城市轨道交通列车开行方案的确定

:2003-06-03:　(1959-),,,,.E-mail:[e-mail]孙　焰,施其洲,赵　源,孔庆瑜(,　200092):,.,..:;;;:U231.92;U292　　　　　　:A　　　　:0253-374X(2004)08-1005-04MethodonMakingTrainRunning-planforUrbanRailwayTrafficSUNYan,SHIQi-zhou,ZHAOYuan,KONGQing-yu(DepartmentofTransportManagementEngineering,TongjiUniversity,Shanghai200092,China)Abstract:Thepaperstudiestheautomaticprogramofoptimalrunning-planoftrainnumberoncomputerfortheurbanrailwaytrafficwithallkindsofcyclingconsidered.Themathematicalformulasarefirstlyobtainedforminimalnumberoftrains.Theoptimalmodelisformedforthetrainrunning-plan,inwhichtheratesofvirtualloadingcanreachthemaximum.Thecomputeralgorithmisdesignedfortheverymodel,andtheoptimalrunningcanbegotautomatically.Keywords:urbanrailwaytraffic;running-plan;optimalmodel;algorithm　　,,,,..,,,、、.,.,.,.,,,,.,,.,,.1　,,.,32820048()JOURNALOFTONGJIUNIVERSITY(NATURALSCIENCE)Vol.32No.8　Aug.2004.,.,.m,,,1.1　—Fig.1　Relationshipbetweentimeandplaceoftrain'smovingdii(i=1,2,…,m)();ti,ti、i(i=1,2,…,m)();tii(i=0,1,2,…,m)().,N.()[1],、2、.1.1　m=1.d1.,,,.,,T=t1+t1+t0+t1　　k,T=kd1,.N1=[T/d1]=[(t1+t1+t0+t1)/d1](1),[x]x.(1),N1:N1=[(t0+t1)/d1+(t1+t1)/d1],、,.,t1=t1=2200s,t0=t1=130s,d1=240s,:N1=[19.42]=20().1.2　22m=2.d1d2,,,(1),21.,,(1),,2.2　2Fig.2　Optimalreturningmethodofatrainwithtwodivisions　　d2d1,1d2/d11,1(1-d1/d2)t1,2,1,N2′=t1-(d1/d2)t1+t1+t0+t1d1+t2+t2+t2d2(2)　　,d1d2,　N2″=t1+t0+t1d1+t1-(d2/d1)t1+t2+t2+t2d2(3),(2)(3),N2=t1+t0+t1d1+t2+t2+t2d2+1006　　　()32　　　　d1-d2d1d2t1(4)d2=d1,2,(4).1,,1,(1)(4).1.3　(4)m,Nm=t0d1+tmdm+∑mi=1ti+tidi+∑m-1i=1|di+1-di|didi+1ti(5)　　(5),.,,Nm.,m=3,d1=360s,d2=240s,d3=420s,t0=t1=t2=t3=130s,t1=t1=900s,t2=t2=1700s,t3=t3=1200s.(5),:Nm=[26.99]=27().1.4　,0m[2],t0=tm,N0=∑mi=1ti+tidi+∑mi=1|di+1-di|didi+1ti(6)2　,,.,,,.,.,,.m;()()C1C2;N;Fij(i=1,…,m;j=1,…,24);()ti,ti(i=1,2,…,m);()ti(i=0,1,2,…,m).Dij(i=1,…,m;j=1,…,24)Tij(Dij≠Di,j-1,Tij=1;Dij=Di,j-1,Tij=0).DijTij:①,DijC1≤Fij≤DijC2,i=1,2,…,m,j=1,2,…,24;②,di=minj3600/Dij≥Ii,i=1,2,…,m;Iii;③,(1-Tij)Dij=(1-Tij)Di,j-1,i=1,2,…,m,j=1,2,…,24;,Tij=0,Dij=Di,j-1;④,N≥Nm.DijTij:①,maxZ1=∑mi=1∑24j=1FijDijC2;②,minZ2=∑mi=1∑24j=1Tij.(①)(④).,.①①,.①minZ1′=∑mi=1∑24j=1|Fij-DijC2|:minZ1=∑mi=1∑24j=1|Fij-DijC2|minZ2=∑mi=1∑24j=1Tijs.t.