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

2. 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. Invitation to Computer Science, Java Version, Third Edition 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. Invitation to Computer Science, Java Version, Third Edition 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. Invitation to Computer Science, Java Version, Third Edition 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. Invitation to Computer Science, Java Version, Third Edition 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. Invitation to Computer Science, Java Version, Third Edition 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. Invitation to Computer Science, Java Version, Third Edition 8 Figure 12.1 Using a Simulation in an Interactive Design Environment

9. Invitation to Computer Science, Java Version, Third Edition 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. Invitation to Computer Science, Java Version, Third Edition 10 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 Computational Models, Accuracy, and Errors (continued)

11. Invitation to Computer Science, Java Version, Third Edition 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. Invitation to Computer Science, Java Version, Third Edition 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. Invitation to Computer Science, Java Version, Third Edition 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 system’s behavior

14. Invitation to Computer Science, Java Version, Third Edition 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. Invitation to Computer Science, Java Version, Third Edition 15 Figure 12.3 System to Be Modeled

16. Invitation to Computer Science, Java Version, Third Edition 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. Invitation to Computer Science, Java Version, Third Edition 17 Figure 12.4 Algorithm for New Customer Arrival

18. Invitation to Computer Science, Java Version, Third Edition 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. Invitation to Computer Science, Java Version, Third Edition 19 Figure 12.5 Statistical Distribution of Customer Service Time

20. Invitation to Computer Science, Java Version, Third Edition 20 Figure 12.6 Algorithm for Generating Random Numbers That Follow the Distribution Given in Figure 12.5

21. Invitation to Computer Science, Java Version, Third Edition 21 Figure 12.7 Algorithm for Customer Departure Event

22. Invitation to Computer Science, Java Version, Third Edition 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. Invitation to Computer Science, Java Version, Third Edition 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. Invitation to Computer Science, Java Version, Third Edition 24 Figure 12.8 The Main Algorithm of Our Simulation Model

25. Invitation to Computer Science, Java Version, Third Edition 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. Invitation to Computer Science, Java Version, Third Edition 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. Invitation to Computer Science, Java Version, Third Edition 27 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 Running the Model and Visualizing Results (continued)

28. Invitation to Computer Science, Java Version, Third Edition 28 Figure 12.9 Using a Two-Dimensional Graph to Display Output

29. Invitation to Computer Science, Java Version, Third Edition 29 Figure 12.10: Using a Two-Dimensional Graph to Display and Compare Two Data Values

30. Invitation to Computer Science, Java Version, Third Edition 30 Figure 12.11 Three-Dimensional Image of a Region of the Earth’s Surface

31. Invitation to Computer Science, Java Version, Third Edition 31 Figure 12.12 Three-Dimensional Model of a Methyl Nitrite Molecule

32. Invitation to Computer Science, Java Version, Third Edition 32 Figure 12.13 Visualization of Gas Dispersion

33. Invitation to Computer Science, Java Version, Third Edition 33 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 Running the Model and Visualizing Results (continued)

34. Invitation to Computer Science, Java Version, Third Edition 34 Figure 12.14 Use of Animation to Model Ozone Layers in the Atmosphere

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