SPRING 2009

AMS 550 Operations Research: Stochastic Models

Mondays and Fridays 12:50 – 2:10 PM, MEVLVILLE LIBR E4315

 

Professor Eugene A. Feinberg, Office: 1-110 Math Tower

632-7189, Eugene.Feinberg@sunysb.edu, http://www.ams.sunysb.edu/~feinberg

Office Hours: Mondays and Fridays 11:00 – 12:00 and by appointment.

TA: TBA: TA’s office hours: TBA

Students should use the Blackboard for course information including assignments.

Textbook: S.M. Ross, Introduction to Probability Models.  Ninth Edition, Academic Press, 2007.

This course is a non-measure theoretic introduction to stochastic processes used in operations research, electrical engineering, and statistics.

Prerequisites: Elementary probability (AMS507 or AMS310), at least two semesters of undergraduate calculus (AMS504 is useful but not required).

Course outline

1.     Introduction and Preliminaries

2.     Discrete-time Markov Chains

3.     The Poisson Process and Related Topics

4.     Continuous-time Markov Chains

5.     Renewal Theory and Its Applications

6.     Elements of Queueing Theory

7.     Martingales, Brownian Motion, and Stochastic Integration with applications to Option Pricing

Tentative test dates:

1st midterm: February 23

2nd midterm: March 30

Final: May 18, 2:00 – 4:30 PM

 

Grading policy: 20% Home work average, 20% 1st Midterm, 25% 2nd Midterm, 35% Final.

There will be weekly homework assignments. They will be posted on the web and will be due by the beginning on the class on the date indicated in the assignment. Two lowest homework grades will be disregarded.  Late homework assignments will not be accepted.

Some relevant textbooks:

V. Kulkarni, Modeling and Analysis of Stochastic Systems, CRC Press, 1995.

G.F. Lawler, Introduction to Stochastic Processes, Chapman & Hall, 1995.

S.M. Ross, Stochastic Processes.  Second Edition, Wiley, 1996.

S.M. Ross, Applied Probability Models with Optimization Applications, Holden-Day, San Francisco, 1970.

H.M. Taylor and S. Karlin, An Introduction to Stochastic Modeling.  Third Edition, Academic Press, 1998.

H. Tijms, Stochastic Models, Wiley, New York, 1994.

H. Tijms, A First Course in Stochastic Models, Wiley, 2003.

R.W. Wolf, Stochastic Modeling and the Theory of Queues, Prentice Hall, 1989.

If you have a physical, psychiatric/emotional, medical or learning disability that may impact on your ability to carry out assigned course work, I urge you to contact the staff in the Disabled Student Services office (DSS), room 133 Humanities, 632-6748/TDD. DSS will review your concerns and determine, with you, what accommodations are necessary and appropriate. All information and documentation on disability is confidential.