뗚38뻭ꆡ뗚5웚ꆡVol138No152006쓪5퓂ꆡ맾ꆡ뛻ꆡ뇵ꆡ릤ꆡ튵ꆡ듳ꆡ톧ꆡ톧ꆡ놨JOURNALOFHARBININSTITUTEOFTECHNOLOGYMay2006ꆡꆡꆡꆡꆡꆡ볲떥뒮솪럾컱쾵춳뗄럖컶벰펦폃쯯ꆡ?1,췵ꆡ폂2(1.맾뛻뇵릤돌듳톧샭톧풺,뫚쇺붭맾뛻뇵150001,E2mail:swgoodluck@;2.맾뛻뇵릤튵듳톧샭톧풺,뫚쇺붭맾뛻뇵150001)햪ꆡ튪:뛔폐솽룶럾컱첨뗄볲떥뒮솪럾컱쾵춳,퓚늻춬뗄업뛓맦퓲쿂뗄업뛓쟩뿶,뷸탐샭싛짏뗄럖컶,늢뛔믬뫏훆업뛓쾵춳뷸탐쿠펦뗄럖컶,틔뇣붫웤췆맣늢붨솢쒣탍폃폚뷢뻶쪵볊컊쳢.맘볼듊:뒮솪;업뛓쾵춳;믬뫏훆훐춼럖샠뫅:O226컄쿗뇪쪶싫:A컄헂뇠뫅:0367-6234(2006)05-0808-03TheanalysisandapplicationofthesimpletandemservesystemSUNW1ei,WANGY2ong(,HarbinEngineeringUniversity,Harbin150001,China,E2mail:swgoodluck@;,HarbinInstituteofTechnology,Harbin150001,China)Abstract:,:tandem;queuingsystem;mixedꆡꆡퟷ캪업뛓싛훐튻쿮훘튪퇐뺿쓚죝뗄뒮솪럾컱p(ijt)=P(N(t)=(i,j)),쾵춳ꆪꆪꆪ벴룷탅풪(맋뿍)퓚쾵춳훐탨뺭맽튻쾵틗횤{N(t),tꇝ0}쫇튻룶십뛻뿆럲맽돌.쇐럾컱뷗뛎닅샫뾪뗄쾵춳,폐ퟅ훘튪뗄쿖쪵틢틥.뛸쟒,떱쾵춳뒦폚춳볆욽뫢ힴ첬쪱(볻컄쿗컄쿗[1]룸돶쇋쿠펦뗄뗝췆뇭쪾램.놾컄뛔폐솽[2]),폐룶럾컱첨볲떥뒮솪럾컱쾵춳,퓚죽훖늻춬뗄업뛓lim(jt)=0,iꇝꇺꇞpꇤi맦퓲뗄쟩뿶쿂,폃돵뗈랽램뷸탐샭싛짏뗄럖컶폫ꆡꆡ쿂쏦뻍쾵춳뒦폚춳볆욽뫢뗄ힴ첬,뛔쾵춳죽룅삨.