Industrial Engineering Distinguished Seminar Series - Professor Robert D. Foley

Event Date: April 17, 2012
Time: 4:30pm
Location: Fu Room - Potter, Room 234

Professor Robert D. Foley

Industrial and Systems Engineering

Georgia Institute of Technology

 

Rare Events and Markov Chains:  A Constructive Large Deviations Theory
 

ABSTRACT

Rare events are events that have small probabilities of occurring.  Even though the probabilities are small, rare events can be important.  Rare events might correspond to queue lengths exploding or buffers overflowing in a manufacturing system.  Even though these ``large deviations'' are rare, it can be important to know just how rare.

Consider a system that can be modeled as a Markov process and has a stationary distribution that cannot be computed explicitly.  We are developing methods for deriving exact asymptotic expressions of the stationary distribution.  Furthermore, the methodology gives insight into how these large deviations develop, which would allow system designers to know how to improve the system.

During the seminar, I will illustrate the methodology by analyzing a particular queuing system.  I will also point out how some of the ideas in this research can be used in rare event simulation.

AUTHOR BIO

Robert D. Foley is a Professor of Industrial and Systems Engineering at Georgia Tech.  His research interests are in applied probability including material handling and queuing systems.  He has been a co-author on a series of papers attempting to develop a constructive theory of large deviations for some of the Markov models that often arise in Operations Research.  He received his PhD and MS from the Industrial and Operations Engineering Department of The University of Michigan.