// firewire protocol with integer semantics
// dxp/gxn 14/06/01

// CLOCKS
// x1 (x2) clock for node1 (node2)
// y1 and y2 (z1 and z2) clocks for wire12 (wire21)

mdp

// maximum and minimum delays
// fast
const int rc_fast_max = 85;
const int rc_fast_min = 76;
// slow
const int rc_slow_max = 167;
const int rc_slow_min = 159;
// delay caused by the wire length
const int delay=3;
// probability of choosing fast
const double fast1; // = 0.5;
const double slow1=1-fast1;
const double fast2; // = 0.5;
const double slow2=1-fast2;

module wire12
	
	// local state
	w12 : [0..9];
	// 0 - empty
	// 1 -	rec_req
	// 2 -  rec_req_ack
	// 3 -	rec_ack
	// 4 -	rec_ack_idle
	// 5 -	rec_idle
	// 6 -	rec_idle_req
	// 7 -	rec_ack_req
	// 8 -	rec_req_idle
	// 9 -	rec_idle_ack
	
	// clock for wire12
	y1 : [0..delay+1];
	y2 : [0..delay+1];

	// empty
	// do not need y1 and y2 to increase as always reset when this state is left
	// similarly can reset y1 and y2 when we re-enter this state
	[snd_req12]  w12=0 -> (w12'=1) & (y1'=0) & (y2'=0);
	[snd_ack12]  w12=0 -> (w12'=3) & (y1'=0) & (y2'=0);
	[snd_idle12] w12=0 -> (w12'=5) & (y1'=0) & (y2'=0);
	[time]       w12=0 -> (w12'=w12);	
	// rec_req
	[snd_req12]  w12=1 -> (w12'=1);
	[rec_req12]  w12=1 -> (w12'=0) & (y1'=0) & (y2'=0);
	[snd_ack12]  w12=1 -> (w12'=2) & (y2'=0);
	[snd_idle12] w12=1 -> (w12'=8) & (y2'=0);
	[time]       w12=1 & y2<delay ->  (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1));
	// rec_req_ack
	[snd_ack12] w12=2 -> (w12'=2);
	[rec_req12] w12=2 -> (w12'=3);
	[time]      w12=2 & y1<delay ->  (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1));
	// rec_ack
	[snd_ack12]  w12=3 -> (w12'=3);
	[rec_ack12]  w12=3 -> (w12'=0) & (y1'=0) & (y2'=0);
	[snd_idle12] w12=3 -> (w12'=4) & (y2'=0);
	[snd_req12]  w12=3 -> (w12'=7) & (y2'=0);
	[time]       w12=3 & y2<delay ->  (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1));
	// rec_ack_idle
	[snd_idle12] w12=4 -> (w12'=4);
	[rec_ack12]  w12=4 -> (w12'=5);
	[time]       w12=4 & y1<delay ->  (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1));
	// rec_idle
	[snd_idle12] w12=5 -> (w12'=5);
	[rec_idle12] w12=5 -> (w12'=0) & (y1'=0) & (y2'=0);
	[snd_req12]  w12=5 -> (w12'=6) & (y2'=0);
	[snd_ack12]  w12=5 -> (w12'=9) & (y2'=0);
	[time]       w12=5 & y2<delay ->  (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1));
	// rec_idle_req
	[snd_req12]  w12=6 -> (w12'=6);
	[rec_idle12] w12=6 -> (w12'=1);
	[time]       w12=6 & y1<delay ->  (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1));
	// rec_ack_req
	[snd_req12] w12=7 -> (w12'=7);
	[rec_ack12] w12=7 -> (w12'=1);
	[time]      w12=7 & y1<delay ->  (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1));
	// rec_req_idle
	[snd_idle12] w12=8 -> (w12'=8);
	[rec_req12]  w12=8 -> (w12'=5);
	[time]       w12=8 & y1<delay ->  (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1));
	// rec_idle_ack
	[snd_ack12]  w12=9 -> (w12'=9);
	[rec_idle12] w12=9 -> (w12'=3);
	[time]       w12=9 & y1<delay ->  (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1));
	
endmodule

module node1
	
	// clock for node1
	x1 : [0..168];
	
