# Stochastic Models in Operations Research

## Course Syllabus

Click here to get a copy of the
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: [email protected]
### 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