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

Parallel DEVS An Introduction Using PythonPDEVS Yentl Van Tendeloo, Hans Vangheluwe

Introduction

Process Interaction Cellular Automata Discrete Event Activity Scanning State Charts Petri Nets Discrete Event Event Scheduling Finite State Automata Discrete Event DEVS

Experimentation

X t S t Y t

simple_experiment.py from pypdevs.simulator import Simulator from mymodel import MyModel model = MyModel() simulator = Simulator(model) simulator.setVerbose() simulator.simulate()

Atomic Models

X Red 60s t S Yellow 3s t 57 120 177 60 Y Green 57s t

Red 60s 𝑁 = 𝑇 , 𝜀 𝑗𝑜𝑢 𝑢𝑏 , 𝑇 : set of sequential states 𝑇 = {red, yellow, green} 𝜀 𝑗𝑜𝑢 : 𝑇 → 𝑇 Yellow 𝜀 𝑗𝑜𝑢 = {red → green, 3s green → yellow, yellow → red} 𝑢𝑏 : S → ℝ 0,+∞ 𝑢𝑏 = {red → 60, green → 57, yellow → 3} Green 57s

𝑇 = {red, yellow, green} atomic_int.py 𝜀 𝑗𝑜𝑢 = { red → green, from pypdevs.DEVS import * green → yellow, yellow → red} class TrafficLightAutonomous(AtomicDEVS): 𝑢𝑏 = {red → 60, def __init__(self): green → 57, AtomicDEVS.__init __(self, “Light”) yellow → 3} self.state = “red” def intTransition(self): state = self.state return {“red”: “green”, “yellow”: “red”, “green”: “yellow”}[state] def timeAdvance(self): time = 0 state = self.state current_state = green return {“red”: 60, while True: “yellow”: 3, time += ta(current_state) “green”: 57}[state] current_state = 𝜀 𝑗𝑜𝑢 (current_state)

X Red 60s t !red S Yellow !green 3s !yellow t 57 120 177 60 Y Green 57s t

Red 𝑁 = , 𝑇, 𝜀 𝑗𝑜𝑢 , , 𝑢𝑏 60s 𝑍 𝜇 𝑇 = {red, yellow, green} 𝜀 𝑗𝑜𝑢 = { red → green, !red green → yellow, yellow → red} 𝑢𝑏 = {red → 60, green → 57, Yellow !green yellow → 3} 3s 𝑍 : set of output events 𝑍 = {“red”, “green”, “yellow”} !yellow 𝜇 : 𝑇 → 𝑍 𝑐 𝜇 = { green → [“yellow”], yellow → [“red”], Green red → [“green”]} 57s

atomic_out.py 𝑍 = {“red”, “green”, “yellow”} from pypdevs.DEVS import * 𝜇 = {green → “yellow”, yellow → “red”, class TrafficLightWithOutput(AtomicDEVS): red → “green”} def __init__(self): AtomicDEVS.__init __(self, “light”) self.state = “red” self.observe = self.addOutPort (“observer”) … def outputFnc(self): state = self.state if state == “red”: v = “green” time = 0 elif state == “yellow”: current_state = green v = “red” while True: elif state == “green”: time += ta(current_state) v = “yellow” output( 𝜇 (current_state)) return {self.observe: [v]} current_state = 𝜀 𝑗𝑜𝑢 (current_state)

X Red 60s ?manual t !red ?auto S Manual Yellow !green ∞s 3s ?manual t 57 120 177 !yellow 60 Y Green ?manual 57s t

𝑁 = 𝑌 , 𝑍, 𝑇, 𝜀 𝑗𝑜𝑢 , 𝜀 𝑓𝑦𝑢 , 𝜇, 𝑢𝑏 𝑍 = {“red”, “green”, “yellow”} Red 𝑇 = {red, yellow, green, manual} 60s ?manual 𝜀 𝑗𝑜𝑢 = {red → green, green → yellow, yellow → red} !red 𝜇 = {green → “yellow”, ?auto yellow → “red”, red → “green”} 𝑢𝑏 = {red → 60, Manual Yellow !green green → 57, ∞s 3s yellow → 3, ?manual manual → ∞ } 𝑌 : set of input events !yellow 𝑌 = {“auto”, “manual”} 𝜀 𝑓𝑦𝑢 : Q × 𝑌 𝑐 → 𝑇 Green ?manual 𝜀 𝑓𝑦𝑢 = {( (*, *), [“manual”]) → “manual”, 57s ( (“manual”, *), [“auto”]) → “red”}

