classic devs
play

Classic DEVS An Introduction Using PythonPDEVS Yentl Van Tendeloo, - PowerPoint PPT Presentation

Jul 25, 2023 β€’42 likes β€’1.06k views

Classic DEVS An Introduction Using PythonPDEVS Yentl Van Tendeloo, Hans Vangheluwe Introduction Bernard P . Zeigler. Bernard P . Zeigler. Bernard P . Zeigler, Herbert Praehofer, Theory Of Modelling And Simulation . Multifacetted Modelling

  1. Autonomous (with output) red π‘’π‘“π‘šπ‘π‘§ 𝑠𝑓𝑒 𝑁 = , 𝑇, π‘Ÿ π‘—π‘œπ‘—π‘’ , πœ€ π‘—π‘œπ‘’ , , 𝑒𝑏 𝑍 πœ‡ 𝑇 = {red, yellow, green} πœ€ π‘—π‘œπ‘’ = { red β†’ green, !show_red green β†’ yellow, yellow β†’ red} π‘Ÿ π‘—π‘œπ‘—π‘’ = (green, 0) 𝑒𝑏 = {red β†’ π‘’π‘“π‘šπ‘π‘§ 𝑠𝑓𝑒 , yellow !show_green green β†’ π‘’π‘“π‘šπ‘π‘§ π‘•π‘ π‘“π‘“π‘œ , π‘’π‘“π‘šπ‘π‘§ π‘§π‘“π‘šπ‘šπ‘π‘₯ yellow β†’ π‘’π‘“π‘šπ‘π‘§ π‘§π‘“π‘šπ‘šπ‘π‘₯ } 𝑍 : set of output events 𝑍 = {β€œ show_red ”, β€œ show_green ”, β€œ show_yellow ”} !show_yellow πœ‡ : 𝑇 β†’ 𝑍 βˆͺ {𝜚} πœ‡ = { green β†’ β€œ show_yellow ”, green 𝑓 = 0𝑑 yellow β†’ β€œ show_red ”, π‘’π‘“π‘šπ‘π‘§ π‘•π‘ π‘“π‘“π‘œ red β†’ β€œ show_green ”}

  2. Abstract Syntax Concrete Syntax atomic_out.py 𝑇 = {red, yellow, green} π‘Ÿ π‘—π‘œπ‘—π‘’ = (green, 0) from pypdevs.DEVS import * πœ€ π‘—π‘œπ‘’ = { red β†’ green, green β†’ yellow, class TrafficLightWithOutput(AtomicDEVS): yellow β†’ red} def __init__( self, …): 𝑒𝑏 = {red β†’ π‘’π‘“π‘šπ‘π‘§ 𝑠𝑓𝑒 , AtomicDEVS.__init __(self, β€œlight”) green β†’ π‘’π‘“π‘šπ‘π‘§ π‘•π‘ π‘“π‘“π‘œ , self.observe = self.addOutPort (β€œobserver”) yellow β†’ π‘’π‘“π‘šπ‘π‘§ π‘§π‘“π‘šπ‘šπ‘π‘₯ } … 𝑍 = {β€œ show_red ”, β€œ show_green ”, … β€œ show_yellow ”} πœ‡ = {green β†’ β€œ show_yellow ”, def outputFnc(self): yellow β†’ β€œ show_red ”, state = self.state red β†’ β€œ show_green ”} if state == β€œred”: return {self.observe: β€œ show_green ”} Operational Semantics elif state == β€œyellow”: time = 0 return {self.observe: β€œ show_red ”} current_state = initial_state elif state == β€œgreen”: last_time = -initial_elapsed return {self.observe: β€œ show_yellow ”} while not termination_condition(): time = last_time + ta(current_state) output( πœ‡ (current_state)) current_state = πœ€ π‘—π‘œπ‘’ (current_state) last_time = time

  3. __ Current Time: 0.00 __________________________________________ INITIAL CONDITIONS in model <light> Initial State: green Next scheduled internal transition at time 57.00 __ Current Time: 57.00 __________________________________________ INTERNAL TRANSITION in model <light> New State: yellow Output Port Configuration: port <observer>: show_yellow Next scheduled internal transition at time 60.00 __ Current Time: 60.00 __________________________________________ INTERNAL TRANSITION in model <light> New State: red Output Port Configuration: port <observer>: show_red Next scheduled internal transition at time 120.00

  4. X toManual red π‘’π‘“π‘šπ‘π‘§ 𝑠𝑓𝑒 ?toManual toAuto t !show_red ?toAuto S manual !show_green red yellow manual yellow π‘’π‘“π‘šπ‘π‘§ π‘§π‘“π‘šπ‘šπ‘π‘₯ ∞ green ?toManual t !show_yellow Y show_green green ?toManual π‘’π‘“π‘šπ‘π‘§ π‘•π‘ π‘“π‘“π‘œ 𝑓 = 0𝑑 t

  5. Reactive π‘Œ πœ€ 𝑓𝑦𝑒 𝑁 = , 𝑍, 𝑇, π‘Ÿ π‘—π‘œπ‘—π‘’ , πœ€ π‘—π‘œπ‘’ , , πœ‡, 𝑒𝑏 𝑍 = {β€œ show_red ”, β€œ show_green ”, β€œ show_yellow ”} red 𝑇 = {red, yellow, green, manual} π‘’π‘“π‘šπ‘π‘§ 𝑠𝑓𝑒 ?toManual π‘Ÿ π‘—π‘œπ‘—π‘’ = (green, 0) πœ€ π‘—π‘œπ‘’ = {red β†’ green, green β†’ yellow, !show_red yellow β†’ red} ?toAuto πœ‡ = {green β†’ β€œ show_yellow ”, yellow β†’ β€œ show_red ”, !show_green red β†’ β€œ show_green ”} yellow manual 𝑒𝑏 = {red β†’ π‘’π‘“π‘šπ‘π‘§ 𝑠𝑓𝑒 , π‘’π‘“π‘šπ‘π‘§ π‘§π‘“π‘šπ‘šπ‘π‘₯ ∞ green β†’ π‘’π‘“π‘šπ‘π‘§ π‘•π‘ π‘“π‘“π‘œ , ?toManual yellow β†’ π‘’π‘“π‘šπ‘π‘§ π‘§π‘“π‘šπ‘šπ‘π‘₯ , manual β†’ +∞ } !show_yellow π‘Œ : set of input events π‘Œ = {β€œ toAuto ”, β€œ toManual ”} green ?toManual πœ€ 𝑓𝑦𝑒 : Q Γ— π‘Œ β†’ 𝑇 π‘’π‘“π‘šπ‘π‘§ π‘•π‘ π‘“π‘“π‘œ 𝑅 = 𝑑, 𝑓 𝑑 ∈ 𝑇, 0 ≀ 𝑓 ≀ 𝑒𝑏(𝑑) πœ€ 𝑓𝑦𝑒 = {( (*, *), β€œ toManual ”) β†’ β€œmanual”, ( (β€œmanual”, *), β€œ toAuto ”) β†’ β€œred”} 𝑓 = 0𝑑

  6. Abstract Syntax 𝑍 = {β€œ show_red ”, β€œ show_green ”, β€œ show_yellow ”} Operational Semantics 𝑇 = {red, yellow, green, manual} time = 0 π‘Ÿ π‘—π‘œπ‘—π‘’ = (green, 0) current_state = initial_state πœ€ π‘—π‘œπ‘’ = {red β†’ green, last_time = -initial_elapsed green β†’ yellow, while not termination_condition(): yellow β†’ red} next_time = last_time + ta(current_state) πœ‡ = {green β†’ β€œ show_yellow ”, if time_next_ev <= next_time: yellow β†’ β€œ show_red ”, e = time_next_ev – last_time red β†’ β€œ show_green ”} time = time_next_ev 𝑒𝑏 = {red β†’ π‘’π‘“π‘šπ‘π‘§ 𝑠𝑓𝑒 , current_state = πœ€ 𝑓𝑦𝑒 ((current_state, e), next_ev) green β†’ π‘’π‘“π‘šπ‘π‘§ π‘•π‘ π‘“π‘“π‘œ , else: yellow β†’ π‘’π‘“π‘šπ‘π‘§ π‘§π‘“π‘šπ‘šπ‘π‘₯ , time = next_time manual β†’ ∞ } output( πœ‡ (current_state)) π‘Œ = {β€œ toAuto ”, β€œ toManual ”} current_state = πœ€ _ π‘—π‘œπ‘’ (current_state) πœ€ 𝑓𝑦𝑒 = {( (*, *), β€œ toManual ”) β†’ manual, last_time = time ( (manual, *), β€œ toAuto ”) β†’ red}

