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1,2,2,3(1.,756000;2.,710049;3.,510641):,,.,,,.,.:;;;;;;:TB114.1:A:1000-5781(2006)05-0484-06StudyontheschedulingstrategiesforonlinevehiclewiththerecoverablecongestedverticesHUMao2lin1,2,XUYin2feng2,XUWei2jun3(1.DepartmentofMathematics,NingxiaNormalUniversity,Guyuan756000,China;2.SchoolofManagement,XianjiaotongUniversity,Xian710049,China;3.SchoolofManagement,SouthChinaUniversityofTechnology,Guangzhou510641,China)Abstract:Concerningabouttheproblemoftheunforeseencongestedverticesintheactualtransportationofmaterials,thepaper,usingamethodofcompetitiveanalysis,studiestheschedulingstrategiesforonlinevehiclewiththerecoverablecongestedverticestorealizetheaimofaless2minimum2timefortheonlineve2hicletraveling.Takingintoaccountthedynamicmattersofthecongestedvertices,weintroducethethreestrategiesofthegreedystrategy,repositionstrategyandwaitingstrategyrespectivly,systematicallyintroducetheadvantagesanddisadvantagesofthethreestrategiesontheircompetitiveperformances,andthengivetheselectionstrategyanditsalgorithmicmodel.Throughanalyzingthecompetitiveratioandcompetitiveperformanceoftheselectionstrategy,theresultsclearlyshowthattheselectionstrategyrealcgestheopti2mizationschedulingofonlinevehiclewell.Keywords:onlineproblem;greedystrategy;repositionstrategy;waitingstrategy;selectionstrategy;competitiveratio;competitiveperformance0,,,;,,,.215200610JOURNALOFSYSTEMSENGINEERINGVol.21No.5Oct.2006:2005-04-12;:2005-11-07.:(19731001;70471035);(2004070).,.,,,,,.,[1]O(origin)D(destination).,[28],.[1],.1G=(V,E),V={v1,v2,,vn}G,E={e1,e2,,em}.,,.1)el=vivjE,T(vivj)vivjvivj,T(vivj)=T(vjvi).2)vivj,viO,vjD.3)OD,k(k0),G,k(r1,r2,,rk),Rk,i(r1,r2,,ri)(0ik)Ri,R0.4)vpi(i1)ri,vpOi;eqiri,eqOi.5)t(ri),i=1,2,,k,T(Rk)=ki=1t(ri),T(Rk)=(t(r1),t(r2),,t(rk)),,,.6)GG.7)Topt(OD|Ri)(0ik)r1,r2,,ri,G,OD,i=0Topt(OD).8)Oi(1ik),ri,Topt(OiD|Ri)r1,r2,,riGOiD.9)CTALG(OD|Ri)(1ik)ALGr1,r2,,riOD.10)Topt(OD)+T(Rk)Topt(OD|Rk),Topt(OD)+T(Rk)Topt(OD|Rk),,D.,1:1Topt(OD)Topt(OD|R1)Topt(OD|R2)Topt(OD|Rk)2,,[1].2A,ARk=(r1,r2,,rk)2k+1-1[1].2,15845:12k+1-1,,.,.,,,(),().,,.,.,.,,.[1]3B,BRk=(r1,r2,,rk)2k+1[1].3,,112k+1.,,..,.C,CTC(OD|Rk)=Topt(OD)+T(Rk),Topt(OD|Rk).CTC(OD|Rk)Topt(OD|Rk)=Topt(OD)+T(Rk)Topt(OD|Rk),kT(Rk):T(Rk),1;T(Rk),.,T(Rk),.,,,?,:1,OD,OOi(1i18)3R3(r1,r2,r3)t(r1)=2,t(r2)=1,t(r3)=0.5,3,33,..11),OO1O2O3DO1r1;r1,O1DO1O4O5D,,O4r2;r1,r2,O4DO4O6D,,O6r3,r1,r2,r3,O6DO6O19D,D.OO1O4O6O19D,,9.1.2),OO1O2O3DO1r1,O1O;r1,OO7O8O9DO7r2,O7O;r1,r2,OO13O14O15DO13r3,O13O;r1,r2,r3,OO16O17O18D68421D.OO1OO7OO13OO16