4 changed files with 312 additions and 0 deletions
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59car_pedestrian_mdp.prism
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64car_pedestrian_simulator.py
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118task_scheduling.prism
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71task_scheduling_simulator.py
@ -0,0 +1,59 @@ |
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mdp |
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const int lanes = 5; // Counting the sidewalks as lanes |
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const int streetLength = 20; |
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const int maxVelocity = 3; |
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const int minVelocity = 1; |
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const int carLaneInit = 2; |
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const double probFalling = 2/9; |
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global move : [0..1] init 0; // 0: car 1: pedestrian |
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formula ped_at_edge = ped_street_pos = 1 | ped_street_pos = streetLength; |
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formula car_at_end = car_street_pos = streetLength; |
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// check ped within [car_pos-velocity..car_pos], same lane |
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formula crash_straight = (car_lane_pos=ped_lane_pos & ped_street_pos>=car_street_pos-velocity & ped_street_pos<=car_street_pos); |
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// check ped street pos within [car_street_pos-velocity..car_street_pos], ped lane pos within [car_lane_pos-1..car_lane_pos] |
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formula crash_left = (switched_left & ped_lane_pos>=car_lane_pos-1 & ped_lane_pos<=car_lane_pos & ped_street_pos>=car_street_pos-velocity & ped_street_pos<=car_street_pos); |
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// check ped street pos within [car_street_pos-velocity..car_street_pos], ped lane pos within [car_lane_pos+1..car_lane_pos] |
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formula crash_right = (switched_right & ped_lane_pos>=car_lane_pos+1 & ped_lane_pos<=car_lane_pos & ped_street_pos>=car_street_pos-velocity & ped_street_pos<=car_street_pos); |
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label "crashed" = crash_straight | crash_left | crash_right; |
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label "maxedOut" = velocity=maxVelocity; |
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label "pedCrossed" = ped_lane_pos=lanes; |
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module car |
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switched_right : bool init false; |
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switched_left : bool init false; |
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car_street_pos : [0..streetLength] init 0; |
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car_lane_pos : [2..lanes-1] init carLaneInit; |
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velocity : [minVelocity..maxVelocity] init minVelocity; |
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// TODO |
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endmodule |
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module pedestrian |
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ped_street_pos : [0..streetLength] init floor(streetLength/4); |
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ped_lane_pos : [1..lanes] init 1; |
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fell_down : [0..2] init 0; // 1-2: getting up |
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[move] move=1 & fell_down=0 -> ((1-probFalling)/4): (ped_lane_pos'=min(lanes,ped_lane_pos+1)) & (move'=0) + |
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((1-probFalling)/4): (ped_lane_pos'=max(1,ped_lane_pos-1)) & (move'=0) + |
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((1-probFalling)/4): (ped_street_pos'=min(lanes,ped_street_pos+1)) & (move'=0) + |
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((1-probFalling)/4): (ped_street_pos'=max(1,ped_street_pos-1)) & (move'=0) + |
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(probFalling/4): (ped_lane_pos'=min(lanes,ped_lane_pos+1)) & (fell_down'=2) & (move'=0) + |
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(probFalling/4): (ped_lane_pos'=max(1,ped_lane_pos-1)) & (fell_down'=2) & (move'=0) + |
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(probFalling/4): (ped_street_pos'=min(lanes,ped_street_pos+1)) & (fell_down'=2) & (move'=0) + |
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(probFalling/4): (ped_street_pos'=max(1,ped_street_pos-1)) & (fell_down'=2) & (move'=0); |
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[getUp] move=1 & fell_down>0 -> 1: (fell_down'=fell_down-1) & (move'=0); |
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endmodule |
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@ -0,0 +1,64 @@ |
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import stormpy |
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import stormpy.simulator |
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newline = "\n" |
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def printFrame(streetLength, lanes, carPos, pedPos): |
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sidewalk = "#" * (streetLength+1) |
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frame = list(sidewalk + (lanes-2)*("_"*(streetLength+1)) + sidewalk) |
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frame[(int(carPos[0])-1)*(streetLength+1)+int(carPos[1])+1] = "C" |
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frame[(int(pedPos[0])-1)*(streetLength+1)+int(pedPos[1])+1] = "P" |
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for i in range(lanes): |
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frame[i*(streetLength+1)] = newline |
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return "".join(frame) |
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def mdp(): |
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options = stormpy.BuilderOptions([]) |
