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# Applied Mathematics & Statistics

AMS 553, Simulation and Modeling
A comprehensive course in formulation, implementation, and application of simulation models. Topics include data structures, simulation languages, statistical analysis, pseudorandom number generation, and design of simulation experiments. Students apply simulation modeling methods to problems of their own design. This course is offered as CSE 529, AMS 553, and MBA 553.
PrerequisiteAMS 507

Either Tex t Listed Below is Acceptable:
"Simulation Modeling and Analysis", by Averill M. Law and David Kelton,  4th Edition, McGraw-Hill, ISBN#: 978-0-07-3294414; OR
"Simulation Modeling and Analysis", by Averill M. Law,  5e, McGraw-Hill, ISBN #: 978-0-07-340132-4

Starting in spring 2009.

Learning Outcomes:

1) Understand the capabilities and limitations of discrete event simulation models and be able to build and run simulation models for simple queueing and inventory systems.

2) Demonstrate an understanding of the basic concepts in random number generation:
* Understand the structure of basic linear congruential generators;
* Use statistical methods to test the independence and uniformity of a sequence of random numbers.

3) Demonstrate an understanding of the concepts in random variate generation:
* Familiarity with the different approaches for generating random variates;
* Understand the working principles of different algorithms and be able to apply these algorithms to different situations;
* Familiarity with the algorithms for generating some commonly encountered stochastic processes.

4) Demonstrate an understanding of the concepts in input analysis:
* Familiarity with various statistical tools used in describing and analyzing a given data set;
* Use the date collected from an actual process to fit an input distribution;
* Be able to apply statistical methods to test the goodness of fit.

5) Demonstrate an understanding of the concepts in output analysis:
* Understand the transient and steady state behavior of an simulation output process;
* Familiarity with the tools used in analyzing terminating simulations;
* Familiarity with the standard procedures used in analyzing non-terminating simulations, e.g., replication deletion, batch method method, regenerative method;
* Estimate the number of replication runs needed to achieve a desired level of precision.

6) Demonstrate an understanding of the concepts in variance reduction:
* Understand the working principles of different variance reduction techniques;
* Be able to apply these techniques to different situations to improve the statistical efficiency of simulation outputs.

7) Demonstrate an understanding of the basic concepts in simulation optimization. 