O17O18D,,5.4.3),OO1O2O3DO1r1,2,r1,O2r2,1,r2,O3r3,0.5,r3,D.,4.4.4):OT(OO1O2O3D)=0.9O1r1;r1,OD22T(OO7O8O9D)=2T(OO1O2O3D)=0.91.1,O1DT(O1O4O5D)=1.4O1t(r1)=2r1T(O1O2O3D)=0.32.3,2T(OO7O8O9D)-T(OO1O2O3D)=1.1,O1OOO7O8O9D;O7r2,r1,r2,OD33T(OO13O14O15D)=3.32T(OO7O8O9D)=21.3,O7DT(O7O10O11D)=0.5O7t(r2)=1r2T(O7O8O9D)=0.31.3,T(O7O10O11D)=0.5,O7O10O11D;O10r3;r1,r2,r3,OD44T(OO13O14O15D)=4.43T(OO13O14O15D)=3.31.1,O10DT(O10O12D)=1.3O10t(r3)=0.5r3T(O10O12D)=0.20.7,t(r3)+T(O10O11D)=0.7,O100.5,r3,O10O11DD.,2.9.,:;;T(Rk);4),,,.,4),,,,,,.3iri(i=1,2,,k),Ti=min{(i+1)Topt(OD|Ri)-iTopt(OD|Ri-1),Topt(OiD|Ri),t(ri)+Topt(OiD|Ri-1)}1)Ti=Topt(OiD|Ri),;2)Ti=(i+1)Topt(OD|Ri)-iTopt(OD|Ri-1),;3)Ti=t(ri)+Topt(OiD|Ri-1),.1D,DRk=(r1,r2,,rk)T(Rk)=(t(r1),t(r2),,t(rk))7845:Ti,Topt(OiDRi),(i+1)Topt(ODRi)-iTopt(ODRi-1)t(ri)+Topt(OiDRi-1),,t(ri)+Topt(OiDRi-1),Topt(OiDRi).2k+1.1)i{1,2,,k},Ti=Topt(OiD|Ri),,CTD(OD|Rk)CTD(OD|Rk)w(OO1)+Topt(O1D|R1)+Topt(O2D|R2)++Topt(OkD|Rk)Topt(OD)+(2Topt(OD|R1)-Topt(OD))+(3Topt(OD|R2)-2Topt(OD|R1))++((k+1)Topt(OD|Rk)-kTopt(OD|Rk-1))(k+1)Topt(OD|Rk)2),Pi{1,2,,k},Ti=(i+1)Topt(OD|Ri)-iTopt(OD|Ri-1),3,CTD(OD|Rk)CTD(OD|Rk)(2k+1)Topt(OD|Rk)3)i{1,2,,k},Ti=t(ri)+Topt(OiD|Ri-1),CTD(OD)|Rk)=Topt(OD)+ki=1t(ri)Topt(OD)+ki=1TiTopt(OD)+(2Topt(OD|R1)-Topt(OD))+(3Topt(OD|R2)-2Topt(OD|R1))++((k+1)Topt(OD|Rk)-kTopt(OD|Rk-1))(k+1)Topt(OD|Rk)4)jri1,ri2,,rij(1i1i2ijk,1jk)Ti1=(i1+1)Topt(OD|Ri1)-i1Topt(OD|Ri1-1)Ti2=(i2+1)Topt(OD|Ri2)-i2Topt(OD|Ri2-1)Tij=(ij+1)Topt(OD|Rij)-ijTopt(OD|Rij-1)4:(a),ri1,,1)3),1111CTD(OD|Ri1-1)i1Topt(OD|Rk),Ti1=(i1+1)Topt(OD|Ri1)-i1Topt(OD|Ri1-1),,,1211().,11=11+122i1opt(OD|Rk)(b)2,ri2,,1)3),2121CTD(OD|Ri2-1)(i2-i1)Topt(OD|Rk)Ti2=(i2+1)Topt(OD|Ri2)-i2Topt(OD|Ri2-1),,,2221().,2j2=21+222(i2-i1)Topt(OD|Rk)(c)j,rij,,(b),jlj2(ij-ij-1)Topt(OD|Rk)(d)j+1,D,1)3),j+1j+1(k-ij+1)Topt(OD|Rk),O,D,CTD(OD|Rk)j+1m=1m2i1Topt(OD|Rk)+2(i2-i1)Topt(OD|Rk)++2(ij-ij-1)Topt(OD|Rk)+(k-ij+1)Topt(OD|Rk)=(k+ij+1)Topt(OD|Rk)884211),2),3),4),,DRk=(r1,r2,,rk)T(Rk)=(t(r1),t(r2),,t(rk))2k+1.4,2k+1,:,.,,,;;,,,.,.,.,,,,,.:[1],.[J].,2003,18(4):324330.[2]ManasseMS,McGeochLA,SleatorDD.Competitivealgorithmsforserverproblems[J].JournalofAlgorithms,1990,11(2):208230.[3]DavidSB,BorodinA.Anewmeasureforthestudyoftheon2linealgorithm[J].Algorithmica,1994,11(1):7391.[4]KoutsoupiasE,PapadimitriouC.Onthek2serverconjecture[J].JournalofACM,1995,42(5):971983.[5]AlonN,KarpPM,PelegD,etal.Agraph2theoreticgameanditsapplicationtothek2serverproblem[J].SIAMJournalonCom2puter,1995,24(1):78100.[6]PinnoiA,TungDT.Vehiclerouting2schedulingforwastecollec