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

2. Announcements Read Chapter 12
Invitation to Computer Science, Java Version, Third Edition

3. Objectives In this chapter, you will learn about
Computational modeling
Running the model and visualizing results
Invitation to Computer Science, Java Version, Third Edition

4. 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
Invitation to Computer Science, Java Version, Third Edition

5. 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
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6. 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
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7. 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
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8. 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
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9. Using a Simulation in an Interactive Design Environment
Figure 12.1
Using a Simulation in an
Interactive Design Environment
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10. 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
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11. 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
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12. 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
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13. 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
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14. 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 system’s behavior
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15. Example Models Coin Flipping Example Conway’s Game of Life Example
Opening a restaurant Example
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16. Conway’s Game of Life
Von Neumann wondered if it was possible for a machine to build copies of itself
Conway created a simple zero-person game that is a complete von-neumann machine.
Game is “played” on a grid
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17. Conway’s Game of Life Any live cell with < 2 live
Neighbors dies (loneliness)
Any live cell with > 3 live
Neighbors dies (overcrowding)
Any live cell with 2 or 3 live
Neighbors continues living
Any empty cell with exactly
3 live neighbors comes alive
(birth)
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18. Is it Possible?
Create an initial condition that does not change from generation to generation?
Create an initial condition that oscillates from generation to generation?
Create an initial condition that moves through space from generation to generation?
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19. What additional Hypotheses?
Will all initial conditions eventually
All die out?
Reach some stable state (no changes)?
Reach some state of oscillation?
Is it possible to make an initial state that will grow indefinitely?
Is it possible to make an initial state that will create copies of itself?
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20. An Example of Model Building (Restaurant)
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
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21. Figure 12.3 System to Be Modeled
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22. 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
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23. Algorithm for New Customer Arrival
Figure 12.4
Algorithm for New Customer Arrival
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24. 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
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25. Statistical Distribution of Customer Service Time
Figure 12.5
Statistical Distribution of Customer Service Time
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26. Figure 12.6
Algorithm for Generating Random Numbers That Follow the Distribution Given in Figure 12.5
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27. Algorithm for Customer Departure Event
Figure 12.7
Algorithm for Customer Departure Event
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28. An Example of Model Building (continued)
Must initialize parameters to the model
Model must collect data that accurately measures performance of the McBurgers restaurant
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29. An Example of Model Building (continued)
When simulation is ready, the computer will
Run the simulation
Process all M customers
Print out the results
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30. The Main Algorithm of Our Simulation Model
Figure 12.8
The Main Algorithm of Our Simulation Model
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31. 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
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32. 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
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33. 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 model’s output
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34. Using a Two-Dimensional Graph to Display Output
Figure 12.9
Using a Two-Dimensional Graph to Display Output
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35. Figure 12.10: Using a Two-Dimensional Graph to Display and Compare Two Data Values
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36. Three-Dimensional Image of a Region of the Earth’s Surface
Figure 12.11
Three-Dimensional Image of a Region of the Earth’s Surface
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37. Three-Dimensional Model of a Methyl Nitrite Molecule
Figure 12.12
Three-Dimensional Model of a Methyl Nitrite Molecule
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38. Visualization of Gas Dispersion
Figure 12.13
Visualization of Gas Dispersion
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39. Running the Model and Visualizing Results (continued)
Image animation
One of the most powerful and useful forms of visualization
Shows how model’s output changes over time
Created using many images, each showing system state at a slightly later point in time
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40. Use of Animation to Model Ozone Layers in the Atmosphere
Figure 12.14
Use of Animation to Model Ozone Layers in the Atmosphere
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41. 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
Invitation to Computer Science, Java Version, Third Edition

42. 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
Invitation to Computer Science, Java Version, Third Edition