交通分配預(yù)測(cè)

Section5TrafficAssignment

第五節(jié)交通分配預(yù)測(cè)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(shù)Amathematicalformularepresentingthetravelimpedance,levelofserviceofthelinkAsknownaslinkcostfunctionTraveltimeisthemeasureusedmostoften.(有時(shí)候會(huì)考慮距離和固定費(fèi)用：linkdistance+fixedcosts)CrucialtotrafficassignmentWeek116ByL.Wu,FacultyofCivilEng.,NFULinkPerformanceFunctions

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

路阻函數(shù)BPRfunctionWeek118ByL.Wu,FacultyofCivilEng.,NFULinkPerformanceFunctions

路阻函數(shù)Week119ByL.Wu,FacultyofCivilEng.,NFULinkPerformanceFunctions

路阻函數(shù)AdditionalNotes…Whyconvex?Foraminimizationprogram,aconvexobjectivefunctionisthesufficient(secondorder)conditionfortheoptimalsolutiontoexist(assumingthattheconstraintsetisaconvexset).TheHessianmatrixofaconvexfunctionisnotedasPositiveDefinite(P.D.).Week1110ByL.Wu,FacultyofCivilEng.,NFUPrinciplesTrafficAssignment交交通分分配原原理Thefinalstepinthemodelingprocess.Vehicletripsfromonezonetoanotherareassignedtospecifictravelroutesbetweenzones.Thisassignmentisdoneonthebasisofminimumgeneralizedcost(最小的的通用用費(fèi)用用)oftravelbetweeneachO-Dpairofzones－但并并不表表示路路徑唯唯一！！Thisgeneralizedcostasdefinedearlierisalinearcombinationofthelinkjourneytimeandthelinkdistance+fixedcostssuchasparkingortolls.Whenwearedonewehaveanassignednetwork!Week1111ByL.Wu,FacultyofCivilEng.,NFUTrafficAssignmentWeek1112ByL.Wu,FacultyofCivilEng.,NFUWeek1113ByL.Wu,FacultyofCivilEng.,NFUWeek1114ByL.Wu,FacultyofCivilEng.,NFU交通分配配模型分分類交通分配配模型通通常分為為非平衡模模型：non-equilibriummodels最短路（（全有全全無）交交通分配配法－－shortestpathmethod(alsocalledall-or-nothingmethod)容量限制制法－minimumpathwithcapacityrestraintsmethod多路徑概概率交通通分配法法(probabilityofmulti-pathmethod)容量限制制－多路路徑分配配平衡模型型：EquilibriummodelsUserEquilibriumSystemOptimizationWeek1115ByL.Wu,FacultyofCivilEng.,NFUShortestPathMethod最短路分配法法也叫全有全無無分配法是一種靜態(tài)的的交通分配方方法；取兩點(diǎn)間的行行駛時(shí)間為常常數(shù)；在分配中，取取路權(quán)（兩交交叉口間的出出行時(shí)間）為為常數(shù)，即假假設(shè)車輛的路路段行駛車速速、交叉口延延誤不受路段段、交叉口交交通負(fù)荷的影影響。每一OD點(diǎn)對(duì)應(yīng)的OD量被全部分配配在連接該OD點(diǎn)對(duì)的最短線線路上，其他他道路上分配配不到交通量量。所有的OD對(duì)的OD量按上述原則則全部分配在在路網(wǎng)上，累累加各路段的的交通量。Week1116ByL.Wu,FacultyofCivilEng.,NFUShortestPathMethod(cont’d)最短路分配法法該分配法進(jìn)行行交通分配時(shí)時(shí)，不考慮路路段通行能力力的限制；也不考慮過多多的交通量將將影響行車速速度；特點(diǎn)：計(jì)計(jì)算簡(jiǎn)單單；是其其他分配配方法的的基礎(chǔ)。。缺點(diǎn)：交交通量在在路網(wǎng)上上分配不不均，出出行的交交通量全全部集中中在最短短路上；；且網(wǎng)絡(luò)絡(luò)總費(fèi)用用值較大大?？傎M(fèi)用＝＝關(guān)鍵是求求最短路路：最常常用的方方法有Dijkstra算法。Week1117ByL.Wu,FacultyofCivilEng.,NFUShortestPathMethod(cont’d)最短路分分配法最短路交交通分配配法的步步驟確定路段段行駛時(shí)時(shí)間。