훖업뛓맦퓲럖뇰뷸탐쳖싛늢룸돶웤쿠펦뗄쾵춳횸뇪.1ꆡ훷튪샭싛ꆡ업뛓맦퓲캪뗈듽훆뗄럾컱쾵춳쾵춳릲폐솽룶럾컱첨뒮솪,쎿룶첨짏횻폐튻벴솽룶럾컱첨잰뻹죝탭맋뿍업뛓뗈듽럾컱,룶럾컱풱,맋뿍떽듯볤룴뗄탲쇐캪ꇞ{Jn}n=1,쟒쟒맋뿍뗄뗈듽뿕볤컞쿞.Jnꆫꚣ(1,ꛋ),(n=1,2,ꆭꆭ),쫗쿈평쾵춳뗄ힴ첬틆랽돌ퟩ폐죧쿂캢럖랽벴떽듯맽돌쫇떽듯싊캪ꛋ뗄늴쯉맽돌,잰튻뷗뛎돌ퟩ[3]:뗄쫤죫쇷쫇뫳튻뷗뛎뗄쫤돶쇷,맋뿍퓚솽룶럾컱0=-ꛋp00+ꛌ2p01,첨뗄럾컱쪱볤뻹럾듓횸쫽럖늼,럾컱싊럖뇰쫇ꛌ10=ꛋpi-1,0-(ꛋ+ꛌ1)pi0+ꛌ2pi1,폫ꛌ2.짨퓚쪱뿌t쾵춳뗄ힴ첬캪N(t)=(i,j),0=ꛌ1p1,j-1-(ꛋ+ꛌ2)p0j+ꛌ(2p01),j+1,듋쪱뗚튻룶첨잰맋뿍쫽쫇i,뗚뛾룶럾컱첨잰뗄맋0=ꛋp1,j-1-(ꛋ+ꛌ1+ꛌ2)pij+뿍쫇j,늢쟒쇮ꆡꆡꛌ1pp>0).i+1,j-1+ꛌ2i,j+1,(i,j쫕룥죕웚ꆡꆡ짨:2005-03-10.ퟷ헟볲뷩:쯯ꆡ?(1980-),얮,훺뷌.lim(jt)=ptꇺꇞpiijꆡ(Πi,jꇝ0).
뗚5웚쯯ꆡ?,뗈:볲떥뒮솪럾컱쾵춳뗄럖컶벰펦폃ꆤ809ꆤ샻폃룅싊쒸몯쫽뫍죥킪뚨샭뗄탔훊뿉평쪽(1)ꛋꛌ횪,뗚튻룶럾컱첨뗄맋뿍ퟜ쫽뗈폚i뗄룅싊캪P쎦=p01+p10+pb1=3ꛋ2+43ꛋ2+4ꛋꛌ+2ꛌ2.죴ꛑꇔꛋui=ꇆꇞp(ꛑiij=1-ꛑ1)1,(iꇝ0)ꛌ,쓇쎴퓚0<ꛑ<1쪱,쾵춳뒦폚욽j=0뗚뛾룶럾컱첨뗄맋뿍ퟜ쫽뗈폚j뗄룅싊캪컈ힴ첬.쿔좻,ꛑ뛔폚쾵춳뗄룷탔쓜횸뇪폐뫜듳뗄펰쿬.퓚ꛑꇺ1뗄쟩뿶쿂,뿉틔뗃떽틔짏룷쿮뗄뷼vj=ꇆꇞpij=(1-ꛑ2)ꛑi2,(jꇝ0)i=0쯆횵:쫂쪵짏^^^,뿉틔춨맽횱뷓퇩횤횪[4]L쾵=1,P쎦=8,P쯰==(1-ꛑ1)(1-ꛑ2)ꛑi1ꛑj2,(i,j=1,2,ꆭ)ꛑ1ꇔꛋ평폚ꛌ,ꆡꛑ2ꇔꛋ1ꛌ.2P평듋뿉볻쯰=3ꛑ2+4ꛑ3ꛑ2+4ꛑ+2,떱맋뿍샠탍캨튻쪱,솽룶럾컱첨쯤뒦폚춬튻뒮솪쾵춳훐,떫뛾헟뗄맋뿍쫽쫇뇋듋뛀쫇맘폚ꛑꇊ0,1뗄뗝퓶몯쫽,ꛑ풽킡쯰쪧싊뻍솢뗄,늢쟒럾듓쿠춬럖늼.뛸쫂쪵짏,뛔폚듋훖뗈쯦횮복킡.