Monotonicity and comparison results for nonnegative dynamic systems. Part II: Continuous-time case

Nico M. van Dijk; Karel Sladký

Kybernetika (2006)

  • Volume: 42, Issue: 2, page 161-180
  • ISSN: 0023-5954

Abstract

top
This second Part II, which follows a first Part I for the discrete-time case (see [DijkSl1]), deals with monotonicity and comparison results, as generalization of the pure stochastic case, for stochastic dynamic systems with arbitrary nonnegative generators in the continuous-time case. In contrast with the discrete-time case the generalization is no longer straightforward. A discrete-time transformation will therefore be developed first. Next, results from Part I can be adopted. The conditions, the technicalities and the results will be studied in detail for a reliability application that initiated the research. This concerns a reliability network with dependent components that can breakdown. A secure analytic performance bound is obtained.

How to cite

top

Dijk, Nico M. van, and Sladký, Karel. "Monotonicity and comparison results for nonnegative dynamic systems. Part II: Continuous-time case." Kybernetika 42.2 (2006): 161-180. <http://eudml.org/doc/33799>.

@article{Dijk2006,
abstract = {This second Part II, which follows a first Part I for the discrete-time case (see [DijkSl1]), deals with monotonicity and comparison results, as generalization of the pure stochastic case, for stochastic dynamic systems with arbitrary nonnegative generators in the continuous-time case. In contrast with the discrete-time case the generalization is no longer straightforward. A discrete-time transformation will therefore be developed first. Next, results from Part I can be adopted. The conditions, the technicalities and the results will be studied in detail for a reliability application that initiated the research. This concerns a reliability network with dependent components that can breakdown. A secure analytic performance bound is obtained.},
author = {Dijk, Nico M. van, Sladký, Karel},
journal = {Kybernetika},
keywords = {Markov chains; monotonicity; nonnegative matrices; Markov chain; monotonicity; nonnegative matrix},
language = {eng},
number = {2},
pages = {161-180},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Monotonicity and comparison results for nonnegative dynamic systems. Part II: Continuous-time case},
url = {http://eudml.org/doc/33799},
volume = {42},
year = {2006},
}

TY - JOUR
AU - Dijk, Nico M. van
AU - Sladký, Karel
TI - Monotonicity and comparison results for nonnegative dynamic systems. Part II: Continuous-time case
JO - Kybernetika
PY - 2006
PB - Institute of Information Theory and Automation AS CR
VL - 42
IS - 2
SP - 161
EP - 180
AB - This second Part II, which follows a first Part I for the discrete-time case (see [DijkSl1]), deals with monotonicity and comparison results, as generalization of the pure stochastic case, for stochastic dynamic systems with arbitrary nonnegative generators in the continuous-time case. In contrast with the discrete-time case the generalization is no longer straightforward. A discrete-time transformation will therefore be developed first. Next, results from Part I can be adopted. The conditions, the technicalities and the results will be studied in detail for a reliability application that initiated the research. This concerns a reliability network with dependent components that can breakdown. A secure analytic performance bound is obtained.
LA - eng
KW - Markov chains; monotonicity; nonnegative matrices; Markov chain; monotonicity; nonnegative matrix
UR - http://eudml.org/doc/33799
ER -

References

top
  1. Berman A., Plemmons R. J., Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York 1979 Zbl0815.15016MR0544666
  2. Dijk N. M. van, Queuing Networks and Product Forms, Wiley, New York 1993 MR1266845
  3. Dijk N. M. van, Sladký K., Monotonicity and comparison results for nonnegative dynamic systems, Part I: Discrete-time case. Kybernetika 42 (2006), 37–56 MR2208519
  4. Dijk N. M. van, Taylor P. G., On strong stochastic comparison for steady state measures of Markov chains with a performability application, Oper. Res. 36 (2003), 3027–3030 
  5. Gross D., Miller D. R., 10.1287/opre.32.2.343, Oper. Res. 32 (1984), 343–361 (1984) MR0747747DOI10.1287/opre.32.2.343
  6. Keilson J., Kester A., 10.1016/0304-4149(77)90033-3, Stoch. Process. Appl. 5 (1977), 231–241 (1977) Zbl0367.60078MR0458596DOI10.1016/0304-4149(77)90033-3
  7. Massey W. A., 10.1287/moor.12.2.350, Math. Oper. Res. 12 (1987), 350–367 (1987) MR0888982DOI10.1287/moor.12.2.350
  8. Melamed B., Yadin N., 10.1287/opre.32.4.926, Oper. Res. 32 (1984), 926–943 (1984) Zbl0546.90038MR0865588DOI10.1287/opre.32.4.926
  9. Stoyan D., Comparison Methods for Queues and Other Stochastic Models, Wiley, New York 1983 Zbl0536.60085MR0754339

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.