# Stochastic Models in Operations Research

## Course Syllabus

Click here to get a copy of the syllabus in postscript format.
### Course Objective

A study of basic stochastic processes that arise
frequently in the modeling of Operations-Research problems. Each student is
to select and study a research paper, for presentation at the end of the
semester. The topic of the selected paper should be related to the material
in this course. A list of suggested papers will be distributed later.
### Office Hours

Mondays, 3:00pm--5:00pm

Jonsson 4.912
### TAs

To be announced.
### Text

*Stochastic Processes*, by Sheldon M. Ross, 2nd Edition, John Wiley & Sons, 1996.
### Prerequisites

OPRE 6330; or consent of the instructor.
### Grading Scheme

Homework: 30%

Final: 35%

Presentation: 35%

### 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