確定各OD點(diǎn)之間的的最短路路徑。各交通區(qū)區(qū)之間的的交通量量全部放放在路阻阻最小的的路徑上上，其余余的路徑徑上的交交通量為為零。累計(jì)得出出各路段段的交通通量。Week1118ByL.Wu,FacultyofCivilEng.,NFUShortestPathMethod(cont’d)最短路分分配法Example:用最短路路法分配配該OD矩陣ODABCDA0200200500B2000500100C2005000250D5001002500Week1119ByL.Wu,FacultyofCivilEng.,NFUShortestPathMethod(cont’d)最短路分分配法解:（1）確定路路段行駛駛時(shí)間（已知的的）（2）確定A、B、C、D四個(gè)交通通區(qū)的最最短路徑徑?？捎糜肈ijkstra的方法求求得：Week1120ByL.Wu,FacultyofCivilEng.,NFUShortestPathMethod(cont’d)最短路分配法法（3）分配OD量將各OD點(diǎn)對(duì)的OD量分配到與該該OD點(diǎn)對(duì)相對(duì)應(yīng)的的最短路徑上。。Week1121ByL.Wu,FacultyofCivilEng.,NFU容量限制分配配法也是把交通量量分配到最小小路權(quán)的線路路上；考慮了車速與與交通量之間間的關(guān)系，即即考慮了交叉叉口、路段的的通行能力限限制，比較符符合實(shí)際情況況。容量限制分配配法的關(guān)鍵是是路權(quán)的確定定。Week1122ByL.Wu,FacultyofCivilEng.,NFU容量限制分配配法容量限制分配配法的步驟1.用一般方法把把交通表示為為路網(wǎng),以“零流量”路段行程時(shí)間間開始；2.依次對(duì)每個(gè)起起點(diǎn)分區(qū)計(jì)算算通過路網(wǎng)的的最短行程時(shí)時(shí)間的通路；；3.按全有全無分分配模型,將OD點(diǎn)的交通模式式加到路網(wǎng)；；4.計(jì)算分配到每每條路段上的的交通量；5.在流量與行程程時(shí)間的關(guān)系系式中，用分分配給路段的的交通量計(jì)算算路段行程時(shí)時(shí)間，重新計(jì)計(jì)算最短路；；6.按全有全無分分配模型將原原來OD點(diǎn)的交通模式式加到路網(wǎng)上上,但要用由由步驟5得出的新新的最短短路上；；7.返回到步步驟4，繼續(xù)分分配，直直到分配配的交通通量和行行程時(shí)間間穩(wěn)定為為止。Week1123ByL.Wu,FacultyofCivilEng.,NFU容量限制制分配法法容量限制制法進(jìn)行行分配時(shí)時(shí)，需先先將OD表中的每每一個(gè)OD量分解成成k部分，即即分解成成k個(gè)OD分表，然然后分k次用最短短路法分分配，每每次分配配一個(gè)OD分表，并并且每分分配一次次，路權(quán)權(quán)修正一一次，直直到把k個(gè)OD分表全部部分配在在路網(wǎng)上上。Week1124ByL.Wu,FacultyofCivilEng.,NFU容量限制分分配法分配次數(shù)k與每次的OD分配率(%)Week1125ByL.Wu,FacultyofCivilEng.,NFUAB40+202030+1010401020+4030+1030出行量T(A--B)=40+30+20+10容量限制分配配法多路徑概率分分配法出行者希望選選擇效用最大大的路徑出行行－最短路因素但是路網(wǎng)有其其復(fù)雜性和交交通狀況的隨隨機(jī)性，出行行者在選擇出出行路線的時(shí)時(shí)候往往帶有有不確定性－－隨機(jī)因素考慮這兩種因因素的主次地地位，各出行行線路被選用用的概率可用用Logit型的路徑選擇擇模型計(jì)算。。Week1127ByL.Wu,FacultyofCivilEng.,NFU多路徑概率分分配法Week1128ByL.Wu,FacultyofCivilEng.,NFU多路徑概率分分配法多路徑概率分分配法中的有有效路段和有有效出行路徑徑有效路段：定定義有效路段段[i,j]為路段終點(diǎn)j比路段起點(diǎn)i更靠近出行終終點(diǎn)s的路段。有效路徑：由由有效路段組組成的連接OD的路徑。每一OD量只在它相應(yīng)應(yīng)的有效出行行路線上進(jìn)行行分配。Week1129ByL.Wu,FacultyofCivilEng.,NFU多路徑概率分分配法Example:A區(qū)到D區(qū)的OD出行量為為T(1,9)=900veh/d,試用多路路徑概率分配配法將OD分配到路路網(wǎng)上。Week1130ByL.Wu,FacultyofCivilEng.,NFU多路徑概概率分配配法解:(1)計(jì)算各節(jié)節(jié)點(diǎn)至終終點(diǎn)9的最短路路權(quán)：(2)令i等于出行行起點(diǎn)r，即從r開始進(jìn)行行分配；；(3)判別與節(jié)節(jié)點(diǎn)i鄰接的有有效路段段，并計(jì)計(jì)算有效效路徑長(zhǎng)度。。判別條件件：if，則它為為有效路段，有效路徑徑長(zhǎng)度：Week1131ByL.Wu,FacultyofCivilEng.,NFU多路徑概概率分配配法起點(diǎn)1鄰接的兩兩條路段段[1,2]、[1,4]都是有效效路段，，則(4)計(jì)算Logit型的分子子(5)計(jì)算Logit型的分母母Week1132ByL.Wu,FacultyofCivilEng.,NFU多路徑概率分分配法(6)計(jì)算有效路段段的分配率：：Week1133ByL.Wu,Faculty