基于车辆跟驰模型的交通流动力学模型

.4Aug.2010Vol.28JOURNALOFSHAANXIUNIVERSITYOFSCIENCE&TECHNOLOGY113*:10005811(2010)04011306杨文杰1,白云霄1,贾宏恩2(1.,710021;2.,710049):在车辆跟弛模型的基础上,采用微观和宏观相结合的方法,提出了一种新的交通流动力学模型.该模型能够克服现有动力学模型中存在的一些问题,如避免了车流在堵塞密度附近发生扰动而出现超过堵塞密度的现象.通过算例的设计,作者还对不同情况下的交通流进行了数值模拟,结果显示模型具有良好的数值模拟功能,从而证明了其理论意义和实用价值.:交通流;跟弛模型;动力学模型;数值模拟:U491.1+12:A0,,.,,.,()[1].,,[2].,,.,,,,;,,,.1PipesL.A[3]1953,,,:=!,,.,,,,Bando[4]1995(OVM),dvn(t)dt=k[v(x)-vn(t)](1.1)v(x),x;kI.(1.1),.,*:20100422:(1982-),,,,,::(zx08-28)28,,OVM.HelbingOVM(GFM)[5],:dvn(t)dt=k[v(x)-vn(t)]+vnH(-x)(1.2)x∀0,H(x)=1;x0,H(x)=0.(1.2)OVM,,,,.,2001(FVD)[6],:dvn(t)dt=k[v(x)-vn(t)]+vn(1.3),OVM.[7]:xn(t+T)=G(xn-1(t)-xn(t))(1.4)xn(t)tn,xn-1(t)tn-1,T,G(xn-1(t)-xn(t)).,,,,:xn(t+T)=G(xn-1(t)-xn(t))+(xn-1(t)-xn(t))(1.5)0.(1.5),,,,,,,.,,,,.,,vn0,,.(1.5),,.2(1.5),vn(t)=xn(t),xn-1(t)-xn(t)=hn(t)(2.1)(1.5):vn(t+T)=G(hn)+(vn-1(t)-vn(t))(2.2a)dhn(t)dt=vn-1(t)-vn(t)(2.2b),v(x,t),h(x,t),:v(xn(t),t)=vn(t),h(xn-1+xn2,t)=hn(t)(2.3)(2.2a):v(xn(t+T),t+T)=G[h(xn+12hn,t)]+[v(xn-1,t)-v(xn,t)]Thn,,,:v(xn,t)+[v(xn,t)t+v(xn,t)v(xn,t)x]T1144:=G[h(xn,t)]+12h(xn,t)G[h(xn,t)]hh(xn,t)x+v(xn,t)xh(xn,t)(2.4)(2.2b):ddth(xn-1+xn2,t)=v(xn-1,t)-v(xn-t)x=xn-1+xn2,ht+vhx=hvx(2.5).,!=1/h,V(!)=G(h),(2.4)(2.5)v+(vt+vvx)T=V(!)+12V#(!)!!x+!vx!t+(!v)x=0V#(!)!,V#(!)0,∀=-12V#(!)0,:!t+qx=0(2.6a)vt+vvx=-v-V(!)T-∀!T!x+!Tvx(2.6b)q=!v(2.6c)∀0,,,.,,,;,.,,,,.,,.1:(2.6b),=0,Payne;=0,k=0,V(!)=uf,Ross,uf(freeflowspeed).2:p=1T(∀T-!),(2.6b):vt+vvx=-v-V(!)T-1!px(2.7)[8],p,vvx,1!px,v-V(!)T.3(2.6b)!,!vt+!vvx=-!v-!V(!)T-∀T!x+#Tvx:qt+(q2!+∀T!-Tq!)x=!v-!V(!)T(2.6):!t+qx=0qt+(q2!+∀T!-Tq!)x=-!v-!V(!)T(3.1)11528U=!q,F=qq2!+∀T!-Tv,S=0!V(!)-!vT,:Ut+Fx=S(3.2),(3.2):Ut+JUx=SJ=FU=01-q2!2+∀T+Tq!22q!-!T,J,(3.2),.,[911],,LaxFriedrichs[12]:Ujn+1=Unj-1+Unj+12-t2x(Fnj+1-Fnj-1)+tSnj,(CFL):t∃x/vf,n,j,T,t,x..1..!j=0.25(/m),vf=30m/s,l=10km,T=3s,:v=ve(!)=vf(1-!!j).:!(x,0)=0.18,0∃x50000.04,5000∃x∃10000,v(x,0)=ve(!(x,0)):v(0,t)x=0,v(l,t)x=012.图1t为不同时刻的密度分布图2密度分布的时空演化图(0~10min),t=1s,x=50m,∀=0.3,k=0.2.2..!j=0.9,vf=20m/s,l=10km,T=2.5s,!a=0.6.:V(!)=ve(!)=vf(1-!!j).:1164:!(x,0)=!a+#!acos[∃(x-x0)2x]6000∃x8000!ax%[0,6000]&[8000,10000]v(x,0)=ve(!(x,0)):v(0,t)x=0,v(l,t)x=034.图3t为不同时刻的密度分布图4密度分布的时空演化图(0~5min),t=1s,x=50m,∀=0.3,k=0.2.,1,,,,[10];2,,,,,3,.,,,,,.,#0.25,,,.,,,(localcluster),.4,,,,,,,,,.,,,,[11],,,,,.[1]HelbingD,TreiberM.Traffictheoryjams,wavesandclusters[J].Science,1998,282:20012003.[2]ZhangPeng,LiuRuxun.Analysesandremarksontrafficflowmodelalongwithitsimprovement[J].JournalofKunmingUniversityofScienceandTechnology,2000,25(4):118123.