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Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling

Modelling and Simulation to tackle Complexity

Hans Vangheluwe

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling

1

Modelling and Simulation Modelling and Simulation for . . . The Modelling Relationship

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Causes of Complexity Large Number of Components Diversity of Components Non-compositional/Emergent Behaviour Uncertainty

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Dealing with Complexity Multiple Abstraction Levels Optimal Formalism Multi-Formalism Multiple Views/Aspects

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Multi-Paradigm Modelling

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Modelling and Simulation for . . .

Simulation . . . when too costly/dangerous analysis ↔ design

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Modelling and Simulation for . . .

Simulation . . . real experiment not ethical “physical” simulation, training

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Modelling and Simulation for . . .

Simulation . . . evaluate alternatives

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Modelling and Simulation for . . .

Simulation . . . “Do it Right the First Time”

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Modelling and Simulation for . . .

essence: “shooting” problems

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Modelling and Simulation for . . .

defining a “hit”

5 10 15 20 5 10 15 20 25 30

θ

• rigin (0, 2)

target (30, 1) Height (m) Distance (m)

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Modelling and Simulation for . . .

• ptimizing a “performance metric”

10 20 30 40 50 60 70 80 90 5 10 15 20 25 30

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Modelling and Simulation for . . .

• ptimal solution. . . s

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Modelling and Simulation for . . .

Modelling/Simulation . . . and code/app Synthesis

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Modelling and Simulation for . . .

The spectrum of uses of models Documentation Formal Verification (all models, all behaviours) Model Checking (one model, all behaviours) Test Generation Simulation (one model, one behaviour) . . . calibration, validation, optimization, . . . Application Synthesis

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Modelling and Simulation for . . . Requirements (“What?”) Detached or Semi-detached Style (classical, modern, . . . ) Number of Floors Number of rooms of different types (bedrooms, bathrooms, . . . ) Garage, Storage, . . . Cellar Energy-saving measures . . . Design (“How?”)

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Modelling and Simulation for . . .

System Boundaries System to be built/studied Environment with which the system interacts

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Modelling and Simulation for . . .

System vs. “Plant”

www.mathworks.com/products/demos/simulink/PowerWindow/html/PowerWindow1.html

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling The Modelling Relationship

Real-World entity Base Model System S

• nly study behaviour in

experimental context experiment within context Model M Simulation Results Experiment Observed Data

within context

simulate = virtual experiment Model Base a-priori knowledge

validation

REALITY MODEL GOALS

Modelling and Simulation Process

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling The Modelling Relationship

System (real or model) generator transducer acceptor Experimental Frame

Frame Input Variables Frame Output Variables

set of all “contexts” in which model is valid includes experiment descriptions: parameters, initial conditions ∼ re-use, testing

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling

Dealing with Complexity

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Large Number of Components

Crowds

www.3dm3.com

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Large Number of Components

Number of Components – hierarchical (de-)composition

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Diversity of Components

Diversity of Components: Power Window

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Diversity of Components

Diversity of Components: Paper Mill

www.gov.karelia.ru

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Diversity of Components

Paper Mill Model

M,S M,S M,S M,S

Q

M,S

Q

M,S M,S M,S M,S

PaperPulp mill Waste Water Treatment Plant Fish Farm

Effluent Recycle (return) flow Clarifier (DESS) Activated sludge unit (DESS) Mixing Aeration Sedimentation Influent Stormwater tank 1 Stormwater tank 2

• verflow

Switch

WWTP (DESS) System of WWTP and Stormwater tanks (DEVS)

Input/Output function Input function Output function

algae fish

GE RRA X CFA

+

CFF

EDRF

+ GF

X X

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Non-compositional/Emergent Behaviour

Non-compositional/Emergent Behaviour

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Non-compositional/Emergent Behaviour

Engineered Emergent Behaviour

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Uncertainty

Often related to level of abstraction: for example continuous vs. discrete

www.engr.utexas.edu/trafficSims/

uncertainty = imprecise = not rigorous

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling

Guiding principle (∼ physics: principle of minimal action) minimize accidental complexity,

• nly essential complexity remains

Fred P . Brooks. No Silver Bullet – Essence and Accident in Software Engineering. Proceedings of the IFIP Tenth World Computing Conference, pp. 1069–1076, 1986. http://www.lips.utexas.edu/ee382c-15005/Readings/Readings1/05-Broo87.pdf

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling

Solutions multiple abstraction levels

• ptimal formalism

multiple formalisms multiple views

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Multiple Abstraction Levels

Different Abstraction Levels – properties preserved

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Multiple Abstraction Levels

Levels of Abstraction/Views: Morphism

detailed (technical) level abstract (decision) level abstraction simulation M_d M_t trajectory model traj_t traj_d

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Multiple Abstraction Levels

Abstraction Relationship foundation: the information contained in a model M. Different questions (properties) P = I(M) which can be asked concerning the model. These questions either result in true or false. Abstraction and its opposite, refinement are relative to a non-empty set of questions (properties) P. If M1 is an abstraction of M2 with respect to P, for all p ∈ P: M1 | = p ⇒ M2 | = p. This is written M1 ⊒P M2. M1 is said to be a refinement of M2 iff M1 is an abstraction

• f M2. This is written M1 ⊑P M2.

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Optimal Formalism

Most Appropriate Formalism

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Optimal Formalism

Forrester System Dynamics model

• f Predator-Prey interaction

Predator Prey Grazing_efficiency uptake_predator loss_prey predator_surplus_DR prey_surplus_BR

2−species predator−prey system

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Optimal Formalism

Causal Block Diagram model of Harmonic Oscillator

x0 0.0 y0 1.0

IC

x

IC

y −

I OUT

K 1.0 0.0 PLOT

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Optimal Formalism

Petri Net model of Producer – Consumer

P.Calculating 1 Wait4Cons Buffer Buffer−p 1 Wait4Prod 1 C.Calculating Produce Put in Buffer Rem.from buffer Consume

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Optimal Formalism

GPSS model of Telephone Exchange

FN1 12 2 V2 V1 PH 1 LR PH1 V1 H 2 P2 NE P1 S PH1 LNKS R PH1 1 LR PH2 R PH1 LNKS 1 S PH2 FN1 120 Function: 1 LNKS 10

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Multi-Formalism

Multiple Formalisms: Power Window

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Multi-Formalism

Components in Different Formalisms

www.mathworks.com/products/demos/simulink/PowerWindow/html/PowerWindow1.html

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Multi-Formalism

Controller, using Statechart(StateFlow) formalism

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Multi-Formalism

Mechanics subsystem

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Multiple Views/Aspects

Multiple (consistent !) Views (in = Formalisms)

(work by Esther Guerra and Juan de Lara)

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Multiple Views/Aspects

View: Runtime Diagram

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Multiple Views/Aspects

View: Events Diagram

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Multiple Views/Aspects

View: Protocol Statechart

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling Multiple Views/Aspects

No Free Lunch!

Solutions often introduce their own accidental complexity multiple abstraction levels (need morphism)

• ptimal formalism (need precise meaning)

multiple formalisms (need relationship) multiple views (need consistency)

Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling

Multi-Paradigm Modelling ( minimize accidental complexity ) at the most appropriate level of abstraction using the most appropriate formalism(s) Differential Algebraic Equations, Petri Nets, Bond Graphs, Statecharts, CSP , Queueing Networks, Lustre/Esterel, . . . with transformations as first-class models

Pieter J. Mosterman and Hans Vangheluwe. Computer Automated Multi-Paradigm Modeling: An Introduction. Simulation 80(9):433–450, September 2004. Special Issue: Grand Challenges for Modeling and Simulation.