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// power manager example
mdp
const int QMAX =2; // max queue size
// to model the pm making a choice and then a move being made we need
// two clock ticks for each transition
// first the pm decides tick1 and then the system moves tick2
module timer
c : [0..1];
[tick1] c=0 -> (c'=1);
[tick2] c=1 -> (c'=0);
endmodule
//-------------------------------------------------------------------------
// POWER MANAGER
module PM
pm : [0..4] init 4;
// 0 - go to active
// 1 - go to idle
// 2 - go to idlelp
// 3 - go to stby
// 4 - go to sleep
[tick1] true -> (pm'=0);
[tick1] true -> (pm'=1);
[tick1] true -> (pm'=2);
[tick1] true -> (pm'=3);
[tick1] true -> (pm'=4);
endmodule
//-------------------------------------------------------------------------
// SERVICE REQUESTER
module SR
sr : [0..1] init 0;
// 0 idle
// 1 1req
[tick2] sr=0 -> 0.898: (sr'=0) + 0.102: (sr'=1);
[tick2] sr=1 -> 0.454: (sr'=0) + 0.546: (sr'=1);
endmodule
//-------------------------------------------------------------------------
// SERVICE PROVIDER
module SP
sp : [0..10] init 9;
// 0 active
// 1 idle
// 2 active_idlelp
// 3 idlelp
// 4 idlelp_active
// 5 active_stby
// 6 stby
// 7 stby_active
// 8 active_sleep
// 9 sleep
// 10 sleep_active
// states where PM has no control (transient states)
[tick2] sp=2 -> 0.75 : (sp'=2) + 0.25 : (sp'=3); // active_idlelp
[tick2] sp=4 -> 0.25 : (sp'=0) + 0.75 : (sp'=4); // idlelp_active
[tick2] sp=5 -> 0.995 : (sp'=5) + 0.005 : (sp'=6); // active_stby
[tick2] sp=7 -> 0.005 : (sp'=0) + 0.995 : (sp'=7); // stby_active
[tick2] sp=8 -> 0.9983 : (sp'=8) + 0.0017 : (sp'=9); // active_sleep
[tick2] sp=10 -> 0.0017 : (sp'=0) + 0.9983 : (sp'=10); // sleep_active
// states where PM has control
// goto_active
[tick2] sp=0 & pm=0 -> (sp'=0); // active
[tick2] sp=1 & pm=0 -> (sp'=0); // idle
[tick2] sp=3 & pm=0 -> (sp'=4); // idlelp
[tick2] sp=6 & pm=0 -> (sp'=7); // stby
[tick2] sp=9 & pm=0 -> (sp'=10); // sleep
// goto_idle
[tick2] sp=0 & pm=1 -> (sp'=1); // active
[tick2] sp=1 & pm=1 -> (sp'=1); // idle
[tick2] sp=3 & pm=1 -> (sp'=3); // idlelp
[tick2] sp=6 & pm=1 -> (sp'=6); // stby
[tick2] sp=9 & pm=1 -> (sp'=9); // sleep
// goto_idlelp
[tick2] sp=0 & pm=2 -> (sp'=2); // active
[tick2] sp=1 & pm=2 -> (sp'=2); // idle
[tick2] sp=3 & pm=2 -> (sp'=3); // idlelp
[tick2] sp=6 & pm=2 -> (sp'=6); // stby
[tick2] sp=9 & pm=2 -> (sp'=9); // sleep
// goto_stby
[tick2] sp=0 & pm=3 -> (sp'=5); // active
[tick2] sp=1 & pm=3 -> (sp'=5); // idle
[tick2] sp=3 & pm=3 -> (sp'=5); // idlelp
[tick2] sp=6 & pm=3 -> (sp'=6); // stby
[tick2] sp=9 & pm=3 -> (sp'=9); // sleep
// goto_sleep
[tick2] sp=0 & pm=4 -> (sp'=8); // active
[tick2] sp=1 & pm=4 -> (sp'=8); // idle
[tick2] sp=3 & pm=4 -> (sp'=8); // idlelp
[tick2] sp=6 & pm=4 -> (sp'=8); // stby
[tick2] sp=9 & pm=4 -> (sp'=9); // sleep
endmodule
//-------------------------------------------------------------------------
// SQ
module SQ
q : [0..QMAX] init 0;
// serve if busy
[tick2] sr=0 & sp=0 -> (q'=max(q-1,0));
[tick2] sr=1 & sp=0 -> (q'=q);
// otherwise do nothing
[tick2] sr=0 & sp>0 -> (q'=q);
[tick2] sr=1 & sp>0 -> (q'=min(q+1,QMAX));
endmodule
//-------------------------------------------------------------------------
//rewards "time"
// [tick2] bat=1 : 1;
//endrewards
rewards "power"
[tick2] sp=0 & c=1 : 2.5;
[tick2] sp=1 & c=1 : 1.5;
[tick2] sp=2 & c=1 : 2.5;
[tick2] sp=3 & c=1 : 0.8;
[tick2] sp=4 & c=1 : 2.5;
[tick2] sp=5 & c=1 : 2.5;
[tick2] sp=6 & c=1 : 0.3;
[tick2] sp=7 & c=1 : 2.5;
[tick2] sp=8 & c=1 : 2.5;
[tick2] sp=9 & c=1 : 0.1;
[tick2] sp=10 & c=1 : 2.5;
endrewards
// is an instantaneous property but I suppose we can look at average size
// i.e. divide by the expected number of time steps
rewards "queue"
[tick2] c=1 : q;
endrewards
rewards "lost"
[tick2] sr=1 & sp>0 & q=2 : 1;
endrewards