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126 lines
3.8 KiB
126 lines
3.8 KiB
// flexible manufacturing system [CT93]
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// gxn/dxp 11/06/01
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ctmc // model is a ctmc
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const int n = 2; // number of tokens
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// rates from Pi equal #(Pi) * min(1, np/r)
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// where np = (3n)/2 and r = P1+P2+P3+P12
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const int np=floor((3*n)/2);
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formula r = P1+P2+P3+P12;
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module machine1
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P1 : [0..n] init n;
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P1wM1 : [0..n];
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P1M1 : [0..3];
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P1d : [0..n];
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P1s : [0..n];
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P1wP2 : [0..n];
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M1 : [0..3] init 3;
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[t1] (P1>0) & (M1>0) & (P1M1<3) -> P1*min(1,np/r) : (P1'=P1-1) & (P1M1'=P1M1+1) & (M1'=M1-1);
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[t1] (P1>0) & (M1=0) & (P1wM1<n) -> P1*min(1,np/r) : (P1'=P1-1) & (P1wM1'=P1wM1+1);
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[] (P1M1>0) & (P1wM1=0) & (M1<3) & (P1s<n) -> 0.2*P1M1 : (P1M1'=P1M1-1) & (M1'=M1+1) & (P1s'=P1s+1);
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[] (P1M1>0) & (P1wM1>0) & (P1s<n) -> 0.2*P1M1 : (P1wM1'=P1wM1-1) & (P1s'=P1s+1);
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[] (P1M1>0) & (P2wP1=0) & (P1wM1=0) & (M1<3) & (P1wP2<n) -> 0.05*P1M1 : (P1M1'=P1M1-1) & (M1'=M1+1) & (P1wP2'=P1wP2+1);
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[] (P1M1>0) & (P2wP1=0) & (P1wM1>0) & (P1wP2<n) -> 0.05*P1M1 : (P1wM1'=P1wM1-1) & (P1wP2'=P1wP2+1);
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[p1p2] (P1M1>0) & (P2wP1>0) & (P1wM1=0) & (M1<3) -> 0.05*P1M1 : (P1M1'=P1M1-1) & (M1'=M1+1);
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[p1p2] (P1M1>0) & (P2wP1>0) & (P1wM1>0) -> 0.05*P1M1 : (P1wM1'=P1wM1-1);
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[p1p2] (P1wP2>0) -> 1: (P1wP2'=P1wP2-1);
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[] (P1s>0) & (P1+P1s<=n) -> 1/60 : (P1s'=0) & (P1'=P1+P1s);
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[fp12] (P1+P12s<=n) -> 1: (P1'=P1+P12s);
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endmodule
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module machine2
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P2 : [0..n] init n;
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P2wM2 : [0..n];
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P2M2 : [0..1];
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P2s : [0..n];
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P2wP1 : [0..n];
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M2 : [0..1] init 1;
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[t2] (P2>0) & (M2>0) & (P2M2<1) -> P2*min(1,np/r) : (P2'=P2-1) & (P2M2'=P2M2+1) & (M2'=M2-1);
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[t2] (P2>0) & (M2=0) & (P2wM2<n) -> P2*min(1,np/r) : (P2'=P2-1) & (P2wM2'=P2wM2+1);
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[] (P2M2>0) & (P2wM2=0) & (M2<1) & (P2s<n) -> 0.1 : (P2M2'=P2M2-1) & (M2'=M2+1) & (P2s'=P2s+1);
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[] (P2M2>0) & (P2wM2>0) & (P2s<n) -> 0.1 : (P2wM2'=P2wM2-1) & (P2s'=P2s+1);
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[] (P2M2>0) & (P1wP2=0) & (P2wM2=0) & (M2<1) & (P2wP1<n) -> 1/15: (P2M2'=P2M2-1) & (M2'=M2+1) & (P2wP1'=P2wP1+1);
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[] (P2M2>0) & (P1wP2=0) & (P2wM2>0) & (P2wP1<n) -> 1/15: (P2wM2'=P2wM2-1) & (P2wP1'=P2wP1+1);
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[p1p2] (P2M2>0) & (P1wP2>0) & (P2wM2=0) & (M2<1) -> 1/15: (P2M2'=P2M2-1) & (M2'=M2+1);
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[p1p2] (P2M2>0) & (P1wP2>0) & (P2wM2>0) -> 1/15: (P2wM2'=P2wM2-1);
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[p1p2] (P2wP1>0) -> 1 : (P2wP1'=P2wP1-1);
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[] (P2s>0) & (P2+P2s<=n) -> 1/60 : (P2s'=0) & (P2'=P2+P2s);
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[fp12] (P2+P12s<=n) -> 1 : (P2'=P2+P12s);
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[p2p3] (M2>0) -> 1 : (M2'=M2);
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endmodule
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module machine3
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P3 : [0..n] init n;
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P3M2 : [0..n];
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P3s : [0..n];
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[t3] (P3>0) & (P3M2<n) -> P3*min(1,np/r) : (P3'=P3-1) & (P3M2'=P3M2+1);
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[p2p3] (P3M2>0) & (P3s<n) -> 1/2 : (P3M2'=P3M2-1) & (P3s'=P3s+1);
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[] (P3s>0) & (P3+P3s<=n) -> 1/60 : (P3s'=0) & (P3'=P3+P3s);
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endmodule
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module machine12
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P12 : [0..n];
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P12wM3 : [0..n];
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P12M3 : [0..2];
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P12s : [0..n];
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M3 : [0..2] init 2;
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[p1p2] (P12<n) -> 1: (P12'=P12+1);
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[t12] (P12>0) & (M3>0) & (P12M3<2) -> P12*min(1,np/r) : (P12'=P12-1) & (P12M3'=P12M3+1) & (M3'=M3-1);
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[t12] (P12>0) & (M3=0) & (P12wM3<n) -> P12*min(1,np/r) : (P12'=P12-1) & (P12wM3'=P12wM3+1);
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[] (P12M3>0) & (P12wM3=0) & (P12s<n) & (M3<2) -> P12M3 : (P12M3'=P12M3-1) & (P12s'=P12s+1) & (M3'=M3+1);
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[] (P12M3>0) & (P12wM3>0) & (P12s<n) -> P12M3 : (P12wM3'=P12wM3-1) & (P12s'=P12s+1);
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[fp12] (P12s>0) -> 1/60 : (P12s'=0);
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endmodule
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// reward structures
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// throughput of machine1
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rewards "throughput_m1"
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[t1] true : 1;
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endrewards
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// throughput of machine2
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rewards "throughput_m2"
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[t2] true : 1;
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endrewards
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// throughput of machine3
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rewards "throughput_m3"
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[t3] true : 1;
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endrewards
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// throughput of machine12
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rewards "throughput_m12"
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[t12] true : 1;
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endrewards
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// productivity of the system
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rewards "productivity"
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[t1] true : 400;
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[t2] true : 600;
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[t3] true : 100;
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[t12] true : 1100;
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endrewards
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