Petri网基本概念和分析方法

1Petri::N={0,1,2,…},N+={0,1,2,…}..PetriPN=(P,T,F,W,M0),:—P(place);—T(transition);—P…T=«,P»T∫«;—FŒ(PäT)»(PäT);—w:FöN+;—M0:PöN()..PetriN=(P,T,F,W),M0Petri(N,M0).PNPetri,M:PöN.pœP,M(p)=k,pk(token).Petri:P={p1,p2,…,pm},M(pi)=ki,M=(k1,k2,…,km).(p,t)œFŒPäT,pt;(t,p)œFŒTäP,pt.(p,t)œF(t,p)œF,w(p,t)w(t,p).().M:PöNPetri(N,M0),tœT.(1)tM(enable),tp,:M(p)¥w(p,t).(2)tM,M£:pœP,M(p)-w(p,t)ptM£(p)=M(p)+w(t,p)ptM(p)pt(),MM£,MtM£.1.2H2+O2ö2H2OPetri.21.1.PetriPetri,.,(markedgraph).2.Petri..1.2.Petri.p,p,,,,.1.3.,,t1,t2œT,t1,t2,.3.t2,t3,.31.4.Petri.(),.(a)t1,t2,t3.(b)t1,t2,t2t1,t1t3.1.5.Petri.(a)Petri(b)1.6.4.Petri2.1(N,M0)Petri.s=t1…tn:M0t1M1t2M2…tnMn.(N,M0)L(N,M0)L(M0).s=t1…tnœL(M0),M0t1M1t2M2…tnMn,MnM0s,M0[sMn.M0R(N,M0)R(M0).Petri.(N,M0)M,MœR(M0)?2.2kœN.Petri(N,M0)k-,pMœR(M0),M(p)§k.(N,M0),1-.2.3Petri(N,M0),MœR(M0),,.Petri,,.,Petri:2.1..tPetri(N,M0).:(1)L(M0),t,tL0-();5(2)L(M0),t,tL1-();(3)kœN,L(M0),tk,tL2-;(3)L(M0),t,tL3-;(4)MœR(M0),tL3-,tL4-().k=0,1,2,3,4,Petri(N,M0)Lk-,Lk-.:L4-flL3-flL2-flL1-k=1,2,3,Petri(N,M0)Lk-,(N,M0)Lk-,Lk+1-.,2.2.t1,.2.2.,L1-,Petri.2.4Petri(N,M0),MœR(M0),M0œR(M).(N,M0)M£(Homestate),MœR(M0),M£œR(M).,,.2.5Petri(N,M0)M,$M£œR(M0),:pœP,M(p)§M£(p).t,Mt..Petri(N,M0)tL1-‹Mt.62.6Petri(N,M),(N,M)t1,t2,t1t2.,,.2.3.,2.7(N,M)Petri,s,t.s-(t)ts.(N,M)t1,t2,t1,t2:d12=masx|s-(t1)-s-(t2)|.,2.4,d12=1,d34=1,d13=¶.2.4.72.8(N,M)Petri,t1,t2(boundedfair,B-fair),.Petri(N,M)(B-fair),.s,s,s.Petri(N,M),s..(1)B-fair.(2)B-fair.,2.4B-fair,,t3,t4s=t2t1t2t1.......2.3,B-fair,p2,t2.2.5B-fair,.2.5.B-fair/8.Petri3.1Petri()().:,w“”,w:nœN,wn,w≤n=w,w¥w.(N,M0)Petri,(N,M0)T..Step1),“new”.Step2)“new”,:Step2.1)“new”M.Step2.2)MM,M“old”,“new”.Step2.3)M,,M“dead-end”.Step2.4)Mt,:Step2.4.1)MtM£.Step2.4.2)M,M££,M£∫M££,pœP,M£(p)¥M££(p),M£(p)M££(p)pœP,wM£(p).Step2.4.3)M£,MM£t.1.3.1Petri.,(3.2).3.1.Petri(N,M0),M0=(100).93.2.PetriPetri(N,M0)T,.:(1)(N,M0)(R(M0))‹wT.(2)(N,M0)‹01T.(3)t‹Tt.(4)MM0,TM£,M£¥M.Petri(N,M0),T,T(N,M0).,(N,M0).,.Petri(N,M0),w(),.2.3.3Petri,(a),(b)t1,t2,t3,.3.3.Petri,(a),(b).10:(3.4).3.4.3.3Petri.Petri(N,M0)G=(V,E),VT,ETtk,tk:Mi[tkMj,Mi,MjœV.3.3.5(a)(b)3.33.4Petri.