IEN-422, Systems Modeling II

2001 Catalog Data: IEN-422, Systems Modeling II: Stochastic Models

Credits: (4-0-4)

Course Description: Stochastic models in operations research; Review of basic probability, discrete time Markov chains; continuous time Markov chains; discrete and continuous phase type distributions; birth-and-death processes; elementary queuing models involving Poisson arrivals and exponential service times; advance queuing models; basic concepts in simulation and simulation of various processes.

Prerequisites: IEN-321, Systems Modeling I: Deterministic Models

Corequisites:  None

Textbook: Operations Research: Applications and Algorithms, Wayne L. Winston, Third Edition, Duxbury Press, 1994.

References: 1. Stochastic Modeling and the Theory of Queues, R.W. Wolff, Prentice Hall, 1989.  2. Queuing Methods for Services and Manufacturing, R.W. Hall, Prentice Hall, 1991.  3. Matrix-geometric Solutions in Stochastic Models- An algorithmic approach, M.F. Neuts, Dover Publications, 1995 (originally published by Johns Hopkins University Press, 1981).

Course Learning Objectives: Upon completion of this course, the students will:

• Recall, understand and apply appropriate knowledge gained from prerequisite courses (IE PEO 1).
• Explain the needs for stochastic models (IE PEOs 2, 3, 4, 5).
• Explain the importance of Markov chains (IE PEOs 2, 3, 4, 5).
• Apply basic queuing models in practice (IE PEOs 4, 5).
• Interpret the performance measures (IE PEOs 2, 4, 5).
• Demonstrate the use of MATLAB/EXCEL (or some operations research software) (IE PEOs 4, 5).
• Use the tools learned in this course in practice (IE PEOs 3, 4, 5).
• Gain the relationship of knowledge from this course to subsequent courses (IE PEOs 3, 4, 5).

Prerequisites by Topics:

• Probability and Conditional probability

• Independence

• Random variables and measures of random variables

• Poison and exponential distributions

• Matrices

• Basic operations with matrices

• Solving systems of linear equations

Topics Covered:

• Introduction and history to stochastic modeling
• Review of probability and matrix concepts
• Introduction to Markov chains
• Applications of Markov chains
• Computation and interpretation of steady-state probabilities of Markov chains
• Discrete and continuous time phase type distributions
• Introduction to queuing theory
• Birth-and-death processes
• Basic queuing models involving Poisson arrivals and exponential services 
• Advanced queuing models  
• Introduction to Simulation  
• Exams, Quizzes

Class Schedule:  240 minutes per week

Computer Usage: MATLAB/EXCEL will be used extensively.

Laboratory Projects: Several mini-projects and a detailed (group) term project.

Relationship to Professional Component: Engineering Science: Four credit hours

Prepared by: Srinivas R. Chakravarthy                                                       Date: August 4, 2000