  7. Abstract Syntax Concrete Syntax atomic_ext.py 𝑍 = {β€œ show_red ”, β€œ show_green ”, β€œ show_yellow ”} from pypdevs.DEVS import * 𝑇 = {red, yellow, green, manual} π‘Ÿ π‘—π‘œπ‘—π‘’ = (green, 0) class TrafficLight(AtomicDEVS): πœ€ π‘—π‘œπ‘’ = {red β†’ green, def __init__( self, …): green β†’ yellow, AtomicDEVS.__init __(self, β€œlight”) yellow β†’ red} self.interrupt = self.addInPort (β€œinterrupt”) πœ‡ = {green β†’ β€œ show_yellow ”, … yellow β†’ β€œ show_red ”, … red β†’ β€œ show_green ”} 𝑒𝑏 = {red β†’ π‘’π‘“π‘šπ‘π‘§ 𝑠𝑓𝑒 , def extTransition(self, inputs): green β†’ π‘’π‘“π‘šπ‘π‘§ π‘•π‘ π‘“π‘“π‘œ , inp = inputs[self.interrupt] yellow β†’ π‘’π‘“π‘šπ‘π‘§ π‘§π‘“π‘šπ‘šπ‘π‘₯ , if inp == β€œ toManual ”: manual β†’ ∞ } return β€œmanual” π‘Œ = {β€œ toAuto ”, β€œ toManual ”} elif inp == β€œ toAuto ”: πœ€ 𝑓𝑦𝑒 = {( (*, *), β€œ toManual ”) β†’ manual, if self.state == β€œmanual”: ( (manual, *), β€œ toAuto ”) β†’ red} return β€œred”

  8. __ Current Time: 0.00 __________________________________________ INITIAL CONDITIONS in model <light> Initial State: green Next scheduled internal transition at time 57.00 __ Current Time: 57.00 __________________________________________ INTERNAL TRANSITION in model <light> New State: yellow Output Port Configuration: port <observer>: show_yellow Next scheduled internal transition at time 60.00 __ Current Time: 60.00 __________________________________________ INTERNAL TRANSITION in model <light> New State: red Output Port Configuration: port <observer>: show_red Next scheduled internal transition at time 120.00

  9. 𝑅 = 𝑑, 𝑓 𝑑 ∈ 𝑇, 0 ≀ 𝑓 ≀ 𝑒𝑏(𝑑) 𝑓 = 0 0 < 𝑓 < 𝑒𝑏(𝑑) 𝑓 = 𝑒𝑏 𝑑 ?

  10. red π‘’π‘“π‘šπ‘π‘§ 𝑠𝑓𝑒 ?toManual/ !turn_off ?toAuto/ !show_red !show_red !show_green yellow manual π‘’π‘“π‘šπ‘π‘§ π‘§π‘“π‘šπ‘šπ‘π‘₯ ∞ ?toManual/ !turn_off !show_yellow green ?toManual/ π‘’π‘“π‘šπ‘π‘§ π‘•π‘ π‘“π‘“π‘œ !turn_off 𝑓 = 0𝑑

  11. X toManual red π‘’π‘“π‘šπ‘π‘§ 𝑠𝑓𝑒 ?toManual/ toAuto !turn_off t ?toAuto/ !show_red S !show_red manual !show_green red yellow manual yellow π‘’π‘“π‘šπ‘π‘§ π‘§π‘“π‘šπ‘šπ‘π‘₯ ∞ green ?toManual/ !turn_off t !show_yellow Y show_green green ?toManual/ show_red π‘’π‘“π‘šπ‘π‘§ π‘•π‘ π‘“π‘“π‘œ !turn_off turn_off 𝑓 = 0𝑑 t

  12. X toManual red π‘’π‘“π‘šπ‘π‘§ 𝑠𝑓𝑒 ?toManual/ toAuto !turn_off time = 0 current_state = initial_state t ?toAuto/ last_time = -initial_elapsed !show_red S !show_red while not termination_condition(): manual next_time = last_time + ta(current_state) !show_green if time_next_ev <= next_time: red yellow manual e = time_next_ev – last_time yellow π‘’π‘“π‘šπ‘π‘§ π‘§π‘“π‘šπ‘šπ‘π‘₯ time = time_next_ev ∞ green current_state = πœ€ 𝑓𝑦𝑒 ((current_state, e), next_ev) ?toManual/ else: !turn_off t time = next_time !show_yellow output( πœ‡ (current_state)) Y current_state = πœ€ _ π‘—π‘œπ‘’ (current_state) last_time = time show_green green ?toManual/ show_red π‘’π‘“π‘šπ‘π‘§ π‘•π‘ π‘“π‘“π‘œ !turn_off turn_off 𝑓 = 0𝑑 t

  13. X !show_red red toManual going_auto 0𝑑 π‘’π‘“π‘šπ‘π‘§ 𝑠𝑓𝑒 toAuto !show_green t ?toAuto ?toManual !show_red S manual going_auto yellow manual going_manual π‘’π‘“π‘šπ‘π‘§ π‘§π‘“π‘šπ‘šπ‘π‘₯ ∞ red green t !show_yellow !turn_off ?toManual Y show_green green going_manual show_red π‘’π‘“π‘šπ‘π‘§ π‘•π‘ π‘“π‘“π‘œ 0𝑑 turn_off 𝑓 = 0𝑑 t ?toManual

  14. Full Atomic DEVS Specification 𝑁 = π‘Œ, 𝑍, 𝑇, π‘Ÿ π‘—π‘œπ‘—π‘’ , πœ€ π‘—π‘œπ‘’ , πœ€ 𝑓𝑦𝑒 , πœ‡, 𝑒𝑏 π‘Œ : set of input events 𝑍 : set of output events 𝑇 : set of sequential states π‘Ÿ π‘—π‘œπ‘—π‘’ : 𝑅 𝑅 = 𝑑, 𝑓 𝑑 ∈ 𝑇, 0 ≀ 𝑓 ≀ 𝑒𝑏(𝑑) πœ€ π‘—π‘œπ‘’ : 𝑇 β†’ 𝑇 πœ€ 𝑓𝑦𝑒 : 𝑅 Γ— π‘Œ β†’ 𝑇 πœ‡ : 𝑇 β†’ 𝑍 βˆͺ 𝜚 𝑒𝑏 : 𝑇 β†’ ℝ 0,+∞ +

  15. S (πœ€ 𝑓𝑦𝑒 𝑑 𝑗 , 𝑓 , 𝑦 , 0) πœ€ 𝑓𝑦𝑒 𝑓 (𝑑 𝑗 , 0) output πœ‡(𝑑 𝑗 ) 𝑒𝑏 𝑑 𝑗 πœ€ π‘—π‘œπ‘’ (πœ€ π‘—π‘œπ‘’ (𝑑 𝑗 ), 0) t 𝑒 𝑗 + 𝑓 𝑒 𝑗 𝑒 𝑗 + 𝑒𝑏 𝑑 𝑗

  16. Coupled Models

  17. !show_red red going_auto 0𝑑 π‘’π‘“π‘šπ‘π‘§ 𝑠𝑓𝑒 !show_green ?toAuto ?toManual !show_red yellow manual π‘’π‘“π‘šπ‘π‘§ π‘§π‘“π‘šπ‘šπ‘π‘₯ ∞ !show_yellow !turn_off ?toManual green going_manual π‘’π‘“π‘šπ‘π‘§ π‘•π‘ π‘“π‘“π‘œ 0𝑑 𝑓 = 0𝑑 ?toManual

  18. work 3600s !go_to_work !take_break idle 300s 𝑓 = 280𝑑

  19. π’•π’‡π’Žπ’ˆ 𝐷 = 𝐸, 𝑁𝑇 𝑡 π’Žπ’‹π’‰π’Šπ’–πŸ 𝑡 π’’π’‘π’ŽπŸ 𝑁𝑇 = 𝑁 𝑗 𝑗 ∈ 𝐸 𝑁 𝑗 = π‘Œ 𝑗 , 𝑍 𝑗 , 𝑇 𝑗 , π‘Ÿ π‘—π‘œπ‘—π‘’,𝑗 , πœ€ π‘—π‘œπ‘’,𝑗 , πœ€ 𝑓𝑦𝑒,𝑗 , πœ‡ 𝑗 , 𝑒𝑏 𝑗 , βˆ€ 𝑗 ∈ 𝐸

  20. 𝐸 = {π‘šπ‘—π‘•β„Žπ‘’ 1 , π‘žπ‘π‘š 1 } π’•π’‡π’Žπ’ˆ 𝐷 = 𝐸, 𝑁𝑇 𝑡 π’Žπ’‹π’‰π’Šπ’–πŸ 𝑡 π’’π’‘π’ŽπŸ 𝑁𝑇 = 𝑁 𝑗 𝑗 ∈ 𝐸 𝑁 𝑗 = π‘Œ 𝑗 , 𝑍 𝑗 , 𝑇 𝑗 , π‘Ÿ π‘—π‘œπ‘—π‘’,𝑗 , πœ€ π‘—π‘œπ‘’,𝑗 , πœ€ 𝑓𝑦𝑒,𝑗 , πœ‡ 𝑗 , 𝑒𝑏 𝑗 , βˆ€ 𝑗 ∈ 𝐸