𝑌 = {“auto”, “manual”} atomic_ext.py 𝜀 𝑓𝑦𝑢 = {( (*, *), [“manual”]) → “manual”, from pypdevs.DEVS import * ( (“manual”, *), [“auto”]) → “red”} class TrafficLight(AtomicDEVS): def __init__(self): AtomicDEVS.__init __(self, “light”) self.state = “red” self.observe = self.addOutPort (“observer”) self.interrupt = self.addInPort (“interrupt”) time = 0 cur_state = “red” … while True: next_time = time + ta(cur_state) def extTransition(self, inputs): if time_next_ev <= next_time: inp = inputs[self.interrupt][0] cur_state = 𝜀 𝑓𝑦𝑢 ((cur_state, e), next_ev) if inp == “manual”: time = time_next_ev return “manual” else: elif inp == “auto”: time = next_time if self.state == “manual”: output( 𝜇 (current_state)) return “red” current_state = 𝜀 _ 𝑗𝑜𝑢 (current_state)

𝜀 𝑑𝑝𝑜𝑔 𝑁 = 𝑌, 𝑍, 𝑇, 𝜀 𝑗𝑜𝑢 , 𝜀 𝑓𝑦𝑢 , , 𝜇, 𝑢𝑏 𝑌 : set of input events 𝑍 : set of output events 𝑇 : set of sequential states 𝜀 𝑗𝑜𝑢 : 𝑇 → 𝑇 𝜀 𝑓𝑦𝑢 : Q × 𝑌 𝑐 → 𝑇 𝜇 : 𝑇 → 𝑍 𝑐 𝑢𝑏 : S → ℝ 0,+∞ 𝜀 𝑑𝑝𝑜𝑔 : 𝑇 × 𝑌 𝑐 → 𝑇

atomic_conf.py from pypdevs.DEVS import * class TrafficLight(AtomicDEVS): … def confTransition(self, inputs): self.elapsed = 0.0 self.state = self.intTransition() self.state = self.extTransition(inputs) return self.state

Coupled Models

Work 360s !manual !auto Idle 20s

Red Work 60s ?manual 360s !red ?auto !manual !auto Manual Yellow !green ∞s 3s Idle 20s ?manual !yellow Green ?manual M = 𝑌, 𝑍, 𝐸, 𝑁 𝑗 , 𝐽 𝑗 , 𝑎 𝑗,𝑘 57s

trafficlight_system.py from pypdevs.DEVS import * from trafficlight import TrafficLight from policeman import Policeman class TrafficLightSystem(CoupledDEVS): def __init__(self): CoupledDEVS.__init __(self, “system”) self.light = self.addSubModel(TrafficLight()) self.police = self.addSubModel(Policeman()) self.connectPorts(self.police.out, self.light.interrupt)

City Traffic House Road Road Commerce light Generator Queue Queue Queue     Queue Processor Processor Collector     Queue Queue  

Root coordinator (done, t) (done, t) (@,t) (*, t) Coupled DEVS Coordinator (x, t) (*, t) (*, t) (@,t) (y, t) (done, t) (done, t) Simulator Simulator Atomic DEVS Atomic DEVS

Applications

Conclusions

Conclusions (@,t) (Y , t) (X, t) (*, t) (done, t)  Atomic DEVS  Coupled DEVS R  Closure under coupling 60s ?manual Work  Abstract Simulator 360s !red ?auto !manual !auto M Y !green ∞s 3s ?manual Idle 20s !yellow G ?manual 57s

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

Formalisms Standardization Performance Model libraries Applications Dynamic Algorithms Structure Tools Example Real-time Activity Languages Cell DEVS Distribution Reusable Interoperable Verification Parallel