IEN-526, Systems Modeling VI

2001 Catalog Data: IEN-526, Systems Modeling VI: Advanced Stochastic Models

Credits: 4-0-4

This is a continuation of IEN-422. Advanced topics in Stochastic Models; Review of elementary Stochastic Models and Matrix Algebra; Introduction to computational (or algorithmic) probability, Advanced Markov models including semi-Markov arrivals and services, M/G/1 and GI/M/1 type queuing models, GI/G/s queues, approximation to various performance measures, queuing networks, and simulation of various queuing systems.

Prerequisites: Senior I Standing

Corequisities:  None

Textbooks: 1. Fundamentals of Queueing Theory, D. Gross and C.M. Harris, John Wiley and sons, Second Edition. 2. Supplementary class notes.

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).

4. Introduction to Queueing Networks, E. Gelenbe and G. Pujolle, John Wiley and sons, 1999.

5. Queueing Systems, Vols I and II, L. Kleinrock, John Wiley and Sons, 1976.

Course Learning Objectives: Upon completion of this course, the students should be able to:

• Recall, understand and apply appropriate knowledge gained from prerequisite courses [IE PEO’s:1]
• Realize the need for advanced stochastic models [IE PEO’s: 2,3,4,5]
• Recognize the importance of Markov chains [IE PEO’s: 2,3,4,5]
• Recognize the importance of semi-Markov processes [IE PEO’s: 2,3,4,5]
• Apply advanced queuing models in practice [IE PEO’s: 4,5]
• Get insight into interpretation of performance measures [IE PEO’s: 2,4,5]
• Use MATLAB/EXCEL (or some operations research software) extensively and perform rigorous data analysis and interpretation on various queuing models [IE PEO’s: 4,5]
• Use the tools learned in this course in practice [IE PEO’s: 3,4,5]
• Gain the relevance of knowledge from this course to subsequent courses [IE PEO’s: 3,4,5]

Prerequisites By Topics:

• Probability and Conditional probability
• Independence
• Random variables and measures of random variables
• Poisson, exponential distributions, and phase type distributions
• Matrices
• Basic operations with matrices
• Solving systems of linear equations
• Basic concepts in Markov chains and Markov processes
• Elementary queuing models.

Topics Covered:

• Introduction and history to advanced stochastic modeling
• Review of probability and matrix concepts
• Review of Markov chains and applications of Markov chains
• Review of discrete and continuous time phase type distributions
• Review of basic queuing models
• Analysis of advanced queuing models using embedded Markov chains methods
• Introduction to semi-Markov processes and their usefulness in queuing models
• Queuing networks with Poisson arrivals and exponential services
• Simulation of advanced queuing models
• Exams, Quizzes

Class and Laboratory Schedule:  240 minutes per week

Computer Usage: MATLAB/EXCEL will be used extensively.

Laboratory projects: Several miniprojects, report writing, and a detailed (group) term project.

Contribution to Meeting Professional Component: Required course

Relationship to Professional Component: Engineering Science: Four credit hours

Prepared By: Srinivas R. Chakravarthy                                                  Date: February 4, 2001