(1-Tij)Dij=(1-Tij)Di,j-1,　　　　　　i=1,2,…,m,j=2,…,24t0d1+tmdm+∑mi=1ti+tidi+　　　　∑m-1i=1|di+1-di|didi+1ti≤Ndi=minj3600Dij≥Ii,i=1,2,…,m1007　8　,:　　Dij≥0,i=1,2,…,m,j=1,2,…,24Tij=01,i=1,2,…,m,j=2,…,24Ti1=1,i=1,2,…,m3　,,[3].Tij,Dij.Tij(),.,u,.TijDij.:1　Dij.Dij=[Fij/C2],i=1,2,…,m,j=1,2,…,24;2.2　.di=minj3600/Dij,i=1,2,…,m;i=1,2,…,m,diIi,,Dij=Dij-1,2,.3.3　Tij.Tij,Ti1=1,Ti25=1,|Dij-Dij′|≤u,Tij=0;|Dij-Dij′|u,Tij=1;i=1,…,m,j=2,…,24.,j′=max{k|kj,Tik=1},j′Tijj.4.4　TijDij.Tij=1,Dij=∑j″-1k=j′Dik/(j″-j′+1);Tij≠1,Dij=Di,j-1;i=1,…,m,j=1,2,…,24.,j″=min{k|kjTik=1},j″Tijj.5.5　,Nm(5),NNm,,j,6.,.6　Dij,∑j″-1j=j′Fkj∑j″-1j=j′Dkj=mini=1,…,m∑j″-1j=j′Fij∑j″-1j=j′Dij,,j′=max{k|kjTik=1},j″=min{k|kjTik=1}.j=j′,…,j″,Dkj=Dkj-1,5.,,.,120032(1),,12,600,50,、、1,3.3,219,180,23,79.2%.1　Tab.1　Averagepassengerflowincuttingarea5:00～6:006:00～7:007:00～8:008:00～9:009:00～10:0010:00～11:0011:00～12:0012:00～13:0013:00～14:00—341568412726228774482075777734144738553142—89868631382025473458597301670848516685753114:00～15:0015:00～16:0016:00～17:0017:00～18:0018:00～19:0019:00～20:0020:00～21:0021:00～22:0022:00～23:0023:00～24:00—5798357744597704885638842360534744851343305972993—65655681746826457672447223749047492523003217824223　2Fig.3　Runningplanoftrainnumberwithtwodivisions(1014)1008　　　()32　,,,,,.,,,“、、、”.,,,.4　(1)、、、、,“、,、”,,.(2):“、”.(3).(4),“、、、”.,,,,.:[1]　.[J].,2000,(3):15-18.　　CHENDing-feng.TheinvestigationintotravelfeatureofpassengerofShanghaimetroline1[J].TrafficandTransportation,2000,(3):15-18.(inChinese)[2]　.[J].,1999,(3):19-20.　　ZHUBei-ling.Confirmthedistancebetweenstationsrationally[J].RailStandardDesign,1999,(3):19-20.(inChinese)[4]　,　.[J].(),2002,30(4):431-436.　　YEXia-fei,CAIWei.Calculationmethodofurbanrailtransitdevelopmentbenefits[J].JournalofTongjiUniversity(NaturalScience),2002,30(4):431-436.(inChinese)[5]　.[Z].:,2002.(编辑:王东方)(1008):[1]　,　,　,.[M].:,1995.　　LIZhi-zhong,SHIFen,SUNYan,etal.Themathematicmodelingandalgorithmofrailwaytransportationmanagement[M].Wuhan:HuazhongUniversityofScienceandEngineeringPublishingHouse,1995.(inchinese)[2]　.[M].:,1998.　　LUHua-pu.Theoryandmethodoftrafficprogramming[M].Beijing:TsinghuaUniversityPublishingHouse,1998.(inChinese)[3]　PapadimitriouCH.Combinatorialoptimization:Algorithmsandcomplexity[M].London:Prentice-HallInternationalInc,1986.(编辑:曲俊延)1014　　　()32