COMP 522 Modelling and Simulation model everything Hans Vangheluwe - - PowerPoint PPT Presentation

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COMP 522 Modelling and Simulation model everything Hans Vangheluwe - - PowerPoint PPT Presentation

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Fall Term 2008 COMP 522 Modelling and Simulation model everything Hans Vangheluwe Modelling, Simulation and Design Lab (MSDL) School of Computer Science, McGill University, Montr eal, Canada Hans Vangheluwe hv@cs.mcgill.ca

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Fall Term 2008

COMP 522 Modelling and Simulation “model everything”

Hans Vangheluwe

Modelling, Simulation and Design Lab (MSDL) School of Computer Science, McGill University, Montr´ eal, Canada

Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation 1/58

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Overview

  • 1. Course Description
  • 2. Practical Information
  • 3. Why/When Modelling and Simulation?
  • 4. Complex Systems
  • 5. Modelling and Simulation Concepts

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Course Description

The course presents the generic (tool and application domain independent) concepts of modelling and simulation of complex dynamic systems. By the end of this course, you should have a deep understanding of these concepts using a variety of formalisms.

Hierarchy of System Specifications Finite State Automata (FSA) Petri Nets DEVS GPSS Event Scheduling Activity Scanning Process Interaction Discrete Event Statecharts Hybrid Continuous-Time Forrester System Dynamics Population Dynamics Modelica (multi-physics) CSSLs continuous-time CBDs discrete-time CBDs time-less CBDs Causal Block Diagrams Formalisms Animation is theory behind visualized using

Strengths and weaknesses of different formalisms will be explained. This will allow you to choose the most appropriate formalism(s) for a given problem.

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Course Description (ctd.)

You will learn to build modelling and simulation (software) systems. This will give you ample background to understand and use existing modelling and simulation systems. The course presents general modelling and simulation principles by applying them to concrete problems in various application domains: software process modelling and simulation, reactive systems design such as complex graphical user interfaces, population dynamics analysis, traffic analysis, supermarket queueing, . . .

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Practical Information

Main Reference (public!):

  • moncs.cs.mcgill.ca/people/hv/teaching/MS/
  • you will upload your project here!

Assignment submission, discussions: WebCT

  • www.mcgill.ca/mycourses/

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Need help ?

  • Talk to me after class or make an appointment
  • Come and see me during my office hours

Monday 16:00 - 18:00 in MC328

  • Use the discussion forum in WebCT (no direct e-mail!)
  • Arrange to meet one of the TAs (assignment/project-specific)
  • Assignments/projects are never fully specified ! Give feedback !

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What are the pre-requisites ?

  • COMP 251 (data structures and algorithms),
  • COMP 302 (programming languages and paradigms),
  • COMP 350 (numerical computing).

. . . or equivalent (see me). Note:

  • most assignment/project programming in Python

(where appropriate)

  • no prior knowledge required, but read Tutorial at

www.python.org

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Undergraduate or Graduate course ?

  • Challenging course (work load)
  • graduate “flavour” (independent thinking/work)
  • some of the highest grades ever were obtained by ugrads

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How is evaluation done ?

  • 60% on assignments.
  • 30% on the project (work, correctness, presentation).
  • 10% on a mini-quizzes after each theory subject (in-next-class).

Together, assignments, mini-quizzes and project cover the entire course. Hence, there is no final exam.

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Assignment/project rules of the game ?

  • Completely in HTML form: requirements, design, code, discussion.
  • Assignments: submit via WebCT.
  • Project: on course website.
  • Coding in Python www.python.org (where appropriate).
  • Some assignments (and projects) in teams of 2.

Clearly describe work distribution !

  • Original work, some presented in class.
  • Respect deadlines (or do more work to compensate).
  • Alternate subjects may be proposed.

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Assignments cover these topics

  • 1. A Causal Block Diagram simulation tool.
  • 2. Petri Net modelling, simulation and analysis.
  • 3. Statechart modelling, simulation and software synthesis.
  • 4. Event Scheduling simulation tool.
  • 5. DEVS modelling and simulation of computer architecture.
  • 6. GPSS (process interaction) model of a production (queueing)

process.

