Standard Article

Transient Behavior of CTMCs

  1. Salvatore Distefano1,
  2. Kishor S. Trivedi2

Published Online: 15 FEB 2011

DOI: 10.1002/9780470400531.eorms0916

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Distefano, S. and Trivedi, K. S. 2011. Transient Behavior of CTMCs. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. 1

    University of Messina, Department of Mathematics, Messina, Italy

  2. 2

    Duke University, Department of Electrical and Computer Engineering, Durham, North Carolina

Publication History

  1. Published Online: 15 FEB 2011

Abstract

Since their first specification, Markov models have been widely used for modeling many kinds of systems, in different environments, in application fields, and with different purposes. The success of the formalism of Markov chains is due to the simplicity and the effectiveness in (analytically) evaluating discrete state-space systems, providing both transient and steady-state analyses. But the Markovian assumption often limits the applicability of Markov chains. This limitation can be overcome by nonhomogeneous Markov chains and phase type distributions, allowing us to model more general behaviors. This further enhances the importance and the effectiveness of Markov chains and related formalisms. In this article, we focus on the transient behavior of Markov models, providing an overview of their solution techniques.

Keywords:

  • homogeneous and nonhomogeneous Markov chains;
  • uniformization;
  • piecewise approximation;
  • phase type expansion