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Chapter 12: Simulation and Modeling

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Title: Chapter 12: Simulation and Modeling Last modified by: Rudy Created Date: 5/4/2004 3:13:55 PM Document presentation format: On-screen Show Other titles – PowerPoint PPT presentation

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Title: Chapter 12: Simulation and Modeling


1
Chapter 12 Simulation and Modeling
  • Invitation to Computer Science,
  • Java Version, Third Edition

2
Objectives
  • In this chapter, you will learn about
  • Computational modeling
  • Running the model and visualizing results

3
Introduction
  • Simulation and modeling
  • Probably the single most important scientific use
    of computing today
  • Having an impact on quantitative fields, such as
    chemistry, biology, medicine, meteorology,
    ecology, geography, economics, and so on

4
Computational Modeling Introduction to Systems
and Models
  • The scientific method
  • Observe the behavior of a system
  • Formulate a hypothesis about system behavior
  • Design and carry out experiments to prove or
    disprove the validity of the hypothesis
  • Often a model of the system is used

5
Introduction to Systems and Models (continued)
  • A model
  • An abstraction of the system being studied that
    we claim behaves much like the original
  • Computer simulation
  • A physical system is modeled as a set of
    mathematical equations and/or algorithmic
    procedures

6
Introduction to Systems and Models (continued)
  • Computer simulation (continued)
  • Model is translated into a high-level language
    and executed on the Von Neumann computer
  • Computational models
  • Also called simulation models
  • Used to
  • Design new systems
  • Study and improve the behavior of existing systems

7
Introduction to Systems and Models (continued)
  • Computational models (continued)
  • Allow the use of an interactive design
    methodology (sometimes called computational
    steering)
  • Used in most branches of science and engineering

8
Figure 12.1 Using a Simulation in an Interactive
Design Environment
9
Computational Models, Accuracy, and Errors
  • Proper balance between accuracy and complexity
    must be achieved
  • A model must be both
  • An accurate representation of the physical system
  • Simple enough to implement as a program and solve
    on a computer in a reasonable amount of time

10
Computational Models, Accuracy, and Errors
(continued)
  • To build a model
  • Include important factors that act on the system
  • Omit unimportant factors that only make the model
    harder to build, understand, and solve

11
Computational Models, Accuracy, and Errors
(continued)
  • Continuous model
  • A set of equations that describe the behavior of
    a system as a continuous function of time t
  • Models that use statistical approximations
  • Needed for systems that cannot be modeled using
    precise mathematical equations

12
An Example of Model Building
  • Discrete event simulation
  • One of the most popular and widely used
    techniques for building computer models
  • The behavior of a system is modeled only at an
    explicit and finite set of times
  • Only the times when an event takes place are
    modeled
  • Event An activity that changes the state of the
    system

13
An Example of Model Building (continued)
  • To process an event
  • Change the state of the simulated system in the
    same way that the actual system would change if
    the event had occurred in real life
  • Once finished, move to the next event
  • When simulation is complete, the program displays
    results that characterize the systems behavior

14
An Example of Model Building (continued)
  • Problem
  • You are the owner of a new take-out restaurant,
    McBurgers, currently under construction
  • You want to determine the proper number of
    checkout stations needed
  • You decide to build a model of McBurgers to
    determine the optimal number of servers

15
  • Figure 12.3
  • System to Be Modeled

16
An Example of Model Building (continued)
  • First Identify the events that can change the
    system
  • A new customer arriving
  • An existing customer departing after receiving
    food and paying
  • Next Develop an algorithm for each event
  • Should describe exactly what happens to the
    system when this event occurs

17
  • Figure 12.4
  • Algorithm for New Customer Arrival

18
An Example of Model Building (continued)
  • The algorithm for the new customer arrival event
    uses a statistical distribution (Figure 12.5) to
    determine the time required to service the
    customer
  • Can model the statistical distribution of
    customer service time using the algorithm in
    Figure 12.6

19
  • Figure 12.5
  • Statistical Distribution of Customer Service Time

20
  • Figure 12.6
  • Algorithm for Generating Random Numbers That
    Follow the Distribution Given in Figure 12.5

21
  • Figure 12.7
  • Algorithm for Customer Departure Event

22
An Example of Model Building (continued)
  • Must initialize parameters to the model
  • Model must collect data that accurately measures
    performance of the McBurgers restaurant

23
An Example of Model Building (continued)
  • When simulation is ready, the computer will
  • Run the simulation
  • Process all M customers
  • Print out the results

24
  • Figure 12.8
  • The Main Algorithm of Our Simulation Model

25
Running the Model and Visualizing Results
  • Scientific visualization
  • Visualizing data in a way that highlights its
    important characteristics and simplifies its
    interpretation
  • An important part of computational modeling
  • Different from computer graphics

26
Running the Model and Visualizing Results
(continued)
  • Scientific visualization is concerned with
  • Data extraction Determine which data values are
    important to display and which are not
  • Data manipulation Convert the data to other
    forms or to different units to enhance display

27
Running the Model and Visualizing Results
(continued)
  • Output of a computer model can be represented
    visually using
  • A two-dimensional graph
  • A three-dimensional image
  • Visual representation of data helps identify
    important features of the models output

28
  • Figure 12.9
  • Using a Two-Dimensional Graph to Display Output

29
  • Figure 12.10 Using a Two-Dimensional Graph to
    Display and Compare Two Data Values

30
  • Figure 12.11
  • Three-Dimensional Image of a Region of the
    Earths Surface

31
  • Figure 12.12
  • Three-Dimensional Model of a Methyl Nitrite
    Molecule

32
  • Figure 12.13
  • Visualization of Gas Dispersion

33
Running the Model and Visualizing Results
(continued)
  • Image animation
  • One of the most powerful and useful forms of
    visualization
  • Shows how models output changes over time
  • Created using many images, each showing system
    state at a slightly later point in time

34
  • Figure 12.14
  • Use of Animation to Model Ozone Layers in the
    Atmosphere

35
Summary
  • A model is an abstraction of a system that
    behaves much like the original
  • Computer simulation
  • Physical system is modeled using mathematical
    equations and/or algorithmic procedures
  • Model is translated into a high-level language
    program and executed

36
Summary (continued)
  • Computational models allow the use of an
    interactive design methodology
  • Scientific visualization Visualizing data to
    highlight its important characteristics and
    simplify its interpretation
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