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Project

  • For a formalism of choice (possibly construct your own):

build a modelling and/or simulation environment.

  • Using an existing modelling/simulation system:

study a specific problem (games, user interfaces, physical systems, . . . ). Have a look at the course website for examples from previous years. Examples: dead-reckoning in distributed games, SimCity, world dynamics, hybrid systems, solar car, dependable systems, TCP/IP, . . .

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Questions?

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A Variety of Complex Systems . . .

Need to be modelled

  • at most appropriate level of abstraction
  • in most appropriate formalism(s)

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Why simulation? . . . when too costly/dangerous

analysis ↔ design

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Why simulation? . . . real experiment not ethical

training, physical simulation

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Simulation . . . evaluate alternatives

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Simulation . . . evaluate alternatives

www.engr.utexas.edu/trafficSims/

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

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Modelling/Simulation . . . and code/app Synthesis

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Complex Systems: complexity due to . . .

large number of components

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Complex Systems: complexity due to . . .

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Complex Systems: complexity due to . . .

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

heterogeneity of components

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Complex Systems: complexity due to . . .

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Modelling/Simulating Complex Systems . . .

  • at the most appropriate level of abstraction
  • using the most appropriate formalism(s)

Ordinary Differential Equations, Petri Nets, Bond Graphs, Statecharts, Forrester System Dynamics, CSP, Queueing Networks, . . .

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COMP 522: Modelling and Simulation

  • . . . to study (static/dynamic) structure and (dynamic) behaviour
  • . . . for analysis and design of complex systems
  • . . . for different application domains:

computer networks, software design, traffic control, software engineering, biology, physics, chemistry, management, . . .

  • . . . implemented using Computer Science

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What is Modelling and Simulation ?

  • Modelling: represent/re-use/exchange knowledge

about system structure and behaviour

  • Simulation: to accurately and efficiently emulate real behaviour

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Modelling and Simulation Concepts

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

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Experimental Frame (Zeigler)

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

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Behaviour morphism

Real System Abstract Model Experiment Results Simulation Results experiment virtual experiment modelling/abstraction abstraction

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Which topics does the course cover ?

Hierarchy of System Specifications Finite State Automata (FSA) Petri Nets DEVS GPSS Event Scheduling Activity Scanning Process Interaction Discrete Event Statecharts Hybrid Continuous-Time Forrester System Dynamics Population Dynamics Modelica (multi-physics) CSSLs continuous-time CBDs discrete-time CBDs time-less CBDs Causal Block Diagrams Formalisms Animation is theory behind visualized using

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Which topics does the course cover ?

  • 1. Modelling formalism syntax and semantics.

The Causal Block Diagram formalisms.

I O

^−1

IC IC 4.0 K 1.0 M 1.0 V0 0.0 X0

DEP INDEP

Print

DEP INDEP

Plot TIME

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  • 2. Untimed Discrete Event Formalisms:

(a) (non)Deterministic State Automata. (b) Adding Concurrency and Synchronisation: Petri Nets (e.g., specifying network protocols).

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(c) Adding Hierarchy and Orthogonality: Statecharts (e.g., UML, specifying reactive software). (d) (Adding Space: Cellular Automata).

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  • 3. Timed Discrete Event Formalisms:

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(a) Event Scheduling. (b) Activity Scanning. (c) Three Phase Approach. (d) Process Interaction for queueing systems (GPSS).

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

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(e) DEVS as a rigourous basis for hierarchical modelling.

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  • 4. Deterministic Simulation of Stochastic Processes:

(a) Pseudo Random Number Generation. (b) Gathering Statistics (performance metrics).

  • 5. Animation
  • 6. Continuous-time Formalisms:

(a) Ordinary Differential Equations, Algebraic Equations, Differential Algebraic Equations. (b) CSSLs: sorting and algebraic loop detection. (c) Forrester System Dynamics, Population Dynamics.

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Predator Prey Grazing_efficiency uptake_predator loss_prey predator_surplus_DR prey_surplus_BR

2−species predator−prey system

predator prey

trajectories

10 20 30 200 400 600

(d) Object-oriented Physical Systems Modelling: non-causal modelling, Modelica (www.modelica.org). (e) Object-oriented Physical Systems Modelling: Bond Graphs.