쯹틔0<P쯰<7,틲듋뛔폚퇏룱쯰쪧듽샠탍뗄럾컱쾵춳,떱맋뿍샠탍늻캨튻쪱,쎿훖맋9뿍퓚쾵춳훐뗄죋쫽튲쫇뇋듋뛀솢뗄훆럾컱쾵춳,웤쯰쪧싊틠폐웤퇏룱킡폚1뗄짏쿞..ꆡ업뛓맦퓲캪믬뫏훆뗄럾컱쾵춳.2ꆡ업뛓맦퓲캪쯰쪧훆뗄럾컱쾵춳횻쳖싛퇏룱쯰쪧훆헢튻훖쟩뿶.볙뚨뗚튻룶듋훖샠탍뗄럾컱쾵춳뛠훖뛠퇹,볦맋쇋잰쏦럾컱첨놻햼뻝쪱탂떽뗄맋뿍뻍ퟔ탐샫뾪쾵춳쯻쏇솽헟뗄쒳킩쳘뗣,뛸쟒퓚쪵볊짺닺훐,듳뛠쫽뗄짺늻업뛓닺쇷쮮쿟뻹뿉맩캪듋샠.,춬쪱솽룶럾컱첨횮볤쎻폐뿉틔죃맋뿍뗈듽럾컱뗄뗘랽,틲듋떱맋뿍퓚뗚튻룶럾컱첨췪돉쿂쏦볙뚨럾컱첨2잰훁뛠뿉틔폐N-1룶맋럾컱뫳뿍업뛓,뛸뗚튻룶럾컱첨잰늻죝탭업뛓,짨p,죧맻뗚뛾룶럾컱첨헽놻햼폃,쓇쎴듋맋뿍bN(t)뻍햼뻝뗚튻룶럾컱첨캪t쪱뿌뗚튻룶럾컱첨놻햼뛸늻폃뗄룅싊,늢짨,햼뛸늻폃.짨plimb1(t)캪t쪱뿌뗚튻룶첨놻햼뛸늻폃뗄룅tꇺꇞpbN(t)=pbN.싊,늢짨limtϖꇞpb1(t)=pb1,틲듋폐룹뻝듋훖업뛓맦퓲뿉틔폐쿂쏦뗄랽돌ퟩ:20=-ꛋp00+ꛌ2p01,p10=ꛋꛋꛌ+1ꛌ1(ꛌ1+ꛌp00,2)0=ꛋp00-(ꛋ+ꛌ1)p10+ꛌ2p11,ꛋp0=ꛌ2p0,j+1-(ꛋ+ꛌ2)p0j+ꛌ1p1,j-1,01=ꛌp00,2ꆡꆡ0=ꛌꛋ2p1,j+1-(ꛌ1+ꛌ2)p1j+ꛋp0j,2p11=ꛌ00,0=ꛌ1p1,N-1-(ꛋ+ꛌ2)p0N+ꛌ2pbN,2(ꛌ1+ꛌp2)ꛌ0=-ꛋp0N+(ꛌ1+ꛌ2)p1N,pb=1ꛋ2iꛌ2,2(ꛌ1+ꛌp000=-ꛌ1p1,N+ꛌ2pb,N(1ꇜjꇜN).2)뾼싇쳘쫢쟩뿶N=2,ꛌ1=ꛌ2=ꛌ,퓲폐p00=[(ꛌ2(ꛌ1+ꛌ2)(ꛌ1ꛌ2+ꛋꛌ1+ꛋꛌ2)+ꆡꆡꛋꛋ2ꛌ2(ꛌ21+ꛌp1ꛌ2+ꛌ22))/(ꛌ1ꛌ22(ꛌ-11+ꛌ2)].01=+4ꛋꛌ24ꛋ3+8ꛋ2ꛌ+9ꛋꛌ2+4ꛌ3,쓇쎴,퓚ꛌ1=ꛌ2=ꛌ뗄쳘쫢ힴ첬쿂,쾵춳뗄룷쿮횸뇪죧쿂p:02=2ꛋ2ꛌ4ꛋ3+8ꛋ2ꛌ+9ꛋꛌ2+4ꛌ3,1)쾵춳욽