。每一OD量只在纖它相應主的有效李出行路源線上進薪行分配桃。Week兄1129By啄L.教Wu,由Fa仁cul帶ty毒of垃Civ灰il門Eng窗.,捉NFU多路徑支概率分持配法Exam謠ple:A區(qū)到D區(qū)的OD出行量怨為T(1才,9)懇=90追0ve動h/d塵,試用多啊路徑概率分配傷法將OD分配到路嫁網上。Wee妙k1轉130ByL六.Wu梨,Fa素cult疊yof釀Civ時ilE盯ng.,命NFU多路徑咬概率分彼配法解:(壺1)計算各節(jié)財點至終點9的最短路菠權：(2)令i等于出行偶起點r，即從r開始進行顧分配；(3)判別與約節(jié)點i鄰接的有協(xié)效路段，仙并計算有氧效路徑長度短。判別條狂件：if，則它灣為有效路段，有效路小徑長度：Week震1131ByL養(yǎng).Wu射,Fa蠟cult層yof隊Civ挖ilE掉ng.,由NFU多路徑概穗率分配法起點1鄰接的仙兩條路淚段[1,2斤]、[1,若4]都是有寇效路段爸，則(4)計算Logi隊t型的分子(5)計算Log售it型的分母Wee姑k1昆132By識L.堪Wu,兇Fa薯cul釋ty吵of先Civ艇il納Eng患.,皺NFU多路徑概機率分配法(6)計算有效譯路段的分荷配率：Wee席k1駛133ByL表.Wu望,Fa拾cult洗yof掙Civ話ilE譽ng.,建NF