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options.set_build_state_valuations(True) |
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options.set_build_choice_labels(True) |
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options.set_build_all_labels() |
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prism_program = stormpy.parse_prism_program("/media/car_pedestrian_mdp.prism") |
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streetLength = int(str(prism_program.get_constant("streetLength").definition)) |
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lanes = int(str(prism_program.get_constant("lanes").definition)) |
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formula_str = "Pmax=? [G !\"crashed\" ];" |
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#formula_str = "Pmax=? [F \"crashed\" ];" |
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print(stormpy.build_model(prism_program)) |
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formulas = stormpy.parse_properties_for_prism_program(formula_str, prism_program) |
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model = stormpy.build_sparse_model_with_options(prism_program, options) |
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initial_state = model.initial_states[0] |
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assert initial_state == 0 |
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result = stormpy.model_checking(model, formulas[0], extract_scheduler=True) |
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assert result.has_scheduler |
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scheduler = result.scheduler |
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assert scheduler.memoryless |
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assert scheduler.deterministic |
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dtmc = model.apply_scheduler(scheduler) |
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print(dtmc) |
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simulator = stormpy.simulator.create_simulator(dtmc, seed=42) |
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simulator.set_observation_mode(stormpy.simulator.SimulatorObservationMode.PROGRAM_LEVEL) |
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i=0 |
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while True: |
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observation, reward, labels = simulator.step() |
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print(observation, labels) |
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frame = printFrame(int(streetLength), int(lanes), (observation["car_lane_pos"], observation["car_street_pos"]), (observation["ped_lane_pos"], observation["ped_street_pos"])) |
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print(frame) |
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if simulator.is_done() or "pedCrossed" in labels: |
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print("Pedestrian arrived on the other side!") |
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break |
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input("") |
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with open(f"/media/frame{i:03}.txt", "w") as text_file: |
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text_file.write(frame) |
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i+=1 |
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if "crashed" in labels: |
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print("Pedestrian did not arrive on the other side!") |
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break |
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if __name__ == '__main__': |
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mdp() |
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@ -0,0 +1,118 @@ |
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mdp |
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const int MULT_DUR_1 = 8; |
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const int ADD_DUR_1 = 4; |
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const double P1_SUCCESS = 1.0; |
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const int MULT_DUR_2 = 3; |
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const int ADD_DUR_2 = 3; |
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const double P2_SUCCESS = 0.8; |
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// target state (all tasks complete) |
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label "tasks_complete" = (task6=3); |
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label "no_P1_mult" = (mult_tick_1=0); |
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label "no_P2_mult" = (mult_tick_2=0); |
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// reward structure: elapsed time |
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rewards "time" |
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task6!=3 : 1; |
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endrewards |
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// reward structures: energy consumption |
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rewards "energy" |
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p1=0 : 10/1000; // processor 1 idle |
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p1>0 : 100/1000; // processor 1 working |
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p2=0 : 10/1000; // processor 2 idle |
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p2>0 : 100/1000; // processor 2 working |
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endrewards |
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module scheduler |
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//┌t1─┐ ┌t3─────┐ ┌t5───────┐ |
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//│A+B│-->│Cx(A+B)│-->│DxCx(A+B)│--. ┌t6─────────────────────┐ |
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//└───┘\ └───────┘ └─────────┘ \___\│DxCx(A+B)+((A+B)+(CxD))│ |
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//┌t2─┐ \ ┌t4─────────┐ / /└───────────────────────┘ |
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//│CxD│-->│(A+B)+(CxD)│------------° |
