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 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 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 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 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 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 Invitation to Computer Science, Java Version, Third Edition

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

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 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 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 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 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 Invitation to Computer Science, Java Version, Third Edition

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

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

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

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

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

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 model’s output Invitation to Computer Science, Java Version, Third Edition

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

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

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

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

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

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

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