  21. π’•π’‡π’Žπ’ˆ 𝐷 = π‘Œ π‘‘π‘“π‘šπ‘” , 𝑍 π‘‘π‘“π‘šπ‘” , 𝐸, 𝑁𝑇 𝑡 π’Žπ’‹π’‰π’Šπ’–πŸ 𝑡 π’’π’‘π’ŽπŸ 𝑁𝑇 = 𝑁 𝑗 𝑗 ∈ 𝐸 𝑁 𝑗 = π‘Œ 𝑗 , 𝑍 𝑗 , 𝑇 𝑗 , π‘Ÿ π‘—π‘œπ‘—π‘’,𝑗 , πœ€ π‘—π‘œπ‘’,𝑗 , πœ€ 𝑓𝑦𝑒,𝑗 , πœ‡ 𝑗 , 𝑒𝑏 𝑗 , βˆ€ 𝑗 ∈ 𝐸

  22. π’•π’‡π’Žπ’ˆ 𝐷 = π‘Œ π‘‘π‘“π‘šπ‘” , 𝑍 π‘‘π‘“π‘šπ‘” , 𝐸, 𝑁𝑇, 𝐽𝑇 𝑡 π’Žπ’‹π’‰π’Šπ’–πŸ 𝑡 π’’π’‘π’ŽπŸ 𝑁𝑇 = 𝑁 𝑗 𝑗 ∈ 𝐸 𝑁 𝑗 = π‘Œ 𝑗 , 𝑍 𝑗 , 𝑇 𝑗 , π‘Ÿ π‘—π‘œπ‘—π‘’,𝑗 , πœ€ π‘—π‘œπ‘’,𝑗 , πœ€ 𝑓𝑦𝑒,𝑗 , πœ‡ 𝑗 , 𝑒𝑏 𝑗 , βˆ€ 𝑗 ∈ 𝐸 𝐽𝑇 = 𝐽 𝑗 𝑗 ∈ 𝐸 βˆͺ π‘‘π‘“π‘šπ‘” βˆ€ 𝑗 ∈ 𝐸 βˆͺ π‘‘π‘“π‘šπ‘” ∢ 𝐽 𝑗 βŠ† 𝐸 βˆͺ π‘‘π‘“π‘šπ‘” βˆ€ 𝑗 ∈ 𝐸 βˆͺ π‘‘π‘“π‘šπ‘” ∢ 𝑗 βˆ‰ 𝐽 𝑗 𝐽 𝑗 : Influencees of 𝑗

  23. π’•π’‡π’Žπ’ˆ 𝐷 = π‘Œ π‘‘π‘“π‘šπ‘” , 𝑍 π‘‘π‘“π‘šπ‘” , 𝐸, 𝑁𝑇, 𝐽𝑇 𝑡 π’Žπ’‹π’‰π’Šπ’–πŸ 𝑡 π’’π’‘π’ŽπŸ 𝑁𝑇 = 𝑁 𝑗 𝑗 ∈ 𝐸 𝑁 𝑗 = π‘Œ 𝑗 , 𝑍 𝑗 , 𝑇 𝑗 , π‘Ÿ π‘—π‘œπ‘—π‘’,𝑗 , πœ€ π‘—π‘œπ‘’,𝑗 , πœ€ 𝑓𝑦𝑒,𝑗 , πœ‡ 𝑗 , 𝑒𝑏 𝑗 , βˆ€ 𝑗 ∈ 𝐸 𝐽𝑇 = 𝐽 𝑗 𝑗 ∈ 𝐸 βˆͺ π‘‘π‘“π‘šπ‘” βˆ€ 𝑗 ∈ 𝐸 βˆͺ π‘‘π‘“π‘šπ‘” ∢ 𝐽 𝑗 βŠ† 𝐸 βˆͺ π‘‘π‘“π‘šπ‘” βˆ€ 𝑗 ∈ 𝐸 βˆͺ π‘‘π‘“π‘šπ‘” ∢ 𝑗 βˆ‰ 𝐽 𝑗 𝐽 𝑗 : Influencees of 𝑗 𝐽 π‘‘π‘“π‘šπ‘” = {π‘šπ‘—π‘•β„Žπ‘’1} 𝐽 π‘žπ‘π‘š1 = {π‘šπ‘—π‘•β„Žπ‘’1} 𝐽 π‘šπ‘—π‘•β„Žπ‘’1 = {π‘‘π‘“π‘šπ‘”}

  24. 𝑍 π‘žπ‘π‘š1 = {𝑕𝑝_𝑒𝑝_π‘₯𝑝𝑠𝑙, 𝑒𝑏𝑙𝑓_𝑐𝑠𝑓𝑏𝑙} π’•π’‡π’Žπ’ˆ 𝐷 = π‘Œ π‘‘π‘“π‘šπ‘” , 𝑍 π‘‘π‘“π‘šπ‘” , 𝐸, 𝑁𝑇, 𝐽𝑇, π‘Žπ‘‡ 𝑡 π’Žπ’‹π’‰π’Šπ’–πŸ 𝑡 π’’π’‘π’ŽπŸ 𝑁𝑇 = 𝑁 𝑗 𝑗 ∈ 𝐸 𝑁 𝑗 = π‘Œ 𝑗 , 𝑍 𝑗 , 𝑇 𝑗 , π‘Ÿ π‘—π‘œπ‘—π‘’,𝑗 , πœ€ π‘—π‘œπ‘’,𝑗 , πœ€ 𝑓𝑦𝑒,𝑗 , πœ‡ 𝑗 , 𝑒𝑏 𝑗 , βˆ€ 𝑗 ∈ 𝐸 𝐽𝑇 = 𝐽 𝑗 𝑗 ∈ 𝐸 βˆͺ π‘‘π‘“π‘šπ‘” βˆ€ 𝑗 ∈ 𝐸 βˆͺ π‘‘π‘“π‘šπ‘” ∢ 𝐽 𝑗 βŠ† 𝐸 βˆͺ π‘‘π‘“π‘šπ‘” βˆ€ 𝑗 ∈ 𝐸 βˆͺ π‘‘π‘“π‘šπ‘” ∢ 𝑗 βˆ‰ 𝐽 𝑗 π‘Žπ‘‡ = π‘Ž 𝑗,π‘˜ 𝑗 ∈ 𝐸 βˆͺ π‘‘π‘“π‘šπ‘” , π‘˜ ∈ 𝐽 𝑗 π‘Ž π‘‘π‘“π‘šπ‘”,π‘˜ ∢ π‘Œ π‘‘π‘“π‘šπ‘” β†’ π‘Œ π‘˜ , βˆ€ π‘˜ ∈ 𝐸 π‘Ž 𝑗,π‘‘π‘“π‘šπ‘” ∢ 𝑍 𝑗 β†’ 𝑍 π‘‘π‘“π‘šπ‘” , βˆ€ 𝑗 ∈ 𝐸 π‘Ž 𝑗,π‘˜ ∢ 𝑍 𝑗 β†’ π‘Œ π‘˜ , βˆ€ 𝑗, π‘˜ ∈ 𝐸 π‘Œ π‘šπ‘—π‘•β„Žπ‘’1 = {π‘’π‘π‘π‘π‘œπ‘£π‘π‘š, 𝑒𝑝𝐡𝑣𝑒𝑝}

  25. π’•π’‡π’Žπ’ˆ 𝐷 = π‘Œ π‘‘π‘“π‘šπ‘” , 𝑍 π‘‘π‘“π‘šπ‘” , 𝐸, 𝑁𝑇, 𝐽𝑇, π‘Žπ‘‡ 𝑡 π’Žπ’‹π’‰π’Šπ’–πŸ 𝑡 π’’π’‘π’ŽπŸ 𝑁𝑇 = 𝑁 𝑗 𝑗 ∈ 𝐸 𝑁 𝑗 = π‘Œ 𝑗 , 𝑍 𝑗 , 𝑇 𝑗 , π‘Ÿ π‘—π‘œπ‘—π‘’,𝑗 , πœ€ π‘—π‘œπ‘’,𝑗 , πœ€ 𝑓𝑦𝑒,𝑗 , πœ‡ 𝑗 , 𝑒𝑏 𝑗 , βˆ€ 𝑗 ∈ 𝐸 𝐽𝑇 = 𝐽 𝑗 𝑗 ∈ 𝐸 βˆͺ π‘‘π‘“π‘šπ‘” βˆ€ 𝑗 ∈ 𝐸 βˆͺ π‘‘π‘“π‘šπ‘” ∢ 𝐽 𝑗 βŠ† 𝐸 βˆͺ π‘‘π‘“π‘šπ‘” βˆ€ 𝑗 ∈ 𝐸 βˆͺ π‘‘π‘“π‘šπ‘” ∢ 𝑗 βˆ‰ 𝐽 𝑗 π‘Žπ‘‡ = π‘Ž 𝑗,π‘˜ 𝑗 ∈ 𝐸 βˆͺ π‘‘π‘“π‘šπ‘” , π‘˜ ∈ 𝐽 𝑗 π‘Ž π‘‘π‘“π‘šπ‘”,π‘˜ ∢ π‘Œ π‘‘π‘“π‘šπ‘” β†’ π‘Œ π‘˜ , βˆ€ π‘˜ ∈ 𝐸 π‘Ž 𝑗,π‘‘π‘“π‘šπ‘” ∢ 𝑍 𝑗 β†’ 𝑍 π‘‘π‘“π‘šπ‘” , βˆ€ 𝑗 ∈ 𝐸 π‘Ž 𝑗,π‘˜ ∢ 𝑍 𝑗 β†’ π‘Œ π‘˜ , βˆ€ 𝑗, π‘˜ ∈ 𝐸 take_break οƒ  toAuto go_to_work οƒ  toManual