뻹뛓뎤캪ꛋ3pL쾵=p10=+3ꛋ2ꛌ+4ꛋꛌ2ꆡꆡ4ꛋ3+8ꛋ201+p10+2(p11+pb1)=ꛌ+9ꛋꛌ2+4ꛌ3,5ꛋ2+4ꛋꛌꛋ3p3ꛋ2+4ꛋꛌ+2ꛌ=+2ꛋ2ꛌ4ꛋ3+8ꛋ2ꛌ+9ꛋꛌ2+4ꛌ3,ꆡꆡ2)쾵춳럾컱첨쎦뗄룅싊캪ꛋ3p12=pb2=P쎦=p01+p10+2p11+pb1=4ꛋ3+8ꛋ2ꛌ+9ꛋꛌ2+4ꛌ3,4ꛋ2+4ꛋꛌ3ꛋ2+4ꛋꛌ+2ꛌ=4ꛌ3+ꛋ2ꛌ24ꛋ3+8ꛋ2ꛌ+9ꛋꛌ2+4ꛌ)쾵춳쯰쪧싊캪뛸듋쪱쾵춳뗄튻킩횸뇪죧쿂:
ꆤ810ꆤ맾ꆡ뛻ꆡ뇵ꆡ릤ꆡ튵ꆡ듳ꆡ톧ꆡ톧ꆡ놨ꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡ뗚38뻭ꆡ1)욽뻹뛓뎤캪뇭1룸돶쇋솽ퟩ쫽뻝,뿉볻평폚룷훖럑폃ꆢ쾵춳럾컱싊벰떽듯싊뗄늻춬,틽웰욽뻹ퟜ쯰쪧럑폃뗄늻L쾵=9ꛋ3+12ꛋ2ꛌ+8ꛋꛌ24ꛋ3+8ꛋ2ꛌ+9ꛋꛌ2+4ꛌ3.춬.웤훐뗚튻ퟩ뗄죽훖럑폃뻹늻룟폚뗚뛾ퟩ뗄쿠펦ꆡꆡ2)쾵춳쯰쪧싊캪뗄럑폃,횻폐ꛋ폫ꛌ싔룟폚뫳헟뗄쿠펦횵,좴떼훂P쎦=4ꛋ3+5ꛋ2ꛌ+4ꛋꛌ2웤ퟮ훕뗄F횵튪룟폚뗚뛾ퟩ뗄F횵.틲듋,퓚헢샯ꛋ4ꛋ3+8ꛋ2ꛌ+9ꛋꛌ2+4ꛌ3.폫ꛌ뛔폚F뗄좡횵폐ퟅ벫캪훘튪뗄펰쿬.ꆡꆡ3)뗚튻룶럾컱첨쎦뗄룅싊캪뇭1ꆡ쾵춳떥캻쪱볤뗄쯰쪧럑폃벰닎쫽P1,쎦=p10+p11+p12=떥캻abcꛌꛋF3ꛋ3+5ꛋ2ꛌ+4ꛋꛌ2뗚튻ퟩ01801110610601600187991514ꛋ3+8ꛋ2ꛌ+9ꛋꛌ2+4ꛌ3.뗚뛾ퟩ1170111081600156016071110ꆡꆡ4)뗚뛾룶럾컱첨쎦뗄룅싊캪ꆡꆡ떫퓚탭뛠쟩뿶훐,평폚맋뿍뗄샠뇰늻춬,뛸쪹P2,쎦=p01+p02+p11+p12+pb2=쯻쏇뗄떽듯싊폫룷럾컱첨뛔웤뗄럾컱싊튲폐쯹늻3ꛋ3+5ꛋ2ꛌ+4ꛋꛌ2춬.듋쪱,뻍뿉틔틽죫쿠펦뗄뿘훆뇤솿,뛔욽뻹ퟜ4ꛋ3+8ꛋ2ꛌ+9ꛋꛌ2+4ꛌ3.쯰쪧솿볓틔뿘훆,듯떽쟳돶컊쳢ퟮ폅뷢뗄쒿뗄.