  • 7. Putting it all together (theory):

Hierarchy of System Specifications, Systems Theory.

  • 8. Hybrid (continuous-discrete) modelling and simulation.

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Do we live in a Simulation?

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Questions?

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Hierarchy of System Specification

  • f Structure and Behaviour
  • Basis of System Specification:

sets theory, time base, segments and trajectories

  • Hierarchy of System Specification (causal, deterministic)
  • 1. I/O Observation Frame
  • 2. I/O Observation Relation
  • 3. I/O Function Observation
  • 4. I/O System
  • Multicomponent Specifications
  • Non-causal models

ref: Waymore, Zeigler, Klir, . . .

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Set Theory

Properties: {1, 2, . . . , 9} {a, b, . . . , z} N, N+, N+

∞

R, R+, R+

∞

EV = {ARRIV AL, DEPARTURE} EV φ = EV ∪ {φ} Structuring: A × B = {(a, b)|a ∈ A, b ∈ B} G = (E, V ), V ⊆ E × E

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Comparing things

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Nominal Scale: e.g., gender

A scale that assigns a category label to an individual. Establishes no explicit ordering on the category labels. Only a notion of equivalence “=” is defined with properties:

  • 1. Reflexivity: x = x ∨ x = x.
  • 2. Symmetry of equivalence: x = y ⇔ y = x.
  • 3. Transitivity: x = y ∧ y = z → x = z.

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Ordinal Scale: e.g., degree of happiness

A scale in which data can be ranked, but in which no arithmetic transformations are meaningful. It is meaningless to talk about difference (distance). In addition to equivalence, a notion of order < is defined with properties:

  • 1. Symmetry of equivalence: x = y ⇔ y = x.
  • 2. Asymmetry of order: x < y → y < x.
  • 3. Irreflexivity: x < x.
  • 4. Transitivity: x < y ∧ y < z → x < z.

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Partial ordering

The ordering may be partial (some data items cannot be compared).

t1 t2 t3 t4 t5 t6 t7

The ordering may be total (all data items can be compared). ∀x, y ∈ X : x < y ∨ y < x ∨ x = y

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Interval Scale: e.g., Shoe Size

A scale where distances between data are meaningful. On interval measurement scales, one unit on the scale represents the same magnitude of the characteristic being measured across the whole range

  • f the scale. Interval scales do not have a “true” zero point, however,

and therefore it is not possible to make statements about how many times higher one value is than another. In addition to equivalence and order, a notion of interval is defined. The choice of a zero point is arbitrary.

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Ratio Scale: e.g., age

Both intervals between values and ratios of values are meaningful. A meaningful zero point is known. “A is twice as old as B”.

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Time Base

  • Simulation of Dynamic Systems: irreversible passage of time.
  • Time Base T:

– {NOW} (instantaneous) – R: continuous-time – N or isomorphic: discrete-time

  • Ordering:

– Ordinal Scale (possibly partial ordering) – Interval Scale – Ratio Scale

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Time Bases for hybrid system models

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Time Bases for hybrid system models

TD TC (tc, td)

“nested time” for nested experiments.

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Behaviour ≡ Evolution over Time

  • With time base, describe evolution over time
  • Time function, trajectory, signal: f : T → V
  • Restriction to T ′ ⊆ T

f|T ′ : T ′ → V , ∀t ∈ T ′ : f|T ′(t) = f(t) – Past of f: f|Tt – Future of f: f|Tt

  • Restriction to an interval: segment

ω : t1, t2 → V

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Types of Segments

T T T T continuous piecewise continuous piecewise constant discrete event V V V V

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Cashier-Queue System

Physical View Queue Cashier Departure Arrival Departure Queue Abstract View Cashier [ST distribution] [IAT distribution] Arrival

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Trajectories

state= queue_length x cashier_state

queue_length T 1 2 10 20 30 40 50 cashier_state Busy Idle T 10 20 30 40 50 T Input Events Arrival 10 20 30 40 50

E1 E2

T Output Events Departure 10 20 30 40 50

E3 E4

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