  26. π’•π’‡π’Žπ’ˆ 𝐷 = π‘Œ π‘‘π‘“π‘šπ‘” , 𝑍 π‘‘π‘“π‘šπ‘” , 𝐸, 𝑁𝑇, 𝐽𝑇, π‘Žπ‘‡, π‘‘π‘“π‘šπ‘“π‘‘π‘’ 𝑡 π’Žπ’‹π’‰π’Šπ’–πŸ 𝑡 π’’π’‘π’ŽπŸ 𝑁𝑇 = 𝑁 𝑗 𝑗 ∈ 𝐸 𝑁 𝑗 = π‘Œ 𝑗 , 𝑍 𝑗 , 𝑇 𝑗 , π‘Ÿ π‘—π‘œπ‘—π‘’,𝑗 , πœ€ π‘—π‘œπ‘’,𝑗 , πœ€ 𝑓𝑦𝑒,𝑗 , πœ‡ 𝑗 , 𝑒𝑏 𝑗 , βˆ€ 𝑗 ∈ 𝐸 𝐽𝑇 = 𝐽 𝑗 𝑗 ∈ 𝐸 βˆͺ π‘‘π‘“π‘šπ‘” βˆ€ 𝑗 ∈ 𝐸 βˆͺ π‘‘π‘“π‘šπ‘” ∢ 𝐽 𝑗 βŠ† 𝐸 βˆͺ π‘‘π‘“π‘šπ‘” βˆ€ 𝑗 ∈ 𝐸 βˆͺ π‘‘π‘“π‘šπ‘” ∢ 𝑗 βˆ‰ 𝐽 𝑗 π‘Žπ‘‡ = π‘Ž 𝑗,π‘˜ 𝑗 ∈ 𝐸 βˆͺ π‘‘π‘“π‘šπ‘” , π‘˜ ∈ 𝐽 𝑗 π‘Ž π‘‘π‘“π‘šπ‘”,π‘˜ ∢ π‘Œ π‘‘π‘“π‘šπ‘” β†’ π‘Œ π‘˜ , βˆ€ π‘˜ ∈ 𝐸 π‘Ž 𝑗,π‘‘π‘“π‘šπ‘” ∢ 𝑍 𝑗 β†’ 𝑍 π‘‘π‘“π‘šπ‘” , βˆ€ 𝑗 ∈ 𝐸 π‘Ž 𝑗,π‘˜ ∢ 𝑍 𝑗 β†’ π‘Œ π‘˜ , βˆ€ 𝑗, π‘˜ ∈ 𝐸 π‘‘π‘“π‘šπ‘“π‘‘π‘’ ∢ 2 𝐸 β†’ 𝐸 βˆ€ 𝐹 βŠ† 𝐸, 𝐹 β‰  βˆ…: π‘‘π‘“π‘šπ‘“π‘‘π‘’ 𝐹 ∈ 𝐹 take_break οƒ  toAuto go_to_work οƒ  toManual

  27. Concrete Syntax trafficlight_system.py from pypdevs.DEVS import * from trafficlight import TrafficLight from policeman import Policeman def translate(in_evt): mapping = {β€œ take_break ”: β€œ toAuto ”, β€œ go_to_work ”: β€œ toManual ”} return mapping[in_evt] class TrafficLightSystem(CoupledDEVS): def __init__(self): CoupledDEVS.__init __(self, β€œsystem”) self.light = self.addSubModel(TrafficLight()) self.police = self.addSubModel(Policeman()) self.connectPorts(self.police.out, self.light.interrupt, translate) def select(self, immlist): if self.police in immlist: return self.police else: return self.light

  28. __ Current Time: 0.00 __________________________________________ INITIAL CONDITIONS in model <system.light> Initial State: green Next scheduled internal transition at time 57.00 INITIAL CONDITIONS in model <system.policeman> Initial State: idle Next scheduled internal transition at time 20.00

  29. __ Current Time: 20.00 __________________________________________ EXTERNAL TRANSITION in model <system.light> Input Port Configuration: port <interrupt>: toManual New State: going_manual Next scheduled internal transition at time 20.0 INTERNAL TRANSITION in model <system.policeman> New State: working Output Port Configuration: port <output>: go_to_work Next scheduled internal transition at time 3620.00

  30. __ Current Time: 20.00 __________________________________________ INTERNAL TRANSITION in model <system.light> Output Port Configuration: port <observer>: turn_off New State: manual Next scheduled internal transition at time inf

  31. __ Current Time: 3620.00 __________________________________________ EXTERNAL TRANSITION in model <system.light> Input Port Configuration: port <interrupt>: toAuto New State: going_auto Next scheduled internal transition at time 3620.00 INTERNAL TRANSITION in model <system.policeman> New State: idle Output Port Configuration: port <output>: take_break Next scheduled internal transition at time 3920.00

  32. __ Current Time: 3620.00 __________________________________________ INTERNAL TRANSITION in model <system.light> Output Port Configuration: port <observer>: show_red New State: red Next scheduled internal transition at time 3680.00

  33. __ Current Time: 3620.00 __________________________________________ EXTERNAL TRANSITION in model <system.light> Input Port Configuration: port <interrupt>: toAuto New State: going_auto Next scheduled internal transition at time 3620.00 INTERNAL TRANSITION in model <system.policeman> New State: idle Output Port Configuration: port <output>: take_break Next scheduled internal transition at time 3920.00

  34. __ Current Time: 3920.00 __________________________________________ CONFLICT between models: <system.light> * <system.policeman> EXTERNAL TRANSITION in model <system.light> Input Port Configuration: port <interrupt>: toManual New State: going_manual Next scheduled internal transition at time 3920.00 INTERNAL TRANSITION in model <system.policeman> New State: work Output Port Configuration: port <output>: go_to_work Next scheduled internal transition at time 7520.00

  35. Closure under Coupling

  36. π’•π’‡π’Žπ’ˆ 𝑡 π’Žπ’‹π’‰π’Šπ’–πŸ 𝑡 π’’π’‘π’ŽπŸ take_break οƒ  toAuto go_to_work οƒ  toManual ?

  37. ? flatten 𝐷𝑁 = π‘Œ π‘‘π‘“π‘šπ‘” , 𝑍 π‘‘π‘“π‘šπ‘” , 𝐸, 𝑁𝑇, 𝐽𝑇, π‘Žπ‘‡ π‘”π‘šπ‘π‘’π‘’π‘“π‘œ 𝐷𝑁 = π‘Œ, 𝑍, 𝑇, π‘Ÿ π‘—π‘œπ‘—π‘’ , πœ€ π‘—π‘œπ‘’ , πœ€ 𝑓𝑦𝑒 , πœ‡, 𝑒𝑏

  39. CM 1 π‘Œ 𝐷𝑁 2 𝑇 1 π‘”π‘šπ‘π‘’π‘’π‘“π‘œ 𝐷𝑁 = π‘Œ, 𝑍, 𝑇, π‘Ÿ π‘—π‘œπ‘—π‘’ , πœ€ π‘—π‘œπ‘’ , πœ€ 𝑓𝑦𝑒 , πœ‡, 𝑒𝑏 𝑇 2 𝑍 𝐷𝑁

  40. CM 1 π‘Œ 𝐷𝑁 2 𝑇 1 π‘”π‘šπ‘π‘’π‘’π‘“π‘œ 𝐷𝑁 = π‘Œ, 𝑍, 𝑇, π‘Ÿ π‘—π‘œπ‘—π‘’ , πœ€ π‘—π‘œπ‘’ , πœ€ 𝑓𝑦𝑒 , πœ‡, 𝑒𝑏 𝑇 2 π‘Œ = π‘Œ 𝐷𝑁 𝑍 = 𝑍 𝐷𝑁 𝑍 𝐷𝑁

  41. CM 1 π‘Œ 𝐷𝑁 2 𝑓 1 𝑇 1 𝑑 1 , 𝑓 1 π‘”π‘šπ‘π‘’π‘’π‘“π‘œ 𝐷𝑁 = π‘Œ, 𝑍, 𝑇, π‘Ÿ π‘—π‘œπ‘—π‘’ , πœ€ π‘—π‘œπ‘’ , πœ€ 𝑓𝑦𝑒 , πœ‡, 𝑒𝑏 𝑇 2 𝑓 2 𝑑 2 , 𝑓 2 𝑍 𝐷𝑁

