AUT LibraryAUT
View Item 
  •   Open Research
  • AUT Faculties
  • Faculty of Design and Creative Technologies (Te Ara Auaha)
  • School of Engineering, Computer and Mathematical Sciences - Te Kura Mātai Pūhanga, Rorohiko, Pāngarau
  • View Item
  •   Open Research
  • AUT Faculties
  • Faculty of Design and Creative Technologies (Te Ara Auaha)
  • School of Engineering, Computer and Mathematical Sciences - Te Kura Mātai Pūhanga, Rorohiko, Pāngarau
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Accurate calculations of Stationary Distributions and Mean First Passage Times in Markov Renewal Processes and Markov Chains

Hunter, J
Thumbnail
View/Open
spma-2016 Hunter-0015.pdf (520.9Kb)
Permanent link
http://hdl.handle.net/10292/9642
Metadata
Show full metadata
Abstract
This article describes an accurate procedure for computing the mean first passage times of a finite irreducible Markov chain and a Markov renewal process. The method is a refinement to the Kohlas, Zeit fur Oper Res, 30,197-207, (1986) procedure. The technique is numerically stable in that it doesn't involve subtractions. Algebraic expressions for the special cases of one, two, three and four states are derived. A consequence of the procedure is that the stationary distribution of the embedded Markov chain does not need to be derived in advance but can be found accurately from the derived mean first passage times. MatLab is utilized to carry out the computations, using some test problems from the literature.
Keywords
Markov chain; Markov renewal process; Stationary distribution; Mean first passage times
Date
March 18, 2016
Source
Special Matrices, vol.4(1), pp.151 - 175 (25)
Item Type
Journal Article
Publisher
De Gruyter Open
DOI
10.1515/spma-2016-0016
Publisher's Version
http://www.degruyter.com/view/j/spma.2016.4.issue-1/spma-2016-0015/spma-2016-0015.xml?format=INT
Rights Statement
© 2016 J. J. Hunter, published by De Gruyter Open. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.

Contact Us
  • Admin

Hosted by Tuwhera, an initiative of the Auckland University of Technology Library

 

 

Browse

Open ResearchTitlesAuthorsDateSchool of Engineering, Computer and Mathematical Sciences - Te Kura Mātai Pūhanga, Rorohiko, PāngarauTitlesAuthorsDate

Alternative metrics

 

Statistics

For this itemFor all Open Research

Share

 
Follow @AUT_SC

Contact Us
  • Admin

Hosted by Tuwhera, an initiative of the Auckland University of Technology Library