基于车辆跟驰模型的交通流动力学模型.pdf

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06?????????????????112杨文杰,白云霄,贾宏恩(1.?????????,???ν710021;2.?ν???????,???ν710049)??:在车辆跟弛模型的基础上,采用微观和宏观相结合的方法,,,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??????:+12?????:A0??????????????,????????????????,??????????????.??,?????????,???????????a????a??????????????????????.??,????????????????a?????(???????????)a??????[1]??????????.??????????????????????????,??????????.]2]???????????????????,?????????????,??????????????????????,?????????????????.???????,Ч????????????,??????????????????????э??????,???????????????,???????????;?????,????????????,??????????????,??????????.1??????????????????[3]?1953????,???????????,??????????????????????????,????????:????=???!????????????,??????????????????,б?????????a???a???????a??a???.??,????????,????????a?????,????????????????,??б?????????Bando[4]???1995???????????(OVM)????,????dvn(t)=k[v(
x)-vn(t)]()dt??v(
x)??????,???????
x;kI?????.??()????????Ч??????,??????????????????????????????.????????,?????a?*????:2010
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22????:???(1982-),?,???????,??,??,????:????a???a????????:????????????(zx08-28):..114???????Б?28????a?????,??????????б,OVM??????????????????.Helbing???OVM????????????????(GFM)[5],????:dvn(t)=k[v(
x)-vn(t)]+
vnH(-
x)()dt???x?0?,H(x)=1;?x<0?,H(x)=0.??()???OVM???????????,????????,????????б,???????????????,?????????????.?????,???)FVD(???????????2001?????a????????[6],????:dvn(t)=k[v(
x)-vn(t)]+
vn()dt????????????????,????OVM??????????.???[7]???????????????????????????????:xn(t+T)=G(xn-1(t)-xn(t))()??xn(t)?t???n?????,xn-1(t)?t???n-1?????,T??????????????????,G(xn-1(t)-xn(t))???????????.?,???????????????????????,????????????????????????,??????,????????????:xn(t+T)=G(xn-1(t)-xn(t))+(xn-1(t)-xn(t))()??>0???????.??()?????????????a?????????????,?????????,??????,?????????,???????????????????????,???х?????????,??????,?,??????????,???.?????????????????????????????,?????????????????,?????????????????.??????????????,??????????,?
vn>0?,??????ν?????????????????????,???????????????????.??????()???,????????????,???????????.2???????()?,?????vn(t)=xn(t),xn-1(t)-xn(t)=hn(t)()???()??????????:vn(t+T)=G(hn)+(vn-1(t)-vn(t))()dhn(t)=vn-1(t)-vn(t)()dt???????????????,??????э?v(x,t),h(x,t),????:xn-1+xnv(xn(t),t)=vn(t),h(,t)=hn(t)()2???()????:1v(xn(t+T),t+T)=G[h(xn+hn,t)]+[v(xn-1,t)-v(xn,t)]2??????T??hn????????,???????,????????,?:v(xn,t)v(xn,t)v(xn,t)+[+v(xn,t)]Ttx:..?4?????:?????????????????1151G[h(xn,t)]h(xn,t)v(xn,t)=G[h(xn,t)]+h(xn,t)+h(xn,t)()2hxx????()???:dxn-1+xnh(,t)=v(xn-1,t)-v(xn-t)dt2xn-1+xn??x=?,?????2ht+vhx=hvx()????.??,??!=1/h,V(!)=G(h),?()a()????tx1V#(!)!vv+(v+vv)T=V(!)+2!x+!x!t+(!v)x=0V#(!)?!?????,??V#(!)<0,????=-1V#(!)>0,???????:2!t+qx=0()vvv-V(!)?!v+v=--+()txT!Tx!Txq=!v()?????>0,???????????????,???????,???????.??????????????????,?????????????????????,?????,????????????????????;??,??????????????????.????????????????,???????????,??,????,????a??????????????????.????,????????????????????????????,????????????.?1:??