  42. CM 1 π‘Œ 𝐷𝑁 2 𝑓 1 𝑇 1 𝑑 1 , 𝑓 1 π‘”π‘šπ‘π‘’π‘’π‘“π‘œ 𝐷𝑁 = π‘Œ, 𝑍, 𝑇, π‘Ÿ π‘—π‘œπ‘—π‘’ , πœ€ π‘—π‘œπ‘’ , πœ€ 𝑓𝑦𝑒 , πœ‡, 𝑒𝑏 𝑇 2 𝑓 2 𝑇 = Γ— π‘—βˆˆπΈ 𝑅 𝑗 𝑑 2 , 𝑓 2 𝑍 𝐷𝑁

  43. CM 1 π‘Œ 𝐷𝑁 2 𝑓 1 𝑑 1 , 𝑓 1 = π‘Ÿ π‘—π‘œπ‘—π‘’,1 𝑇 1 𝑒𝑏 1 𝑑 1 π‘”π‘šπ‘π‘’π‘’π‘“π‘œ 𝐷𝑁 = π‘Œ, 𝑍, 𝑇, π‘Ÿ π‘—π‘œπ‘—π‘’ , πœ€ π‘—π‘œπ‘’ , πœ€ 𝑓𝑦𝑒 , πœ‡, 𝑒𝑏 𝑇 2 𝑓 2 𝑑 2 , 𝑓 2 = π‘Ÿ π‘—π‘œπ‘—π‘’,2 𝑒𝑏 2 𝑑 2 𝑍 𝐷𝑁

  44. CM 1 π‘Œ 𝐷𝑁 2 𝑓 1 𝑑 1 , 𝑓 1 = π‘Ÿ π‘—π‘œπ‘—π‘’,1 𝑇 1 𝑒𝑏 1 𝑑 1 π‘”π‘šπ‘π‘’π‘’π‘“π‘œ 𝐷𝑁 = π‘Œ, 𝑍, 𝑇, π‘Ÿ π‘—π‘œπ‘—π‘’ , πœ€ π‘—π‘œπ‘’ , πœ€ 𝑓𝑦𝑒 , πœ‡, 𝑒𝑏 𝑇 2 𝑓 2 π‘Ÿ π‘—π‘œπ‘—π‘’ = 𝑑 π‘—π‘œπ‘—π‘’ , 𝑓 π‘—π‘œπ‘—π‘’ 𝑑 2 , 𝑓 2 = π‘Ÿ π‘—π‘œπ‘—π‘’,2 𝑒𝑏 2 𝑑 2 𝑍 𝐷𝑁

  45. CM 1 π‘Œ 𝐷𝑁 2 𝑓 1 𝑑 1 , 𝑓 1 = π‘Ÿ π‘—π‘œπ‘—π‘’,1 𝑇 1 𝑒𝑏 1 𝑑 1 π‘”π‘šπ‘π‘’π‘’π‘“π‘œ 𝐷𝑁 = π‘Œ, 𝑍, 𝑇, π‘Ÿ π‘—π‘œπ‘—π‘’ , πœ€ π‘—π‘œπ‘’ , πœ€ 𝑓𝑦𝑒 , πœ‡, 𝑒𝑏 𝑇 2 𝑓 2 π‘Ÿ π‘—π‘œπ‘—π‘’ = 𝑑 π‘—π‘œπ‘—π‘’ , 𝑓 π‘—π‘œπ‘—π‘’ 𝑑 2 , 𝑓 2 = π‘Ÿ π‘—π‘œπ‘—π‘’,2 𝑑 π‘—π‘œπ‘—π‘’ = … , 𝑑 π‘—π‘œπ‘—π‘’,𝑗 , 𝑓 π‘—π‘œπ‘—π‘’,𝑗 βˆ’ 𝑓 π‘—π‘œπ‘—π‘’ , … 𝑒𝑏 2 𝑑 2 𝑍 𝐷𝑁

  46. CM 1 π‘Œ 𝐷𝑁 2 𝑓 1 𝑑 1 , 𝑓 1 = π‘Ÿ π‘—π‘œπ‘—π‘’,1 𝑇 1 𝑒𝑏 1 𝑑 1 π‘”π‘šπ‘π‘’π‘’π‘“π‘œ 𝐷𝑁 = π‘Œ, 𝑍, 𝑇, π‘Ÿ π‘—π‘œπ‘—π‘’ , πœ€ π‘—π‘œπ‘’ , πœ€ 𝑓𝑦𝑒 , πœ‡, 𝑒𝑏 𝑇 2 𝑓 2 π‘Ÿ π‘—π‘œπ‘—π‘’ = 𝑑 π‘—π‘œπ‘—π‘’ , 𝑓 π‘—π‘œπ‘—π‘’ 𝑑 2 , 𝑓 2 = π‘Ÿ π‘—π‘œπ‘—π‘’,2 𝑑 π‘—π‘œπ‘—π‘’ = … , 𝑑 π‘—π‘œπ‘—π‘’,𝑗 , 𝑓 π‘—π‘œπ‘—π‘’,𝑗 βˆ’ 𝑓 π‘—π‘œπ‘—π‘’ , … 𝑒𝑏 2 𝑑 2 𝑓 π‘—π‘œπ‘—π‘’ = min π‘—βˆˆπΈ 𝑓 π‘—π‘œπ‘—π‘’,𝑗 𝑍 𝐷𝑁

  47. CM 1 π‘Œ 𝐷𝑁 2 𝑓 1 𝑑 1 , 𝑓 1 = π‘Ÿ π‘—π‘œπ‘—π‘’,1 𝑇 1 𝑒𝑏 1 𝑑 1 π‘”π‘šπ‘π‘’π‘’π‘“π‘œ 𝐷𝑁 = π‘Œ, 𝑍, 𝑇, π‘Ÿ π‘—π‘œπ‘—π‘’ , πœ€ π‘—π‘œπ‘’ , πœ€ 𝑓𝑦𝑒 , πœ‡, 𝑒𝑏 𝑇 2 𝑓 2 π‘Ÿ π‘—π‘œπ‘—π‘’ = 𝑑 π‘—π‘œπ‘—π‘’ , 𝑓 π‘—π‘œπ‘—π‘’ 𝑑 2 , 𝑓 2 = π‘Ÿ π‘—π‘œπ‘—π‘’,2 𝑑 π‘—π‘œπ‘—π‘’ = … , 𝑑 π‘—π‘œπ‘—π‘’,𝑗 , 𝑓 π‘—π‘œπ‘—π‘’,𝑗 βˆ’ 𝑓 π‘—π‘œπ‘—π‘’ , … 𝑒𝑏 2 𝑑 2 𝑓 π‘—π‘œπ‘—π‘’ = min π‘—βˆˆπΈ 𝑓 π‘—π‘œπ‘—π‘’,𝑗 𝑑 π‘—π‘œπ‘—π‘’,𝑗 , 𝑓 π‘—π‘œπ‘—π‘’,𝑗 = π‘Ÿ π‘—π‘œπ‘—π‘’,𝑗 𝑍 𝐷𝑁

  48. CM 1 π‘Œ 𝐷𝑁 2 𝑇 1 𝑒𝑏 1 𝑓 1 π‘”π‘šπ‘π‘’π‘’π‘“π‘œ 𝐷𝑁 = π‘Œ, 𝑍, 𝑇, π‘Ÿ π‘—π‘œπ‘—π‘’ , πœ€ π‘—π‘œπ‘’ , πœ€ 𝑓𝑦𝑒 , πœ‡, 𝑒𝑏 𝑇 2 𝑒𝑏 2 𝑍 𝐷𝑁 𝑒

  49. CM 1 π‘Œ 𝐷𝑁 2 𝑇 1 𝑒𝑏 1 𝑓 1 𝜏 1 π‘”π‘šπ‘π‘’π‘’π‘“π‘œ 𝐷𝑁 = π‘Œ, 𝑍, 𝑇, π‘Ÿ π‘—π‘œπ‘—π‘’ , πœ€ π‘—π‘œπ‘’ , πœ€ 𝑓𝑦𝑒 , πœ‡, 𝑒𝑏 𝑇 2 + 𝑒𝑏 ∢ 𝑇 β†’ ℝ 0,+∞ 𝑒𝑏 2 𝑒𝑏 𝑑 = min π‘—βˆˆπΈ 𝜏 𝑗 = 𝑒𝑏 𝑗 𝑑 𝑗 βˆ’ 𝑓 𝑗 𝜏 2 𝑍 𝐷𝑁 𝑒