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//└───┘ └───────────┘ |
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task1 : [0..3]; // A+B, add |
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task2 : [0..3]; // CxD, mult |
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task3 : [0..3]; // Cx(A+B), mult |
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task4 : [0..3]; // (A+B)+(CxD), add |
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task5 : [0..3]; // DxCx(A+B), mult |
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task6 : [0..3]; // (DxCx(A+B)) + ((A+B)+(CxD)), add |
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p1_idle : bool init true; |
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p2_idle : bool init true; |
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// task status: |
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// 0 - not started |
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// 1 - running on processor 1 |
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// 2 - running on processor 2 |
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// 3 - task complete |
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// start task 1 |
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[t1p1] task1=0 & p1_idle-> (task1'=1) & (p1_idle'=false); |
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[t1p2] task1=0 & p2_idle-> (task1'=2) & (p2_idle'=false); |
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// start task 2 |
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[t2p1] task2=0 & p1_idle-> (task2'=1) & (p1_idle'=false); |
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[t2p2] task2=0 & p2_idle-> (task2'=2) & (p2_idle'=false); |
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// start task 3 (must wait for task 1 to complete) |
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[t3p1] task3=0 & task1=3 & p1_idle-> (task3'=1) & (p1_idle'=false); |
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[t3p2] task3=0 & task1=3 & p2_idle-> (task3'=2) & (p2_idle'=false); |
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// start task 4 (must wait for tasks 1 and 2 to complete) |
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[t4p1] task4=0 & task1=3 & task2=3 & p1_idle-> (task4'=1) & (p1_idle'=false); |
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[t4p2] task4=0 & task1=3 & task2=3 & p2_idle-> (task4'=2) & (p2_idle'=false); |
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// start task 5 (must wait for task 3 to complete) |
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[t5p1] task5=0 & task3=3 & p1_idle-> (task5'=1) & (p1_idle'=false); |
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[t5p2] task5=0 & task3=3 & p2_idle-> (task5'=2) & (p2_idle'=false); |
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// start task 6 (must wait for tasks 4 and 5 to complete) |
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[t6p1] task6=0 & task4=3 & task5=3 & p1_idle -> (task6'=1) & (p1_idle'=false); |
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[t6p2] task6=0 & task4=3 & task5=3 & p2_idle -> (task6'=2) & (p2_idle'=false); |
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// a task finishes on processor 1 |
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[p1_done] task1=1 & p1=3 -> (task1'=3) & (p1_idle'=true); |
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[p1_done] task2=1 & p1=3 -> (task2'=3) & (p1_idle'=true); |
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[p1_done] task3=1 & p1=3 -> (task3'=3) & (p1_idle'=true); |
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[p1_done] task4=1 & p1=3 -> (task4'=3) & (p1_idle'=true); |
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[p1_done] task5=1 & p1=3 -> (task5'=3) & (p1_idle'=true); |
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[p1_done] task6=1 & p1=3 -> (task6'=3) & (p1_idle'=true); |
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// a task finishes on processor 2 |
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[p2_done] task1=2 & p2=3 -> (task1'=3) & (p2_idle'=true); |
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[p2_done] task2=2 & p2=3 -> (task2'=3) & (p2_idle'=true); |
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[p2_done] task3=2 & p2=3 -> (task3'=3) & (p2_idle'=true); |
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[p2_done] task4=2 & p2=3 -> (task4'=3) & (p2_idle'=true); |
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[p2_done] task5=2 & p2=3 -> (task5'=3) & (p2_idle'=true); |
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[p2_done] task6=2 & p2=3 -> (task6'=3) & (p2_idle'=true); |
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[] task6=3 -> 1 : true; |
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[] task6=3 -> 1 : true; |
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endmodule |
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// processor 1 |
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module P1 |
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p1 : [0..3]; // 0 inactive, 1 - adding, 2 - multiplying, 3 - done |
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mult_tick_1 : ; |
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add_tick_1 : ; |
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[p1_done] p1=3 -> 1: (p1'=0) & (mult_tick_1'=0) & (add_tick_1'=0); // finished task |
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endmodule |
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// processor 2 |
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// Note: You may also use module renaming to define processor 2 |
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module P2 |
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p2 : [0..3]; // 0 inactive, 1 - adding, 2 - multiplying, 3 - done |
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mult_tick_2 : ; |
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add_tick_2 : ; |
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[p2_done] p2=3 -> 1: (p2'=0) & (mult_tick_2'=0) & (add_tick_2'=0); // finished task |
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endmodule |
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@ -0,0 +1,71 @@ |
