基于广义最小二乘模型的动态交通OD矩阵估计

200411:100026788(2004)0120136205OD,,(,710049):,OD,ODL,L,,;,L:OD;;:U491:AGLSModelBasedDynamicOrigin2DestinationMatrixEstimationforTrafficSystemsLINYong,CAIYuan2li,HUANGYong2xuan(SchoolofElectronicandInformationEngineering,Xi’anJiaotongUniversity,Xi’an710049,China)Abstract:BasedonGeneralizedLeastSquare(GLS)model,adynamicorigin2destination(OD)matrixestimationalgorithmwithslidingwindowisproposed.TheODmatrixcanbeestimatedthroughthesurveillanceoftrafficcountsandtravelingtimeonlinksinatrafficnetwork.Ananalyticalformulatocalculatethekeyassignmentmatrixisalsopresented.Thealgorithmisarecursiveprocedurewithfewaprioridata,andthereexistsnodivergenceintheestimation.Withtheslidingwindow,moresurveil2lancedatacanbeutilizedeffectively,andmeasurementnoisescanberestrainedefficiently.Alotofsim2ulationtestsshowthattheestimationaccuracyoftheproposedmethodismuchhigherthanthatofCascetta’srecursivealgorithm,andthereisonlyalittleincreaseincomputationcost.Keywords:dynamicODmatrix;GLSalgorithm;estimation:2002211204:(60175015):(1973-),,,,OD,Email:[e-mail];(1963-),,,,,,,;,,,L1OD,OD,(Origin)(Destination),LLODOD(OD)L(ITS),OD(ATIS)(ATMS),,Paramics[1]MITSim[2]L,OD,L,ODL,(OD)OD,LOD,,ODL,OD[3]L©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.ODLOD,,L[4],ODL,OD,;,OD(),ODL,OD:L(ODOD)OD;L,OD,[5]L,,,;,OD,LCascetta[6]ODODL,ODODODL:L,,OD,OD;,ODLCascetta,[6]L(OD),L,Cascetta:,OD,,ODLL,,OD,ODODL,,L,L,:,,L2OD2.1[6],ODOD,ODZODxdh=argmin[f1(xh,xah)+f2(yh,ydh)],xh0(1),xhRnODOD,xrh(r=1,2,,nOD)hrOD,nODOD;xahxh,xah=xdh-1;yhRnlh,nl;ydh,(1)xh;f1f2Zxdh=argmin(xh-xah)TW-1h(xh-xah)+yh-6h-1p=h-paphxdp-ahhxhTR-1hyh-6h-1p=h-paphxdp-ahhxh(2),aphnlnOD,pODxph;pODZOD,7311OD©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.(xd1,xd2,,xdN)=argmin[f1(xd1,xd2,,xdN,xa1,xa2,,xaN)+f2(y1,y2,,yN;yd1,yd2,,ydN)](3)xiE0,Pi=1,2,,NZ,f1f2,(3)xdh=argmin6Nh=1[(xh-xah)TW-1h(xh-xah)]+6Nh=1yh-6hp=h-paphxpTR-1hyh-6hp=h-paphxp(4)2.2,ZXh=[xThxTh-1xTh-p]T(p+1)OD,ZAh=[ahhah-1hah-ph]ODWh=Var(Xah)Xdh=argmin[(Xh-Xah)TW-1h(Xh-Xah)+(yh-AhXh)TR-1h(yh-AhXh)](5),OD,Xah=Xdh-1;,XahODZ,ODxh(p+1),ODXi(i=h,h+1,,h+p)1nOD,(nOD+1)2nOD,,pnOD(p+1)nODZ(p+1),,xhZ(5)W-1hR-1hZ,Z,WhRh,(OLS),,,Z(5),,Z2.3,aphZCascetta[6],p(H)k(k,p),,HZ,(k,p),,OD,HZ,ODrKr,nODODK,K=K1K2KnODZk=1,2,,KOD,LkZFkhhkODZh,xrh=6kKrFkh(6)qkhODrhk,6kKrqkh=1,Pr,h,ODFkh=xrhqkh(7)83120041:hn(t)=$Xn(t)öVn(t)Z,Vn(t)$Xn(t)tL©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.qkh,LogitZ,lylh=6hp=h-p6Kk=1AkplhFkp+vlh(8),Akplh,pkhlZ,arplh=6kKrAkplhqkp(9)ZAkplhZCascetta,(k,p);,,Z(k,p)l$k=[Gkp1l,Gkp2l],Gkp1l,Gkp2l(k,p)l(l);h$h=[(h-1)H,hH],Hp,Akplh=û$h$kûöû$kû(10),ûûZGkp1lGkp2lZ(k,p)p,,,Z,:;;,();ZOD,H,,(10)Z[3],ODH1015,,Z311,OD{(1,5),(1,6),(2,6),(2,5)},N=15,15Z,15,;,Z,p=3,OD(1,5)(1,6)OD,[7]OD,15ZOD(2,6)OD(1,5),(2,5)OD(1,5)1.5ZOD2,,-30OD,Z1ö3,ahh=1ö31ö300001ö31ö3000000000000ah-1h=2ö32ö300002ö32ö31ö31ö31ö31ö300000000ah-2h=000000002ö32ö32ö32ö31ö3001ö301ö31ö30ah-3h=0000000000002ö3002ö302ö32ö30OD,N(0,R2InOD);9311OD©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.N(0,10Inl,nlZ3(a)R2=40OD(1,5);3(b),ZOD,,(100)ODZx-xdöxd,xxdOD(OD)Z1,Z,,,;,Z2,,Z,Z,OD,,ODZ,,OD,ODZ,Z,,,Z2OD3OD1ODR2=40R2=80R2=200R2=10000.05780.0810.12750.27300.07390.32230.79001.04190.04700.06390.09660.20252ODR2=40R2=80R2=200R2=10000.24280.48411.18031.41370.12980.13310.15170.23944:OD,,Z,,Z,,,,,Z:[1]QuadstoneLimited.ParamicsV4.0systemoverview[BDöOL].http:öö[2]QiYang.Asimulationlaboratoryforevaluationofdynamictrafficmanagementsystems[D].MassachusettsInstituteofTechnology,Cambridge,MA,1997.(144)04120041©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.,Z41),Z:W=[0.480.060.360.040.06]3.3L1(R,U)L2(R,W)LiviÉ0.01410.02560.320.68Ê0.02890.01390.810.19Ë0.02110.010.820.18Ì0.00290.03180.010.99LminvmaxÌ,É,Ê,ËZ,()Z,,,Z2),,:L(CompromiseProgramming)LL,L1997-1999,LL,,L:[1][Z],1998.[2],.[M].:,1995.[3].[J].,2002,24(2):76-78.(140)[3]KalidasAshok.Estimationandpredictionoftime2dependentorigin2destinationflows[D].MassachusettsInstituteofTechnology,Cambridge,MA,1996.[4],,.[J].,1996,13(2):34-43.[5]HanifD.Sherali,TaehyungPark.Estimationofdynamicorigin2destinationtriptablesforageneralnetwork[J].TransportationResearch,2001,35B:217-235.[6]EnnioCascetta,DomenicoInaudi,GeraldMarquis.Dynamicestimatorsoforigin2destinationmatricesusingtrafficcounts[J].TransportationScience,1993,27(4):363-373.[7]YongLin,YuanliCai.Amicroscopicsimulatorforurbantrafficsystems[A].ProceedingsoftheIEEE5thInterna2tionalConferenceonIntelligentTransportationSystems[C],622-626,Singapore,2002.44120041©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.