(a)(b)3.5.Petri.113.2Petri,().,,:3.6.PetriPetriN,:T={t1,...,tn},P={p1,...,pm}.i=1,...,n,j=1,...,m,:a+ij=w(ti,pj),a-ij=w(pj,ti),aij=a+ij-a-ij.nämA=[aij]PetriN.Petri,a-ij,a+ij,aijti,pj,token.,Aiti,.,tiM‹a-ij§M(pj)(j=1,...,m).kœN+,kuknä1,n-10,i1tik.kMkmä1,jk,pjtoken.,PetriN:Mk=Mk-1+ATuk,k=1,2,....(1)Md{u1,...,ud}M0.i=1,...,d,(1),,:Md=M0+ATÊdk=1uk.(2)DM=Md-M0,x=Êdk=1uk,(2):ATx=DM.(3)nä1x,iM0Md,ti.,(3)12:Ay=0(4)y,DMÿy=0.r=rank(A),A=⎟⎟⎠⎞⎜⎜⎝⎛22211211AAAA,A12rär.Bf=[Im,-AT11(AT12)-1],(5)Imm-r.:DMÿy=0‹BfDM=0.:.Petri(N,M0),MdM0.BfDM=0..(N,M0)Petri,Md:mä1z,DM=BTfz,MdM0..,BfDM=BfBTfz.BfBTfmäm,z∫0,BfBTfz∫0,..3.7Petri,M0=(2010)T.t3M1=(3002)T.18.Petri.:AT=⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛−−−−220101011112.13:⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛2003=⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛0102+⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛−−−−220101011112⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛100.,r=rank(A)=2,:A11=⎟⎟⎠⎞⎜⎜⎝⎛−−1112,A12=⎟⎟⎠⎞⎜⎜⎝⎛−2001.(5):Bf=⎟⎟⎠⎞⎜⎜⎝⎛−−2/11102/1201.,DM=M1-M0=(10-12)T,BfDM=0.3.3Petri,.(1)(FSP)(2)(FST)(3)(FPP)14(4)(FTP)(5)(ESP)(6)(EST).3.8Petri.3.8.Petrit2,t1,t2t12,t3,t4t34,20(a)Petri.,,20(b)Petri.,Petri.3.9.Petri15.Petri4.1.Petri,token,.Petri(CP-).•token,token.•token.CP-:•.•.•.•.1..,:(1)q-(A,B,C,D,E),(2)p-(B,C,D,E),(3)R,S,T.4.1.CP-16,,.,R,S,Ttoken.,.Petri:(1)(Declarations):(Types),(Functions),(Operations)(Variables).(2)(inscription):(Name,),(ColourSet,token,token),(Initialmarking).(3)(inscription):(),(guard,Boole).(4)(inscription):(),.(binding)().(t,b),t,bt.,(T2,‚x=p,i=2Ú).(t,b),:(1)ttoken;(2)tb.(t,b),():(1)ttoken;(2)ttoken.2..(a)17(b)(c)4.2.3..4.3.()4..(a)18(b)(c)4.4.5..,token().4.5.6..,token().4.5.196.CP-.4.5.():typeINT=int;typeBOOL=bool;typeDATA=string;typeINTxDATA=productINT*DATA;varn,k:INT;varp,str:DATA;varstop=########;typeInt_0_10=intwith0..10;typeInt_1_10=intwith1..10;vars:Int_0_10;varr:Int_1_10;funOk(s:Int_0_10,r:Int_1_10)=(r§s);4.6.(a),‚n=1,p=“Modellin”Ú.,20tokenA,token(1,“Modellin”).Send,NextSend.4.6.(b),10‚n=1,p=“Modellin”,s=8,r=1...10Ú.Ok(s,r)r§s.4.6.(c)nk.4.6.(d)214.2.CP-().,,..(socketplaces),(portplaces),.7..4.7.CP-224.3.CP-,token()(token).8..(send)(receive),(network)(,2575),Waittoken.4.8.CP-570.SendPacket5702,,2670.570,TransmitPacket.234.9.CP-