  50. CM 1 π‘Œ 𝐷𝑁 2 𝑇 1 𝑒𝑏 1 𝑓 1 𝜏 1 π‘”π‘šπ‘π‘’π‘’π‘“π‘œ 𝐷𝑁 = π‘Œ, 𝑍, 𝑇, π‘Ÿ π‘—π‘œπ‘—π‘’ , πœ€ π‘—π‘œπ‘’ , πœ€ 𝑓𝑦𝑒 , πœ‡, 𝑒𝑏 𝑇 2 + 𝑒𝑏 ∢ 𝑇 β†’ ℝ 0,+∞ 𝑒𝑏 2 𝑒𝑏 𝑑 = min π‘—βˆˆπΈ 𝜏 𝑗 = 𝑒𝑏 𝑗 𝑑 𝑗 βˆ’ 𝑓 𝑗 𝜏 2 𝐽𝑁𝑁 𝑑 = 𝑗 ∈ 𝐸 𝜏 𝑗 = 𝑒𝑏(𝑑) π‘‘π‘“π‘šπ‘“π‘‘π‘’(𝐽𝑁𝑁 𝑑 ) = 𝑗 βˆ— 𝑍 𝐷𝑁 𝑒

  51. CM 1 π‘Œ 𝐷𝑁 2 𝑇 1 π‘”π‘šπ‘π‘’π‘’π‘“π‘œ 𝐷𝑁 = π‘Œ, 𝑍, 𝑇, π‘Ÿ π‘—π‘œπ‘—π‘’ , πœ€ π‘—π‘œπ‘’ , πœ€ 𝑓𝑦𝑒 , πœ‡, 𝑒𝑏 𝑇 2 𝑍 𝐷𝑁 𝑒

  52. CM 1 π‘Œ 𝐷𝑁 2 𝑇 1 𝑧 2 π‘”π‘šπ‘π‘’π‘’π‘“π‘œ 𝐷𝑁 = π‘Œ, 𝑍, 𝑇, π‘Ÿ π‘—π‘œπ‘—π‘’ , πœ€ π‘—π‘œπ‘’ , πœ€ 𝑓𝑦𝑒 , πœ‡, 𝑒𝑏 𝑇 2 πœ‡ 𝑑 = ࡝ π‘Ž 𝑗 βˆ— ,π‘‘π‘“π‘šπ‘” πœ‡ 𝑗 βˆ— 𝑑 𝑗 βˆ— 𝑗𝑔 π‘‘π‘“π‘šπ‘” ∈ 𝐽 𝑗 βˆ— 𝑗𝑔 π‘‘π‘“π‘šπ‘” βˆ‰ 𝐽 𝑗 βˆ— βˆ… 𝑍 𝐷𝑁 𝑒

  53. CM 1 π‘Œ 𝐷𝑁 𝑒𝑏 𝑑 2 𝑇 1 𝑑 1 , 𝑒𝑏 1 𝑑 1 𝑑 1 , 0 π‘”π‘šπ‘π‘’π‘’π‘“π‘œ 𝐷𝑁 = π‘Œ, 𝑍, 𝑇, π‘Ÿ π‘—π‘œπ‘—π‘’ , πœ€ π‘—π‘œπ‘’ , πœ€ 𝑓𝑦𝑒 , πœ‡, 𝑒𝑏 𝑇 2 β€² , 0 𝑑 2 𝑑 2 , 𝑓 2 𝑑 2 , 𝑓 2 + 𝑒𝑏 𝑑 = 𝑒𝑏 2 (𝑑 2 ) 𝑍 𝐷𝑁 𝑒

  54. CM 1 π‘Œ 𝐷𝑁 𝑒𝑏 𝑑 2 𝑇 1 𝑑 1 , 𝑒𝑏 1 𝑑 1 𝑑 1 , 0 π‘”π‘šπ‘π‘’π‘’π‘“π‘œ 𝐷𝑁 = π‘Œ, 𝑍, 𝑇, π‘Ÿ π‘—π‘œπ‘—π‘’ , πœ€ π‘—π‘œπ‘’ , πœ€ 𝑓𝑦𝑒 , πœ‡, 𝑒𝑏 β€² , … 𝑇 2 β€² , 𝑓 πœ€ π‘—π‘œπ‘’ 𝑑 = … , 𝑑 β€² , 0 π‘˜ π‘˜ 𝑑 2 𝑔𝑝𝑠 π‘˜ = 𝑗 βˆ— πœ€ π‘—π‘œπ‘’,π‘˜ 𝑑 π‘˜ , 0 𝑑 2 , 𝑓 2 β€² = 𝑔𝑝𝑠 π‘˜ ∈ 𝐽 𝑗 βˆ— βˆ– π‘‘π‘“π‘šπ‘” ? β€² , 𝑓 𝑑 2 , 𝑓 2 + 𝑒𝑏 𝑑 = 𝑒𝑏 2 (𝑑 2 ) 𝑑 π‘˜ π‘˜ 𝑑 π‘˜ , 𝑓 π‘˜ + 𝑒𝑏 𝑑 π‘“π‘šπ‘‘π‘“ 𝑍 𝐷𝑁 𝑒

  55. 𝑦 2 CM 1 π‘Œ 𝐷𝑁 2 𝑧 1 𝑇 1 β€² , 0 𝑑 1 πœ€ π‘—π‘œπ‘’ 𝑑 1 , 𝑓 1 𝑑 1 , 𝑓 1 + 𝑒𝑏 𝑑 = 𝑒𝑏 1 (𝑑 1 ) π‘”π‘šπ‘π‘’π‘’π‘“π‘œ 𝐷𝑁 = π‘Œ, 𝑍, 𝑇, π‘Ÿ π‘—π‘œπ‘—π‘’ , πœ€ π‘—π‘œπ‘’ , πœ€ 𝑓𝑦𝑒 , πœ‡, 𝑒𝑏 β€² , … 𝑇 2 β€² , 𝑓 πœ€ π‘—π‘œπ‘’ 𝑑 = … , 𝑑 β€² , 0 𝑑 2 π‘˜ π‘˜ 𝑔𝑝𝑠 π‘˜ = 𝑗 βˆ— πœ€ π‘—π‘œπ‘’,π‘˜ 𝑑 π‘˜ , 0 πœ€ 𝑓𝑦𝑒 𝑑 2 , 𝑓 2 𝑑 2 , 𝑓 2 + 𝑒𝑏 𝑑 ≀ 𝑒𝑏 2 𝑑 2 β€² = , π‘Ž 𝑗 βˆ— ,π‘˜ πœ‡ 𝑗 βˆ— 𝑑 𝑗 βˆ— 𝑔𝑝𝑠 π‘˜ ∈ 𝐽 𝑗 βˆ— βˆ– π‘‘π‘“π‘šπ‘” πœ€ 𝑓𝑦𝑒,π‘˜ 𝑑 π‘˜ , 𝑓 π‘˜ + 𝑒𝑏 𝑑 , 0 β€² , 𝑓 𝑑 π‘˜ π‘˜ 𝑑 π‘˜ , 𝑓 π‘˜ + 𝑒𝑏 𝑑 π‘“π‘šπ‘‘π‘“ 𝑍 𝐷𝑁 𝑒

  56. CM 𝑓 1 π‘Œ 𝐷𝑁 2 𝑇 1 𝑓 1 π‘”π‘šπ‘π‘’π‘’π‘“π‘œ 𝐷𝑁 = π‘Œ, 𝑍, 𝑇, π‘Ÿ π‘—π‘œπ‘—π‘’ , πœ€ π‘—π‘œπ‘’ , πœ€ 𝑓𝑦𝑒 , πœ‡, 𝑒𝑏 𝑇 2 𝑍 𝐷𝑁 𝑒

  57. CM 𝑓 1 π‘Œ 𝐷𝑁 2 𝑇 1 𝑓 1 𝑧 π‘‘π‘“π‘šπ‘” π‘”π‘šπ‘π‘’π‘’π‘“π‘œ 𝐷𝑁 = π‘Œ, 𝑍, 𝑇, π‘Ÿ π‘—π‘œπ‘—π‘’ , πœ€ π‘—π‘œπ‘’ , πœ€ 𝑓𝑦𝑒 , πœ‡, 𝑒𝑏 β€² , … 𝑇 2 β€² , 𝑓 𝑗 πœ€ 𝑓𝑦𝑒 𝑑, 𝑓 , 𝑦 = … , 𝑑 𝑗 β€² = ቐ πœ€ 𝑓𝑦𝑒,𝑗 𝑑 𝑗 , 𝑓 𝑗 + 𝑓 , π‘Ž π‘‘π‘“π‘šπ‘”,𝑗 𝑦 , 0 𝑔𝑝𝑠 𝑗 ∈ 𝐽 π‘‘π‘“π‘šπ‘” β€² , 𝑓 𝑗 𝑑 𝑗 𝑑 𝑗 , 𝑓 𝑗 + 𝑓 π‘“π‘šπ‘‘π‘“ 𝑍 𝐷𝑁 𝑒

