Rare events & asymptotics for stationary distribution of Markov chains

Event Details
  • Date/Time:
    • Tuesday November 10, 2009
      10:00 am - 11:00 am
  • Location: IC 109
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    $0.00
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Contact
Anita Race
H. Milton Stewart School of Industrial and Systems Engineering
Contact Anita Race
Summaries

Summary Sentence: Rare events & asymptotics for stationary distribution of Markov chains

Full Summary: Rare events and asymptotics for the stationary distribution of Markov chains

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.

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H. Milton Stewart School of Industrial and Systems Engineering (ISYE)

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Categories
Seminar/Lecture/Colloquium
Keywords
Markov
Status
  • Created By: Anita Race
  • Workflow Status: Draft
  • Created On: Feb 16, 2010 - 9:48am
  • Last Updated: Oct 7, 2016 - 9:50pm