| Title:
|
Monotonicity and comparison results for nonnegative dynamic systems. Part II: Continuous-time case (English) |
| Author:
|
Dijk, Nico M. van |
| Author:
|
Sladký, Karel |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
42 |
| Issue:
|
2 |
| Year:
|
2006 |
| Pages:
|
161-180 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Markov chains |
| Keyword:
|
monotonicity |
| Keyword:
|
nonnegative matrices |
| MSC:
|
39A10 |
| MSC:
|
60J27 |
| MSC:
|
60K10 |
| MSC:
|
90A16 |
| MSC:
|
91B62 |
| idZBL:
|
Zbl 1249.60169 |
| idMR:
|
MR2241783 |
| . |
| Date available:
|
2009-09-24T20:15:05Z |
| Last updated:
|
2015-03-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135707 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/135698 |
| . |
| Reference:
|
[1] Berman A., Plemmons R. J.: Nonnegative Matrices in the Mathematical Sciences.Academic Press, New York 1979 Zbl 0815.15016, MR 0544666 |
| Reference:
|
[2] Dijk N. M. van: Queuing Networks and Product Forms.Wiley, New York 1993 MR 1266845 |
| Reference:
|
[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 MR 2208519 |
| Reference:
|
[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 |
| Reference:
|
[5] Gross D., Miller D. R.: The randomization technique as a modelling tool and solution procedure over discrete state Markov processes.Oper. Res. 32 (1984), 343–361 MR 0747747, 10.1287/opre.32.2.343 |
| Reference:
|
[6] Keilson J., Kester A.: Monotone matrices and monotone Markov processes.Stoch. Process. Appl. 5 (1977), 231–241 Zbl 0367.60078, MR 0458596, 10.1016/0304-4149(77)90033-3 |
| Reference:
|
[7] Massey W. A.: Stochastic ordering for Markov processes on partially ordered spaces.Math. Oper. Res. 12 (1987), 350–367 MR 0888982, 10.1287/moor.12.2.350 |
| Reference:
|
[8] Melamed B., Yadin N.: Randomization procedures in the computation of cumulative-time distributions over discrete state Markov processes.Oper. Res. 32 (1984), 926–943 Zbl 0546.90038, MR 0865588, 10.1287/opre.32.4.926 |
| Reference:
|
[9] Stoyan D.: Comparison Methods for Queues and Other Stochastic Models.Wiley, New York 1983 Zbl 0536.60085, MR 0754339 |
| . |
