Regular periodic dynamic resource networks
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 3, Tome 192 (2021), pp. 117-124.

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

A model of resource flow distribution in a dynamic periodic resource network is examined. Methods for finding the limiting state (distribution) of a resource in a dynamic resource network are developed. It is proved that for regular periodic dynamical networks, the limit state exists and is unique and can be found by methods developed for dynamic networks.
Keywords: dynamic network, regular resource network, resource flow, flow distribution, threshold value, limit state.
@article{INTO_2021_192_a12,
     author = {V. A. Skorokhodov and D. O. Sviridkin},
     title = {Regular periodic dynamic resource networks},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {117--124},
     publisher = {mathdoc},
     volume = {192},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_192_a12/}
}
TY  - JOUR
AU  - V. A. Skorokhodov
AU  - D. O. Sviridkin
TI  - Regular periodic dynamic resource networks
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2021
SP  - 117
EP  - 124
VL  - 192
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2021_192_a12/
LA  - ru
ID  - INTO_2021_192_a12
ER  - 
%0 Journal Article
%A V. A. Skorokhodov
%A D. O. Sviridkin
%T Regular periodic dynamic resource networks
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2021
%P 117-124
%V 192
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2021_192_a12/
%G ru
%F INTO_2021_192_a12
V. A. Skorokhodov; D. O. Sviridkin. Regular periodic dynamic resource networks. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 3, Tome 192 (2021), pp. 117-124. http://geodesic.mathdoc.fr/item/INTO_2021_192_a12/

[1] Gantmakher F. R., Teoriya matrits, Fizmatlit, M., 2010

[2] Erusalimskii Ya. M., Skorokhodov V. A., Kuzminova M. V., Petrosyan A. G., Grafy s nestandartnoi dostizhimostyu: zadachi, prilozheniya, YuFU, Rostov-na-Donu, 2009

[3] Zhilyakova L. Yu., “Nesimmetrichnye resursnye seti. I. Protsessy stabilizatsii pri malykh resursakh”, Avtomat. telemekh., 4 (2011), 133–143

[4] Zhilyakova L. Yu., “Ergodicheskie tsiklicheskie resursnye seti. I. Kolebaniya i ravnovesnye sostoyaniya pri malykh resursakh”, Upravl. bol. sist., 43 (2013), 34–54

[5] Zhilyakova L. Yu., “Ergodicheskie tsiklicheskie resursnye seti. II. Bolshie resursy”, Upravl. bol. sist., 45 (2013), 6–29

[6] Kuznetsov O. P., Zhilyakova L. Yu., “Dvustoronnie resursnye seti — novaya potokovaya model”, Dokl. RAN., 433:5 (2010), 609–612

[7] Kuzminova M. V., “Periodicheskie dinamicheskie grafy. Zadacha o maksimalnom potoke”, Izv. vuzov. Sev.-Kav. reg. Estestv. nauki., 5 (2008), 16–20

[8] Novikov F. A., Diskretnaya matematika, Piter, SPb., 2013

[9] Skorokhodov V. A., Abdulrakhman Kh., “Dinamicheskie resursnye seti. Sluchai malogo resursa”, Vestn. VGU. Fiz. Mat., 4 (2018), 186–194

[10] Skorokhodov V. A., “Potoki v setyakh s menyayuscheisya dlitelnostyu prokhozhdeniya”, Izv. vuzov. Sev.-Kav. reg. Estestv. nauki., 1 (2011), 21–26

[11] Skorokhodov V. A., “Ustoichivost i statsionarnoe raspredelenie na grafakh s nestandartnoi dostizhimostyu”, Izv. vuzov. Sev.-Kav. reg. Estestv. nauki., 4 (2007), 17–21

[12] Skorokhodov V. A., “Zadacha nakhozhdeniya porogovogo znacheniya v ergodicheskoi resursnoi seti”, Upravl. bol. sist., 63 (2016), 6–23

[13] Aronson J. E., “A survey of dynamic network flows”, Ann. Oper. Res., 20 (1989), 1–66

[14] Erzin A. I., Takhonov I. I., “The problem of finding of balanced flow”, J. Appl. Industr. Math., 8:3 (23) (2005), 58–68

[15] Fonoberova M., Lozovanu D., “The maximum flow in dynamic networks”, Comput. Sci. J. Moldova., 3:36 (2004), 387–396

[16] Fonoberova M., Lozovanu D., “The minimum cost multicommodity flow problem in dynamic networks and an algorithm for its solving”, Comput. Sci. J. Moldova., 1:37 (2005), 29–36

[17] Ford L. R., Fulkerson D. R., “Constructing maximal dynamic flows from static flows”, Oper. Res., 6 (1958), 419–433

[18] Klinz B. Woeginger C., “One, two, three, many, or: complexity aspects of dynamic network flows with dedicated arcs”, Oper. Res. Lett., 22 (1998), 119–127

[19] Kuznetsov O. P., “Nonsymmetric resource networks. The study of limit states”, Manag. Prod. Eng. Rev., 2:3 (2011), 33–39

[20] Orlin J. B., “Maximum-throughput dynamic network flows”, Math. Progr., 27 (1983), 214–231

[21] Skorokhodov V. A., Chebotareva A. S., “The Maximum Flow Problem in a Network with Special Conditions of Flow Distribution”, J. Appl. Industr. Math., 9:3 (2015), 435–446