ꆡꆡ뿉볻,듋쪱쯤좻솽룶럾컱첨럖쫴폚늻춬뗄업쫂쪵짏,퓚쪵볊컊쳢훐,평폚럾컱맦퓲뗈훮뛠뛓샠탍,떫횻튪뛾헟뗄럾컱싊쿠춬,쓇쎴쯼쏇쎦뗄틲쯘펰쿬틽웰붨솢뗄업뛓쒣탍늻춬,쒣탍훐뗄룷룅싊뻍쫇쿠춬뗄.뛸쟒,럾컱첨뗄샻폃싊쫇쯦ퟅ럾쿮횸뇪튲폐쯹닮틬.떫뒦샭컊쳢뗄랽램쫇듳춬킡컱첨죝솿뗄퓶듳뛸퓶듳뗄,틲뛸,퓚쾵춳뗄떽듯싊틬뗄.쇭췢,샻폃볆쯣믺쒣쓢,뿉틔쪵쿖업뛓싛퓚벰럾컱싊좷뚨뗄쟩뿶쿂,쫊떱뗄퓶볓럾컱첨뗄죝룷룶쇬폲뗄펦폃,죧퓚럀뿕럀폹쾵춳훐,떱쒿뇪뷸솿,뻍뿉틔폐킧뗄쳡룟쾵춳뗄럾컱킧싊.죫룟엚뗄믰솦랶캧,뻍폐룟엚뛔뗚튻닣캴믷믙믲2ꆡ펦ꆡ폃춻럀뗄쒿뇪뷸탐뗚뛾닣삹뷘,탎돉춳튻뗄럀뿕믰솦쾵춳,쳡룟쇋럀폹낲좫룅싊.퓚웳튵펪쿺닟싔쿖쪵짺믮훐,퇐뺿쯦믺럾컱쾵춳뗄훷튪쒿뗄훐,틔뫏춬뫍킭틩캪쿟쯷,냑펪쿺믮뚯훐뗄룷룶뮷뻍쫇틔ퟮ폅뗄짨놸(쒣탍)뗃떽ퟮ듳뗄킧틦[5].쿂뷚폐믺뒮솪웰살,틑탎돉췪헻뗄펪쿺췸싧,쪵쿖닺쏦뻍뛔잰쏦룸돶뗄욷뫍뺭쿺짌뗄뚯첬맜샭.N=2,ꛌ1=ꛌ2=ꛌꆡꆡ퓚놾컄뗄믹뒡짏,룹뻝릤ퟷ뗄탨튪뷸탐뷸튻믬뫏훆럾컱쒣탍뗄킧틦뷸탐볲떥뗄럖컶.늽뗄퇐뺿,뻍뿉틔듯떽돤럖샻폃풴,붵뗍쯰쪧뗄볙짨쾵춳훐폐죽훖럑폃:쒿뗄.1)럾컱럑.폫욽뻹럾컱쯙뛈돉헽뇈,틔욽뻹럾컱쯙뛈퓚떥캻쪱볤뗄럾컱럑폃쫇a닎뾼컄쿗:.2)뗈듽럑.폫욽뻹뛓뎤돉헽뇈.쎿룶맋뿍퓚[1]훜볒솼,볖ꆡ늨.폐ퟨ죻뗄뛠벶뒮솪업뛓쾵춳럖컶쾵춳훐뚺쇴,쾵춳탨횧뢶뗄업뛓럑폃쫇b.[J].쾵춳뿆톧폫쫽톧,1988,18(1):)볤뷓쯰쪧럑.벴평폚쯰쪧맋뿍뛸쯰쪧뗴[2]탬맢믔.쯦믺럾컱쾵춳[M].놱뺩:뿆톧돶냦짧,뗄샻죳.쯰쪧쾵쫽쫇c1988..쯹틔떥캻쪱볤쓚뗄욽뻹ퟜ쯰쪧쫇[3]=service[M].OperationResearch,ꛌ+bL쾵+cP쯰.붨솢ퟮ폅뮯컊쳢[4]뮪ꆡ탋.업뛓싛폫쯦믺럾컱쾵춳[M].짏몣:짏몣랭틫돶냦릫쮾,=2aꛌ+bL쾵+cP쯰,[5]슽럯즽.업뛓싛벰웤펦폃[M].뎤즳:뫾쓏뿆톧뿆벼ꆡꆡ<ꛋ<ꛌ.돶냦짧,1984.(뇠벭ꆡ췵킡캨)샻폃ퟮ폅뮯뚨샭뻍쓜좷뚨듋컊쳢뗄ퟮ폅횵ꛋ폫ꛌ.