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import stormpy |
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import stormpy.simulator |
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def mdp(): |
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options = stormpy.BuilderOptions([]) |
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options.set_build_state_valuations(True) |
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options.set_build_choice_labels(True) |
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options.set_build_all_labels() |
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options.set_build_all_reward_models() |
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program = stormpy.parse_prism_program("/media/task_graph_scheduling.prism") |
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formula_str = "R{\"time\"}min=? [ F \"tasks_complete\" ];" |
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formulas = stormpy.parse_properties_for_prism_program(formula_str, program) |
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model = stormpy.build_sparse_model_with_options(program, options) |
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print(model) |
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initial_state = model.initial_states[0] |
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assert initial_state == 0 |
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result = stormpy.model_checking(model, formulas[0], extract_scheduler=True) |
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assert result.has_scheduler |
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scheduler = result.scheduler |
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assert scheduler.memoryless |
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assert scheduler.deterministic |
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dtmc = model.apply_scheduler(scheduler) |
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print(dtmc) |
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simulator = stormpy.simulator.create_simulator(dtmc, seed=42) |
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simulator.set_observation_mode(stormpy.simulator.SimulatorObservationMode.PROGRAM_LEVEL) |
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step_counter = 0 |
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busy1_counter = 0 |
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busy2_counter = 0 |
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print(""" |
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┌t1─┐ ┌t3─────┐ ┌t5───────┐ |
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│A+B│-->│Cx(A+B)│-->│DxCx(A+B)│--. ┌t6─────────────────────┐ |
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└───┘\ └───────┘ └─────────┘ \___\│DxCx(A+B)+((A+B)+(CxD))│ |
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┌t2─┐ \ ┌t4─────────┐ / /└───────────────────────┘ |
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│CxD│-->│(A+B)+(CxD)│------------° |
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└───┘ └───────────┘ |
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""") |
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print(" " * 32 + "[+,x,x,+,x,+]") |
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while True: |
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if simulator.is_done(): |
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print(f"Tasks complete! Ratio: (approx.): {busy1_counter/(busy1_counter+busy2_counter):1.4f}/{busy2_counter/(busy1_counter+busy2_counter):1.4f}, Steps needed (approx.): {step_counter}") |
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break |
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observation, reward, labels = simulator.step() |
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#input("") |
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busy1 = str(observation["p1_idle"]) != ("true") |
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busy2 = str(observation["p2_idle"]) != ("true") |
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if busy1: busy1_counter += 1 |
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if busy2: busy2_counter += 1 |
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tasks = [str(observation[f"task{i}"]) for i in range(1,7)] |
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print(f"Step {step_counter:3}: P1/2:{'busy' if busy1 else 'idle'}/{'busy' if busy2 else 'idle'} tasks: [{','.join(tasks)}], {str(observation['add_tick_1'])},{str(observation['mult_tick_1'])},{str(observation['add_tick_2'])},{str(observation['mult_tick_2'])},labels: {labels if len(labels) != 0 else ''}, ") |
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step_counter += 1 |
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try: |
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with open("/media/induced_scheduling_dtmc.dot", "w") as text_file: |
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text_file.write(dtmc.to_dot()) |
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except Exception as e: |
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print(e) |
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print("Could not write to file.") |
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input("Hit enter to evaluate: 'P=? [ F<={i} \"tasks_complete\" ]' on the DTMC:") |
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print(dtmc) |
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for i in range(30,61): |
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formula_str = f"P=? [ F<={i} \"tasks_complete\" ]" |
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formulas = stormpy.parse_properties_for_prism_program(formula_str, program) |
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result = stormpy.model_checking(dtmc, formulas[0]) |
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print(f"Probability to finish within {i} timesteps : {result.at(dtmc.initial_states[0]):>1.12f}") |
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if __name__ == '__main__': |
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mdp() |
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