Geodesic
The method of regenerating systems modeling
Matematičeskoe modelirovanie, Tome 30 (2018) no. 6, pp. 134-144.

Voir la notice de l'article provenant de la source Math-Net.Ru

The article tells about a kind of algorithm of phase consolidation for regenerating systems analysis. The theorem on the stay time in a subset of continuous states is presented and proven. A modeling example of the maintenance devices with devaluate failures using this theorem and the method of trajectories is presented. A modeling results comparison of the method of trajectories and of a known from the literature method, based on the solution of Markov renewal equations, is given. The comparison has proven the accuracy of the proposed modeling method.
Keywords: semi-Markov system, method of trajectories, devaluate failures, stationary distribution, distribution function, recovery process.
Mots-clés : algorithm of phase consolidation 
@article{MM_2018_30_6_a7,
     author = {M. V. Zamoryonov and V. Ya. Kopp and D. V. Zamoryonova},
     title = {The method of regenerating systems modeling},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {134--144},
     publisher = {mathdoc},
     volume = {30},
     number = {6},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2018_30_6_a7/}
}
TY  - JOUR
AU  - M. V. Zamoryonov
AU  - V. Ya. Kopp
AU  - D. V. Zamoryonova
TI  - The method of regenerating systems modeling
JO  - Matematičeskoe modelirovanie
PY  - 2018
SP  - 134
EP  - 144
VL  - 30
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2018_30_6_a7/
LA  - ru
ID  - MM_2018_30_6_a7
ER  - 
%0 Journal Article
%A M. V. Zamoryonov
%A V. Ya. Kopp
%A D. V. Zamoryonova
%T The method of regenerating systems modeling
%J Matematičeskoe modelirovanie
%D 2018
%P 134-144
%V 30
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2018_30_6_a7/
%G ru
%F MM_2018_30_6_a7
M. V. Zamoryonov; V. Ya. Kopp; D. V. Zamoryonova. The method of regenerating systems modeling. Matematičeskoe modelirovanie, Tome 30 (2018) no. 6, pp. 134-144. http://geodesic.mathdoc.fr/item/MM_2018_30_6_a7/

[1] Korolyuk V. S., Stokhasticheskie modeli sistem, ed. A.F. Turbin, Nauk. dumka, Kiev, 1989, 208 pp.

[2] Brodi S. M., Vlasenko O. N., Marchenko B. G., Raschet i planirovanie ispyitaniy sistem na nadezhnost, Naukova dumka, Kiev, 1970, 192 pp.

[3] Korolyuk V. S., Turbin A. F., Protsessy markovskogo vosstanovleniia v zadachakh nadezhnosti sistem, Nauk. dumka, Kiev, 1982, 236 pp.

[4] V.S. Korolyuk, A.F. Turbin, Polumarkovskie protsessyi i ikh prilozheniia, Nauk. dumka, Kiev, 1976, 181 pp.

[5] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsiy i funktsionalnogo analiza, Uchebnik dlia un-tov, 6-e izd., ispr., Nauka, M., 1989, 623 pp.

[6] Mikhlin S. G., Integralnye uravneniia i ikh prilozheniia k nekotorym problemam mehaniki, matematicheskoy fiziki i tehniki, Gostehizdat, M., 1949, 380 pp.

[7] V.Ya. Kopp, Yu. E. Obzherin, A.I. Peschanskiy, Modelirovanie avtomatizirovannyikh liniy, Monografiia, Izd-vo SevNTU, Sevastopol, 2006, 240 pp.

[8] Obzherin Yu.E., Boyko Ye.G., Semi-Markov Models. Control of Restorable Systems with Latent Failures, Elsevier, Academic press, USA, 2015, 214 pp. | MR | Zbl

[9] Peschansky A. I., Semi-Markov Models of One-Server Loss Queues with Recurrent Input, LAP LAMPERT Academic Publishing, Germany, 2013, 138 pp.

[10] Kopp V.Ya., Obzherin Yu.E., Peschanskiy A. I., Stokhasticheskie modeli avtomatizirovannyikh proizvodstvennyikh sistem s vremennym rezervirovaniem, Izd-vo SevNTU, Sevastopol, 2000, 284 pp.

[11] V.Ya. Kopp, M.V. Zamoryonov, Yu.E. Obzherin, M.Yu. Larin, “Ispolzovanie metoda traektoriy dlia postroeniia polumarkovskoy modeli struktury «tekhnologicheskaia iacheika–nakopitel»”, Nauch.-tekhn. vedom. SPbGPU. Informatika. Telekommunikatsii. Upravlenie, 2016, no. 3(247), 23–34

[12] Bayhelt F., Franken P., Nadezhnost i tekhnicheskoe obsluzhivanie. Matematicheskiy podhod, Radio i sviaz, M., 1988, 392 pp.

[13] Koks D. R., Smit V. L., Teoriia vosstanovleniia, ed. Ju.K. Beljaev, Sov. radio, M., 1967, 301 pp.

[14] Feller V., Vvedenie v teoriiu veroiatnostei i ee prilozheniia, Mir, M., 1978, 752 pp.

[15] Kopp V. Ya., Modelirovanie avtomatizirovannyikh proizvodstvennykh sistem, SevNTU, Sevastopol, 2012, 700 pp.