  58. π‘”π‘šπ‘π‘’π‘’π‘“π‘œ 𝐷𝑁 = π‘Œ, 𝑍, 𝑇, π‘Ÿ π‘—π‘œπ‘—π‘’ , πœ€ π‘—π‘œπ‘’ , πœ€ 𝑓𝑦𝑒 , πœ‡, 𝑒𝑏 π‘Œ = π‘Œ 𝐷𝑁 𝑍 = 𝑍 𝐷𝑁 𝑇 = Γ— π‘—βˆˆπΈ 𝑅 𝑗 𝑅 = 𝑑, 𝑓 𝑑 ∈ 𝑇, 0 ≀ 𝑓 ≀ 𝑒𝑏(𝑑) π‘Ÿ π‘—π‘œπ‘—π‘’ = 𝑑 π‘—π‘œπ‘—π‘’ , 𝑓 π‘—π‘œπ‘—π‘’ ∈ 𝑅 𝑑 π‘—π‘œπ‘—π‘’ = (… , 𝑑 π‘—π‘œπ‘—π‘’,𝑗 , 𝑓 π‘—π‘œπ‘—π‘’,𝑗 βˆ’ 𝑓 π‘—π‘œπ‘—π‘’ , … ) 𝑓 π‘—π‘œπ‘—π‘’ = min π‘—βˆˆπΈ 𝑓 π‘—π‘œπ‘—π‘’,𝑗 𝑑 π‘—π‘œπ‘—π‘’,𝑗 , 𝑓 π‘—π‘œπ‘—π‘’,𝑗 = π‘Ÿ π‘—π‘œπ‘—π‘’,𝑗 β€² , … β€² , 𝑓 πœ€ π‘—π‘œπ‘’ 𝑑 = … , 𝑑 π‘˜ π‘˜ 𝑔𝑝𝑠 π‘˜ = 𝑗 βˆ— πœ€ π‘—π‘œπ‘’,π‘˜ 𝑑 π‘˜ , 0 β€² = , π‘Ž 𝑗 βˆ— ,π‘˜ πœ‡ 𝑗 βˆ— 𝑑 𝑗 βˆ— β€² , 𝑓 πœ€ 𝑓𝑦𝑒,π‘˜ 𝑑 π‘˜ , 𝑓 π‘˜ + 𝑒𝑏 𝑑 , 0 𝑔𝑝𝑠 π‘˜ ∈ 𝐽 𝑗 βˆ— 𝑑 π‘˜ π‘˜ 𝑑 π‘˜ , 𝑓 π‘˜ + 𝑒𝑏 𝑑 π‘“π‘šπ‘‘π‘“ β€² , … β€² , 𝑓 𝑗 πœ€ 𝑓𝑦𝑒 𝑑, 𝑓 , 𝑦 = … , 𝑑 𝑗 β€² = ቐ πœ€ 𝑓𝑦𝑒,𝑗 𝑑 𝑗 , 𝑓 𝑗 + 𝑓 , π‘Ž π‘‘π‘“π‘šπ‘”,𝑗 𝑦 , 0 𝑔𝑝𝑠 𝑗 ∈ 𝐽 π‘‘π‘“π‘šπ‘” β€² , 𝑓 𝑗 𝑑 𝑗 𝑑 𝑗 , 𝑓 𝑗 + 𝑓 π‘“π‘šπ‘‘π‘“ πœ‡ 𝑑 = ΰ΅π‘Ž 𝑗 βˆ— ,π‘‘π‘“π‘šπ‘” πœ‡ 𝑗 βˆ— 𝑑 𝑗 βˆ— 𝑗𝑔 π‘‘π‘“π‘šπ‘” ∈ 𝐽 𝑗 βˆ— 𝑗𝑔 π‘‘π‘“π‘šπ‘” βˆ‰ 𝐽 𝑗 βˆ— 𝜚 𝑗 βˆ— = π‘‘π‘“π‘šπ‘“π‘‘π‘’(𝐽𝑁𝑁 𝑑 ) 𝐽𝑁𝑁 𝑑 = 𝑗 ∈ 𝐸 𝜏 𝑗 = 𝑒𝑏(𝑑) 𝑒𝑏 𝑑 = min π‘—βˆˆπΈ 𝜏 𝑗 = 𝑒𝑏 𝑗 𝑑 𝑗 βˆ’ 𝑓 𝑗

  59. Hierarchical Simulator

  60. Root coordinator (i, t) (*, t) (done, t) (done, t) Coupled DEVS Coordinator (i, t) (*, t) (x, t) (y, t) (done, t) (done, t) (done, t) (done, t) Simulator Simulator Atomic DEVS Atomic DEVS

  65. DEVS Semantics Operational Denotational Semantics Semantics Abstract Atomic DEVS [1] Simulator Hierarchical Closure under Coupled DEVS Simulator Coupling [1] Ashvin Radiya and Robert G. Sargent. A logic-based foundation of discrete event modeling and simulation. ACM Transactions on Modeling and Computer Simulation, 1(1):3-51, 1994.

  66. Conclusions (*, t) (done, t) (i,t) (y, t) (x, t)  Atomic DEVS π’•π’‡π’Žπ’ˆ 𝑡 π’Žπ’‹π’‰π’Šπ’–πŸ 𝑡 π’’π’‘π’ŽπŸ  Coupled DEVS  Closure under coupling  Abstract Simulator take_break οƒ  toAuto go_to_work οƒ  toManual

  67. http://msdl.cs.mcgill.ca/projects/PythonPDEVS

  68. Limitations of Classic DEVS  Parallel implementation  Parallel DEVS [1]  Select function is artificial  Parallel DEVS [1]  Dynamic Structure systems  Dynamic Structure DEVS [2] [1] A.C.-H. Chow. Parallel DEVS: A parallel, hierarchical, modular modeling formalism and its distributed simulator. Transactions of the Society for Computer Simulation International, 13(2):55-68, 1996. [2] F . Barros. The dynamic structure discrete event system specification formalism. Transactions of the Society for Computer Simulation International, 13(1):35-46, 1996.

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

Distributed classic DEVS simulator with TimeWarp Amr Al Mallah Outline Classical DEVS Simulator

Distributed classic DEVS simulator with TimeWarp Amr Al Mallah Outline Classical DEVS Simulator

Distributed classic DEVS simulator with TimeWarp Amr Al Mallah Outline Classical DEVS Simulator Distributed DEVS Simulator Conservative Parallel Simulator Optimistic (Time warp) Parallel Simulator Conclusion Classical DEVS Simulator Text

439 views β€’ 32 slides
Infrastructure for DEVS Modelling and Experiment Hongyan Song August 2006 Modelling,

Infrastructure for DEVS Modelling and Experiment Hongyan Song August 2006 Modelling,

Infrastructure for DEVS Modelling and Experiment Hongyan Song August 2006 Modelling, Simulation, and Design Lab School of Computer Science McGill University Outline Motivations and Ideas DEVS Visual Modelling Representing DEVS in

631 views β€’ 19 slides
Classic ML Where is ML used? CS 5860 - Introduction to Formal Methods What is Classic ML? ML

Classic ML Where is ML used? CS 5860 - Introduction to Formal Methods What is Classic ML? ML

Classic ML an EventML Where does ML come from? Classic ML Where is ML used? CS 5860 - Introduction to Formal Methods What is Classic ML? ML types Vincent Rahli Nuprl team Polymorphism Recursion Cornell University Typing rules September

125 views β€’ 11 slides
PASSION FOR CLASSIC Welcome to Como Classic Boats, Lake Comos premier classic wooden boat

PASSION FOR CLASSIC Welcome to Como Classic Boats, Lake Comos premier classic wooden boat

MENAGGIO VARENNA BELLAGIO TREMEZZO PASSION FOR CLASSIC Welcome to Como Classic Boats, Lake Comos premier classic wooden boat rental company with driver. Located and operated in Laglio, next to George Clooneys villa and LEZZENO to the

234 views β€’ 8 slides
DEVS Flattening with muModelica and pyDEVS Jesse Doherty Outline Introduction

DEVS Flattening with muModelica and pyDEVS Jesse Doherty Outline Introduction

DEVS Flattening with muModelica and pyDEVS Jesse Doherty Outline Introduction Motivations Tools Solution Conclusion Introduction DEVS Atomic S ,ta, int , X , ext ,Y , Coupled X self ,Y self

606 views β€’ 21 slides
DEVS standardization: some thoughts Hans Vangheluwe Juan de Lara, Jean-S ebastien Bolduc,

DEVS standardization: some thoughts Hans Vangheluwe Juan de Lara, Jean-S ebastien Bolduc,

DEVS Standards Group meeting Winter Simulation Conference 2001 Washington, DC December 11, 2001 DEVS standardization: some thoughts Hans Vangheluwe Juan de Lara, Jean-S ebastien Bolduc, Ernesto Posse Modelling, Simulation and Design Lab

491 views β€’ 27 slides
PASSION FOR CLASSIC Welcome to Como Classic Boats, Lake Alle Darsene di Loppia Comos premier

PASSION FOR CLASSIC Welcome to Como Classic Boats, Lake Alle Darsene di Loppia Comos premier

MENAGGIO VARENNA BELLAGIO TREMEZZO PASSION FOR CLASSIC Welcome to Como Classic Boats, Lake Alle Darsene di Loppia Comos premier classic wooden boat rental company with driver. Located and operated in Laglio, next to George Clooneys

240 views β€’ 8 slides
Parallel DEVS Modelling of Traffic in AToM 3 Ximeng Sun School of Computer Science, McGill

Parallel DEVS Modelling of Traffic in AToM 3 Ximeng Sun School of Computer Science, McGill

Parallel DEVS Modelling of Traffic in AToM 3 Ximeng Sun School of Computer Science, McGill University xsun16@cs.mcgill.ca automatically generated models from mapping Traffic Abstract models to DEVS models by using graph transformation.

