*********************************
There is now a CONTENT FREEZE for Mercury while we switch to a new platform. It began on Friday, March 10 at 6pm and will end on Wednesday, March 15 at noon. No new content can be created during this time, but all material in the system as of the beginning of the freeze will be migrated to the new platform, including users and groups. Functionally the new site is identical to the old one. webteam@gatech.edu
*********************************
TITLE: Rare events and asymptotics for the stationary distribution of Markov chains
SPEAKER: Dr. Robert Foley
ABSTRACT:
Markov processes are frequently used to model complex systems in a wide variety of areas including queueing and telecommunications. Often the Markov process has a stationary distribution $pi$ that cannot be explicitly determined. If $pi(x)$ is small, then state $x$ is rarely visited. Even though a state is visited infrequently, the state may represent an important event such as a failed system or an excessively large number of packets in a buffer in a telecommunications network. In well-designed systems, such events should be rare, but it can be critical to know how rare. Even attempting to estimate $pi(x)$ through simulation is fraught with difficulty when state $x$ is rarely visited. Consider a sequence of states $x_ell$ with $pi(x_ell) to 0$. Under certain conditions, we can derive exact asymptotic expressions for $pi(x_ell)$. That is, let $x_ell$ be a sequence of states with $pi(x_ell) to 0$. We can find $a_ell$ where $pi(x_ell)/a_ell to 1$. This approach can even handle situations in which the fluid limit of the large deviation path is not a straight line. We illustrate the approach on a queueing system.
