Stochastic Models in Operations Research
Course Syllabus
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syllabus in pdf format.
Course Description
This course is a systematic study of important classes of stochastic models in
operations research. Topics include renewal theory, Markov chains, semi-Markov
processes, queueing models, stochastic ordering concepts, Brownian motion, and
(if time permits) stochastic scheduling.
Office Hours
Wednesdays, 4:00pm--6:00pm
JSOM 3.201
TAs
Meng Li
Office: JSOM 3.205
Office Hours: Tuesdays, 4:00pm--6:00pm
Telephone: 972-883-2382
E-mail: meng.li@utdallas.edu
Text
Stochastic Processes, by Sheldon M. Ross, 2nd Edition, John Wiley & Sons, 1996.
Prerequisites
OPRE 7310; or consent of the instructor.
Grading Scheme
Homework: 30%
Final: 40%
Presentation: 30%
Course Outline
Chapters 3, 4, 5, and parts of 6, 7, 8. (Other related materials will be
announced in class.)
- Poisson (Review) and Renewal Processes
- Basic Limiting Properties
- Key Renewal Theorem and Applications
- Renewal Reward Processes
- Regenerative Processes and Applications
- Markov Chains
- Motivating Examples
- Classification of States
- Ergodic Theorem
- Some Applications
- Continuous-Time Markov Chains
- Kolmogorov Differential Equations
- Uniformization
- Limiting Results
- Time Reversibility
- Semi-Markov Processes
- Steady-State Results
- Generalized Semi-Markov Processes
- Queueing Applications
- Queueing Theory
- L = lamda W
- Poisson Arrivals See Time Averages --- PASTA
- Sample-Path Analysis of Single-Server Queues
- Stochastic Ordering Concepts
- Stochastic Order (First-Order Stochastic Dominance)
- Coupling Methods
- Variability Order (or Higher-Order Stochastic Dominance)
- Hazard Rate Order
- Likelihood Ratio Order
- Brownian Motion
- Random-Walk Construction of Brownian Motion
- Basic Properties
- Variations of Brownian Motion
- Stochastic Differential Equations
- Applications to Options Pricing and New-Product Diffusion
Papers Suggested for Presentation
Assignments