()?,??=0,??Payne??;??=0,k=0,V(!)=uf,??Ross??,??uf???????(freeflowspeed).1?2:??p=T(?T-!),??()???:vvv-V(!)1p+v=--()txT!xv1pv-V(!)??????[8]??????,p???,v????,????,????.x!xT3??????????????()??ш???!,??vv!v-!V(!)?!#v!t+!vx=-T-Tx+Tx?????:2(q+?!-q)q!TT!!v-!V(!)+=txT????????()??:!q+=0tx2()(q+?!-q)q!TT!!v-!V(!)+=-txT:..116???????Б?28?q0!2??U=,F=q?,S=!V(!)-!v,????????????????:q+!-v!TTTU+F=S()tx??????,??????()??????????:UU+J=Stx01F2??J==q?q2q,????????J?????????,????U-2++2-!TT!!!T()?????????????,???????ο?????????.???,]11
9]??????????,???????????????????????????????????????????????????,??????????????Lax
Friedrichs??[12]:Unjnj-1+Unjnj+1Ujn+1=-
t(Fnjnj+1-Fnjnj-1)+
tSnjnj22
x??????,????????j,??????n??,vf/x
?t
:?)??CFL(????,T?????,
t?????,
x?????.?????????????????.??1.???????????????.????????,km10=l???,s/m30=vf????,)m/?(=j!????T=3s,??ef!????
????:v=v(!)=v(1-!j).,0?x<5000????:!(x,0)=,v(x,0)=ve(!(x,0)),5000?x?10000ш???:v(0,t)=0,v(l,t)=0xx??????1a?2??.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,?=,k=.??2.?????????????????.????????,km10=l???,s/m20=vf????,=j!????T=,!a=.??????
????:V(!)=ve(!)=vf(1-!).!j????::..?4?????:?????????????????117?(x-x0)!a+#!acos[]6000?x<8000!(x,0)=2
xv(x,0)=ve(!(x,0))!ax%[0,6000]&[8000,10000]ш???:v(0,t)=0,v(l,t)=0xx??????3a?4??.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,?=,k=.?????????????????????,?1???,????????,????????,????????????,??????[10]??????????????,?2???;??????,???????,?????,?????????????????????????????,????????3????,???????????.???,??????б??,?????????????????????????,???????????,?????????????????,?????????.???????,?<#?????????,????,????????,????.????????????????????????,?????????,???????,??????(localcluster),??????????.4???Ч?????????????????????,?????????,????????????????????,????ш??????,???????????????????????????,?????????????????????a??????????????????????,????????,?????????????????э?????,??????????????,??????????????.??,??????????,?????????????????????,??????????,????]11]???,????????????????????????????????????????????б?????,?????????????,????,????????,????????????.????[1]HelbingD,
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43.[12][M].Birkh
user,Basel,
jie,BAIYun
xiao,JIAHong
en(,ShaanxiUniversityofScience&Technology,Xi#an710021,China;
ence,Xi#anJiaotongUniversity,Xi#an710049,China)Abstract:Inthispaper,amacroscopictrafficflowmodelisestablishedbyvirtueofthemeth

ings,forexample,whenthedensityofthevehicleshaveaperturba
tionnearbythejamdensity,
:trafficflow;carfollowingmodel;dynamicalmodel;numericalsimulation(上接第107页)FOGEFFECTSANDTHECORRESPONDINGREALIZATIONINDIRECTX3D12XUCheng
hu,TIANDong
ping(,BaojiUniversityofArtsandScience,Baoji721007,China;
puterSoftware,BaojiUniversityofArtsandScience,Baoji721007,China)Abstract:onceptsoffoginD3D,anddiscusstheprocessofplishvariousfogsandcorrespondingformulas,fogparameters,fogblending,fogcolor,,plishedusingC++,thispaperconcludeswhenusingavertexshader,,inrange
basedfog,,:APIfunction;Fog;Direct3Dprogram;DirectXprogram