// kanban manufacturing example [CT96]
// dxp/gxn 3/2/00

ctmc

// number of tokens 
const int t = 1; 

// rates
const double in1      = 1.0;
const double out4     = 0.9;
const double synch123 = 0.4;
const double synch234 = 0.5;
const double back     = 0.3;
const double redo1    = 0.36;
const double redo2    = 0.42;
const double redo3    = 0.39;
const double redo4    = 0.33;
const double ok1      = 0.84;
const double ok2      = 0.98;
const double ok3      = 0.91;
const double ok4      = 0.77;

module k1

	w1 : [0..t];
	x1 : [0..t];
	y1 : [0..t];
	z1 : [0..t];
	
	[in]   (w1<t) & (x1<t) -> in1 	 : (w1'=w1+1) & (x1'=x1+1);
	[]   (x1>0) & (y1<t) -> redo1	 : (x1'=x1-1) & (y1'=y1+1);
	[]   (x1>0) & (z1<t) -> ok1 	 : (x1'=x1-1) & (z1'=z1+1);
	[]   (y1>0) & (x1<t) -> back	 : (y1'=y1-1) & (x1'=x1+1);
	[s1] (z1>0) & (w1>0) -> synch123 : (z1'=z1-1) & (w1'=w1-1);

endmodule

module k2

	w2 : [0..t];
	x2 : [0..t];
	y2 : [0..t];
	z2 : [0..t];
	
	[s1] (w2<t) & (x2<t) -> 1	 : (w2'=w2+1) & (x2'=x2+1);
	[]   (x2>0) & (y2<t) -> redo2 : (x2'=x2-1) & (y2'=y2+1);
	[]   (x2>0) & (z2<t) -> ok2   : (x2'=x2-1) & (z2'=z2+1);
	[]   (y2>0) & (x2<t) -> back  : (y2'=y2-1) & (x2'=x2+1);
	[s2] (z2>0) & (w2>0) -> 1	 : (z2'=z2-1) & (w2'=w2-1);

endmodule

module k3

	w3 : [0..t];
	x3 : [0..t];
	y3 : [0..t];
	z3 : [0..t];
	
	[s1] (w3<t) & (x3<t) -> 1	 : (w3'=w3+1) & (x3'=x3+1);
	[]   (x3>0) & (y3<t) -> redo3 : (x3'=x3-1) & (y3'=y3+1);
	[]   (x3>0) & (z3<t) -> ok3   : (x3'=x3-1) & (z3'=z3+1);
	[]   (y3>0) & (x3<t) -> back  : (y3'=y3-1) & (x3'=x3+1);
	[s2] (z3>0) & (w3>0) -> 1	 : (z3'=z3-1) & (w3'=w3-1);


endmodule

module k4

	w4 : [0..t];
	x4 : [0..t];
	y4 : [0..t];
	z4 : [0..t];
	
	[s2] (w4<t) & (x4<t) -> synch234 : (w4'=w4+1) & (x4'=x4+1);
	[]   (x4>0) & (y4<t) -> redo4	: (x4'=x4-1) & (y4'=y4+1);
	[]   (x4>0) & (z4<t) -> ok4  	: (x4'=x4-1) & (z4'=z4+1);
	[]   (y4>0) & (x4<t) -> back 	: (y4'=y4-1) & (x4'=x4+1);
	[]   (z4>0) & (w4>0) -> out4 	: (z4'=z4-1) & (w4'=w4-1);

endmodule

// reward structures

// tokens in cell1
rewards "tokens_cell1"
	true : x1+y1+z1;
endrewards

// tokens in cell2
rewards "tokens_cell2"
	true : x2+y2+z2;
endrewards

// tokens in cell3
rewards "tokens_cell3"
	true : x3+y3+z3;
endrewards

// tokens in cell4
rewards "tokens_cell4"
	true : x4+y4+z4;
endrewards

// throughput of the system
rewards "throughput"
	[in] true : 1;
endrewards