[3]Pipe.L.A.Aoperationaloftrafficdynamics[J].J.Appl.Phys,1953,24:274281.[4]BandoM,HasebeK,NakayamaA,etal.Dynamicalmodeloftrafficcongestionandnumericalsimulation[J].PhysRevE,1995,51:10351042.[5]HelbingD,TilchB.Generalizedforcemodeloftrafficdynamics[J].PhysRevE,1998,58:133138.11728[6],,.[J].,2000,45(17):18951899.[7]WhithamG.B.LinearandNonlinearWaves[M].WileyIntescience,NewYork,1974.[8]PhillipsWF.ANewContinuumTrafficModelObtainedfromKineticTheory[R].IEEETrans.Autom.Control.AC23,1978:10321036.[9]W.H.Press,S.A.Teukolsky,W.T.Vetterling,etal.NumericalRecipeinC:TheArtofScienficComputing[M].CambridgeUniversityPress,Cambriage,2ndedition,1992.[10],.(∋)[J].,2001,18(4):329333.[11],.[J].,1998,26(9):3843.[12]R.J.LeVeque.NumericalMethodsforConservationLaws[M].Birkhuser,Basel,1992.ANEWMACROSCOPICTRAFFICFLOWMODELBASEDONTHECARFOLLOWINGTHEORYYANGWenjie1,BAIYunxiao1,JIAHongen2(1.FacultyofScience,ShaanxiUniversityofScience&Technology,Xi#an710021,China;2.FacultyofScience,Xi#anJiaotongUniversity,Xi#an710049,China)Abstract:Inthispaper,amacroscopictrafficflowmodelisestablishedbyvirtueofthemethodforcombiningmacroscopicandmicroscopic.Themodelisbetterthanothermodelsforovercomingsomeshortcomings,forexample,whenthedensityofthevehicleshaveaperturbationnearbythejamdensity,thephenomenaofovertakingthejamdensityisnotcometrue.Twonumericalexampleswithdifferentinitialandboundaryconditionsshowitsgoodpropertiesofnumericalmodeling.Theseshowsitstheoreticalandpracticalvalue.Keywords:trafficflow;carfollowingmodel;dynamicalmodel;numericalsimulation(上接第107页)FOGEFFECTSANDTHECORRESPONDINGREALIZATIONINDIRECTX3DXUChenghu1,TIANDongping2(1.DepartmentofEducationalScienceandTechnology,BaojiUniversityofArtsandScience,Baoji721007,China;2.InstituteofComputerSoftware,BaojiUniversityofArtsandScience,Baoji721007,China)Abstract:ThepaperintroducesthebasicconceptsoffoginD3D,anddiscusstheprocessofusingD3Dtoaccomplishvariousfogsandcorrespondingformulas,fogparameters,fogblending,fogcolor,vertexfogandpixelfogindetail.Underthedefinitionofvariousfogcomputingmodels,thevertexfoginapplicationprogramshasbeenaccomplishedusingC++code.Intheend,thispaperconcludeswhenusingavertexshader,youmustusevertexfog.Meanwhile,inrangebasedfog,Direct3Dusestheactualdistancefromtheviewpointtoavertexforitsfogcalculations.Direct3Dincreasestheeffectoffogasthedistancebetweenthetwopointsincreases,ratherthanthedepthofthevertexwithininthescene.Keywords:APIfunction;Fog;Direct3Dprogram;DirectXprogram118