Math 454 (Modeling and Simulation)
The Main objective of the course is to learn simulation techniques and implement them on a variety of practical problems. By the end of this course the student should be able to:
1. Formulating real life
problems into mathematical models.
2. Write a model file
using some computer simulation language.
3. Analyze the simulation
output.
4. Documentation and
implementation.
Modeling and simulation make a significant contribution in solving problems arising in science, engineering, economics, management, social and behavioral sciences. This course is about modeling and simulation of systems. Both modeling and simulation aspects are covered in sufficient detail. The emphasis in this course is on practical problem solving and not on theorem proving. The following topics will be covered in this course:
1. General introduction and overview of modeling and simulation, its strength and weakness. How it compares with other alternatives; mathematical models and physical experiments.
2. The fundamental concepts of systems and models. This unit gives an Understanding of the fundamental systems concepts and modeling methodology. This is essential for practical multidisciplinary applications of modeling and simulation.
3. Modeling and Simulation depend heavily on probability and statistical techniques. In this unit we give a brief review of the main concepts in the probability and statistics field.
4. Input Analysis: In this unit we focus on how to collect data from the field and analyze these data in order to fit a theoretical distribution and test whether the hypothesized distribution fits the collected data or not.
5. Random Variables Generation: In this unit we learn how to use computer to generate random numbers that are used in simulation and how to test these random numbers.
6. Output Analysis: We study how to use the output of the simulation to draw a confidence level about the average performance measure of the system we are studying.
7. Selected Applications:
Here we implemented modeling and simulation to solve a variety of practical
- application such as communication system production and inventory control,
manufacturing quality control,
Production scheduling, manpower allocation, reliability
and maintenance.
Students should have a background in elementary probability and statistics. The student should also be familiar with some programming languages.
First Exam
20%
Second Exam
20%
Assignments and a Project*
20%
Final Exam
40%
* The student is required to handle 5-6 assignments during the semester and one project in the last week of the semester.
Neelamkavil, F.
Computer Simulation and Modeling . Wiley,
New York, 1987.
1. Hamdi A. Taha. Simulation
Modeling and SIMNET. Printice
Hall, Englewood Cliffs, NJ, 1988.
2. Law, A. M. and W. D. Kelton.
Simulation Modeling and Analysis. McGrrow
Hill, New York, 1991.
3. Khoshnevis B. Discrete
Systems Simulation. McGrow Hill, New
York,1994.
4. Schriber T. J. An
Introduction to Simulation Using GPSS/H. Wiley,
New York,1991.
| Week of | Lecture | Subject |
| 1 | Introduction to Modeling and Simulation, | |
| 2 | 1 | Monte Carlo simulation, |
| 2 | When to Use Simulation, limitation of Simulation | |
| 3 | 1 | Systems Concept, |
| 2 | Characteristics of Systems | |
| 4 | 1 | Models: Types of Models, modeling Methodology, |
| 2 | Models for various Disciplines, | |
| 5 | 1 | Validating a Model. |
| 2 | Review of Basic Probability and Statistics. | |
| 6 | 1 | Selecting Input Probability Distribution: |
| 2 | Hypothesizing Family of Distributions, | |
| 7 | 1 | Estimation of Parameters, |
| 2 | First Exam | |
| 8 | 1 | Goodness of Fit. |
| 2 | Pseudo Random Number Generation Techniques, | |
| 9 | 1 | Methods for Testing Pseudo Random Numbers. |
| 2 | Generating Random Variates with Arbitrary Distributions, | |
| 10 | 1 | Other Methods for Random Variates Generation. |
| 2 | Generation of arrival processes: Poisson Process, | |
| 11 | 1 | Nonstationary Poisson Process. |
| 2 | Output Analysis: Transient and Steady-State Simulation. | |
| 2 | Estimating Means, Building Confidence Interval, | |
| 12 | 1 | Multiple Replications Method |
| 2 | Batch Means Method. | |
| 13 | 1 | Modeling single servers. |
| 2 | Second Exam | |
| 14 | Modeling single servers | |
| 15 | Modeling single servers continued. |