The goal of this course is to introduce students to basic simulation methods and tools for modeling and simulation of continuous, discrete and combined systems, and provide the foundations for the student to understand computer simulation needs, and to implement and test a variety of simulation and data analysis libraries and programs.

Students should know how to:

Generate random number and random variables

Use Monte-Carlo technique to solve intractable mathematical problems

Build a simulation model with basic operations and inputs

Build a simulation model with detailed operations

Develop algorithm and computer programing for intended simulation

Perform statistical analysis of output from simulation

Having completing this course, students will able to do:

Understand the definition of simulation and how to develop and analyze a simulation model

Understand the fundamental logic, structure, components and management of simulation modeling

Understand the scope and limitations of simulation

Construct simulation models for real-world systems

System analysis and benchmarking

Evaluate performance of existing and new/proposed models real-world systems

Introduction to Simulation: Basic concepts of systems, models, and simulation, Discrete and continuous systems simulation, Purposes of simulation, Advantages and disadvantages of simulation, Steps in a simulation study.

Monte Carlo Simulation: Concept of random numbers, Techniques for generating random numbers, Tests for random numbers. Methods for generating random variates–inverse transformation, composition, convolution, acceptance-rejection. Comparison of the methods, Applications of probability distributions in simulation–Uniform, Exponential, Weibull, Gamma, Normal, Binomial, Poisson, Monte Carlo integration. MCMC method.

Verification and Validation of Simulation Models: Simulation credibility, Techniques for verification and validation of simulation models, Statistical methods for comparing real-world observations and simulation output data.

Analysis of Simulation Data: Identifying the distribution with data, Parameter estimation, Goodness-of-fit tests, Output analysis for terminating and steady state simulations.

Simulation Case Studies: Application of simulation in queuing and inventory systems.

1)

Ross, S. M. (2006). Simulation, 4th ed., Academic Press.

2)

Lazic, S. E., & H. L. Roche (2012). Introducing Monte Carlo Methods with R. [Kroese]

3)

Rubinstein, R. Y., & D. P. Kroese (2011). Simulation and the Monte Carlo method (Vol. 707). John Wiley & Sons.

4)

Banks, J. (1998). Handbook of Simulation, Wiley, New York.

5)

Law, A. M., & W. Kelton (2000). Simulation modeling and analysis. Mac Graw Hill, Boston, Burr Ridge, ua.

6)

Robert, C. P. and G. Casella (2010). Introducing Monte Carlo Methods with R (Vol. 18). New York: Springer. [Daley]

7)

Sing, V. P. (2009). System Modeling and Simulation, New Age International (P) Limited, New Delhi.

8)

Suess, E. A. and B. E. Trumbo (2010). Introduction to Probability Simulation and Gibbs Sampling with R, Springer.