	// local state
	s1 : [0..8];
	// 0 - root contention
	// 1 - rec_idle
	// 2 - rec_req_fast
	// 3 - rec_req_slow
	// 4 - rec_idle_fast
	// 5 - rec_idle_slow
	// 6 - snd_req
	// 7- almost_root
	// 8 - almost_child
	
	// added resets to x1 when not considered again until after rest
	// removed root and child (using almost root and almost child)
	
	// root contention immediate state)
	[snd_idle12] s1=0 -> fast1 : (s1'=2) & (x1'=0) +  slow1 : (s1'=3) & (x1'=0);
	[rec_idle21] s1=0 -> (s1'=1);
	// rec_idle immediate state)
	[snd_idle12] s1=1 -> fast1 : (s1'=4) & (x1'=0) +  slow1 : (s1'=5) & (x1'=0);
	[rec_req21]  s1=1 -> (s1'=0);
	// rec_req_fast
	[rec_idle21] s1=2 -> (s1'=4);	
	[snd_ack12]  s1=2 & x1>=rc_fast_min -> (s1'=7) & (x1'=0);
	[time]       s1=2 & x1<rc_fast_max -> (x1'=min(x1+1,168));
	// rec_req_slow
	[rec_idle21] s1=3 -> (s1'=5);
	[snd_ack12]  s1=3 & x1>=rc_slow_min -> (s1'=7) & (x1'=0);
	[time]       s1=3 & x1<rc_slow_max -> (x1'=min(x1+1,168));
	// rec_idle_fast
	[rec_req21] s1=4 -> (s1'=2);
	[snd_req12] s1=4 & x1>=rc_fast_min -> (s1'=6) & (x1'=0);
	[time]      s1=4 & x1<rc_fast_max -> (x1'=min(x1+1,168));
	// rec_idle_slow
	[rec_req21] s1=5 -> (s1'=3);
	[snd_req12] s1=5 & x1>=rc_slow_min -> (s1'=6) & (x1'=0);
	[time]      s1=5 & x1<rc_slow_max -> (x1'=min(x1+1,168));
	// snd_req 
	// do not use x1 until reset (in state 0 or in state 1) so do not need to increase x1
	// also can set x1 to 0 upon entering this state
	[rec_req21] s1=6 -> (s1'=0);
	[rec_ack21] s1=6 -> (s1'=8);
	[time]      s1=6 -> (s1'=s1);
	// almost root (immediate) 
	// loop in final states to remove deadlock
	[] s1=7 & s2=8 -> (s1'=s1);
	[] s1=8 & s2=7 -> (s1'=s1);
	[time] s1=7 -> (s1'=s1);
	[time] s1=8 -> (s1'=s1);
	
endmodule

// construct remaining automata through renaming
module wire21=wire12[w12=w21, y1=z1, y2=z2, 
	snd_req12=snd_req21, snd_idle12=snd_idle21, snd_ack12=snd_ack21,
	rec_req12=rec_req21, rec_idle12=rec_idle21, rec_ack12=rec_ack21]
endmodule
module node2=node1[s1=s2, s2=s1, x1=x2, fast1=fast2, slow1=slow2,
	rec_req21=rec_req12, rec_idle21=rec_idle12, rec_ack21=rec_ack12,
	snd_req12=snd_req21, snd_idle12=snd_idle21, snd_ack12=snd_ack21]
endmodule

// labels
label "done" = (s1=8 & s2=7) | (s1=7 & s2=8);

// reward structures

// time
rewards "time"	
	[time] true : 1;
endrewards

// time nodes sending
rewards "time_sending"
	[time] (w12>0 | w21>0) : 1;
endrewards