1.35k views β€’ 11 slides
Classic McEliece: conservative code-based cryptography Round 2 https://classic.mceliece.org/

Classic McEliece: conservative code-based cryptography Round 2 https://classic.mceliece.org/

Classic McEliece: conservative code-based cryptography Round 2 https://classic.mceliece.org/ Daniel J. Bernstein 1 , Tung Chou 2 , Tanja Lange 3 , Ingo von Maurich, Rafael Misoczki 4 , Ruben Niederhagen 5 , Edoardo Persichetti 6 , Christiane

439 views β€’ 28 slides
Classic McEliece: conservative code-based cryptography D. J. Bernstein classic.mceliece.org

Classic McEliece: conservative code-based cryptography D. J. Bernstein classic.mceliece.org

1 Classic McEliece: conservative code-based cryptography D. J. Bernstein classic.mceliece.org Fundamental literature: 1962 Prange (attack) + many more attack papers. 1968 Berlekamp (decoder). 19701971 Goppa (codes). 1978 McEliece

775 views β€’ 58 slides
iPhone Development A Web Devs Perspective Ben Sandofsky - ben@sandofsky.com Im Your

iPhone Development A Web Devs Perspective Ben Sandofsky - ben@sandofsky.com Im Your

iPhone Development A Web Devs Perspective Ben Sandofsky - ben@sandofsky.com Im Your Straight Man Im a Ruby guy Put on ad-hoc Yellowpages.com iPhone App Team Worked with the SDK since Beta 1 The Platform You must use

526 views β€’ 14 slides
DEVS modeling of Traffic in AToM3 Presented by Ximeng Sun April 11, 2005 References [1]

DEVS modeling of Traffic in AToM3 Presented by Ximeng Sun April 11, 2005 References [1]

DEVS modeling of Traffic in AToM3 Presented by Ximeng Sun April 11, 2005 References [1] Bernard P. Zeigler, Herbert Praehofer, and Tag Gon Kim. Theory of Modeling and Simulation. Academic Press, 2000. [2] Hans Vangheluwe, Juan de

596 views β€’ 37 slides
Parallel DEVS &amp; DEVSJAVA Presented by Ximeng Sun Mar 16, 2005 References Bernard P.

Parallel DEVS &amp; DEVSJAVA Presented by Ximeng Sun Mar 16, 2005 References Bernard P.

Parallel DEVS &amp; DEVSJAVA Presented by Ximeng Sun Mar 16, 2005 References Bernard P. Zergler, Herbert Praehofer, and Tag Gon Kim. Theory of Modeling and Simulation. Academic Press, 2000. Bernard P. Zergler, Hessam S. Sarjoughian.

537 views β€’ 41 slides
Web devs common system security mistakes Luka Z. Gerzic In memoriam Dragan D. Ve erina -

Web devs common system security mistakes Luka Z. Gerzic In memoriam Dragan D. Ve erina -

Web devs common system security mistakes Luka Z. Gerzic In memoriam Dragan D. Ve erina - vecxo CTO YubcNet 1974 - 2014 # whoami root Atari 520ST was my first box in 87 :) Onix BBS based on RemoteAccess 2.50 &amp; HyperSpace

937 views β€’ 31 slides
The difference between hearing and hearing Domino , R2 Domino Classic | Introduction

The difference between hearing and hearing Domino , R2 Domino Classic | Introduction

Domino Classic The difference between hearing and hearing Domino , R2 Domino Classic | Introduction Listening situations EASY 1-on-1 conversation Watching TV Small meeting Family gathering In a store Outdoors Conference In class

599 views β€’ 26 slides
Bringing Clang and LLVM to Visual C++ users Reid Kleckner Google C++ devs demand a good

Bringing Clang and LLVM to Visual C++ users Reid Kleckner Google C++ devs demand a good

Bringing Clang and LLVM to Visual C++ users Reid Kleckner Google C++ devs demand a good toolchain Fast build times Powerful optimizations: LTO, etc Helpful diagnostics Static analyzers Dynamic instrumentation tools: the

920 views β€’ 45 slides
Achieving Portable Performance for GTC-P with OpenACC on GPU, multi-core CPU, and Sunway

Achieving Portable Performance for GTC-P with OpenACC on GPU, multi-core CPU, and Sunway

Achieving Portable Performance for GTC-P with OpenACC on GPU, multi-core CPU, and Sunway Many-core Processor Step ephen en Wa Wang 1 , James Lin 1,4 , William Tang 2 , Stephane Ethier 2 , Bei Wang 2 , Simon See 1,3 and Satoshi

418 views β€’ 21 slides
Interplanetary Shock Detection and Geomagnetic Storm Evolution JOSH HAGOOD / ROB STEENBURGH

Interplanetary Shock Detection and Geomagnetic Storm Evolution JOSH HAGOOD / ROB STEENBURGH

Interplanetary Shock Detection and Geomagnetic Storm Evolution JOSH HAGOOD / ROB STEENBURGH UNIVERSITY OF MINNESOTA / SPACE WEATHER PREDICTION CENTER MINNEAPOLIS, MN 55455 / BOULDER, CO 80305 Goal Increase accuracy of 3 hourly K P

203 views β€’ 16 slides
Market Settlement Timeline Stakeholder Conference Call August 22, 2019 James Lynn Senior

Market Settlement Timeline Stakeholder Conference Call August 22, 2019 James Lynn Senior

Market Settlement Timeline Stakeholder Conference Call August 22, 2019 James Lynn Senior Advisor ISO PUBLIC ISO PUBLIC Agenda Time Topic Presenter 10:00 Welcome / Policy Process Kristina Osborne 10:15 Review Issue Paper and Straw

285 views β€’ 15 slides
Learning Program m es I m plem entation Septem ber 2 0 1 8 Presentation Outline

Learning Program m es I m plem entation Septem ber 2 0 1 8 Presentation Outline

Learning Program m es I m plem entation Septem ber 2 0 1 8 Presentation Outline Discretionary Grants Allocations and Contracting for 2018/ 2019 Changes in the Skills Development Dispensation New Modular Based Occupational

334 views β€’ 11 slides
Large-scale Physical Model Tests of Micropile Stabilized Slopes J. Erik Loehr and Andrew

Large-scale Physical Model Tests of Micropile Stabilized Slopes J. Erik Loehr and Andrew

Large-scale Physical Model Tests of Micropile Stabilized Slopes J. Erik Loehr and Andrew Boeckmann University of Missouri Columbia John J. Deeken Black and Veatch Stabilization Technique Motivation How is force developed within

622 views β€’ 30 slides
Data Processing at the Speed of 100 Gbps using Apache Crail Patrick Stuedi IBM Research Apache

Data Processing at the Speed of 100 Gbps using Apache Crail Patrick Stuedi IBM Research Apache

Data Processing at the Speed of 100 Gbps using Apache Crail Patrick Stuedi IBM Research Apache Crail (crail.apache.org) Apache Crail (crail.apache.org) Ephemeral Data HDFS, Input data S3 Map-reduce job Broadcast Map Shuffle Reduce

393 views β€’ 36 slides
Microcontroller Driven Electroluminescent Display Jamie Buckmann Christopher Stedman Advised

Microcontroller Driven Electroluminescent Display Jamie Buckmann Christopher Stedman Advised

Microcontroller Driven Electroluminescent Display Jamie Buckmann Christopher Stedman Advised by: Mr. Steve Gutschlag Outline Project Summary Functional Description System Block Diagrams Software Completed Tasked Results

715 views β€’ 24 slides
Atomic Layer Deposition Atomic Layer Deposition (ALD) Erwin Kessels w.m.m.kessels@tue.nl

Atomic Layer Deposition Atomic Layer Deposition (ALD) Erwin Kessels w.m.m.kessels@tue.nl

Atomic Layer Deposition Atomic Layer Deposition (ALD) Erwin Kessels w.m.m.kessels@tue.nl www.phys.tue.nl/pmp Vapor phase deposition technologies Physical Vapor Deposition (PVD) Chemical Vapor Deposition (CVD) sputtering Heat!

597 views β€’ 49 slides

More recommend