Standard Article

Aggregation and Lumping of DTMCs

  1. Marlin U. Thomas

Published Online: 15 JUN 2010

DOI: 10.1002/9780470400531.eorms0013

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Thomas, M. U. 2010. Aggregation and Lumping of DTMCs. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. Air Force Institute of Technology, Department of Electrical and Computer Engineering, Wright-Patterson AFB, Ohio

Publication History

  1. Published Online: 15 JUN 2010

Abstract

Under certain conditions the state space of a discrete time Markov chain (DTMC) can be partitioned into subsets of states called lumpings, each of which can be treated as a single state of a smaller Markov chain. Such a chain is said to be “lumpable” and this article provides an overview of the conditions and methods for examining aggregated chains for lumpability.

Keywords:

  • lumpability;
  • state aggregation;
  • Markov chains;
  • merged states;
  • aggregation