Geodesic
Resource networks with dynamic arc durations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 226 (2023), pp. 108-119.

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In this paper, we study a model for the distribution of a resource flow in a resource network with dynamic durations of passage along arcs. A feature of such networks is the dependence of the duration of passage along arcs on discrete time. This feature significantly affects the process of redistribution of resources. It is shown that in the networks considered, the total resource is preserved, while the total resource can be distributed not only over vertices, but also over some arcs. A relation is obtained for the conservation of the total resource in the network. A method for finding the threshold value in a resource network with dynamic durations of passage along arcs is proposed. It is shown that if the total resource is not less than the threshold value in the original network, then in a network with dynamic durations of passage along arcs, there is a unique limiting flow.
Keywords: dynamic network, ergodic resource network, resource flow, flow distribution, threshold value, resource network initial state. 
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V. A. Skorokhodov; I. M. Erusalimskyi; H. N. Abdulrahman. Resource networks with dynamic arc durations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 226 (2023), pp. 108-119. http://geodesic.mathdoc.fr/item/INTO_2023_226_a10/

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

[2] Zhilyakova L. Yu., “Nesimmetrichnye resursnye seti. I. Protsessy stabilizatsii pri malykh resursakh”, Avtomat. telemekh., 2011, no. 4, 133–143 | MR | Zbl

[3] Zhilyakova L. Yu., “Ergodicheskie tsiklicheskie resursnye seti. I. Kolebaniya i ravnovesnye sostoyaniya pri malykh resursakh”, Upravlenie bolshimi sistemami., 2013, no. 43, 34–54

[4] Zhilyakova L. Yu., “Ergodicheskie tsiklicheskie resursnye seti. II. Bolshie resursy”, Upravlenie bolshimi sistemami., 2013, no. 45, 6–29

[5] Zhilyakova L. Yu., Chaplinskaya N. V., “Issledovanie polnykh odnorodnykh resursnykh setei s «zhadnymi» vershinami”, Upravlenie bolshimi sistemami., 2021, no. 89, 5–44 | MR

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

[7] Kuzminova M. V., “Periodicheskie dinamicheskie grafy. Zadacha o maksimalnom potoke”, Izv. vuzov. Sev.-Kav. reg. Estestv. nauki., 2008, no. 5, 16–20

[8] Skorokhodov V. A., “Potoki v setyakh s menyayuscheisya dlitelnostyu prokhozhdeniya”, Izv. vuzov. Sev.-Kav. reg. Estestv. nauki., 2011, no. 1, 21–26

[9] Skorokhodov V. A., “Potoki v obobschennykh setyakh so svyazannymi dugami”, Model. anal. inform. sist., 19:2 (2012), 41–52

[10] Skorokhodov V. A., “Zadacha nakhozhdeniya porogovogo znacheniya v ergodicheskoi resursnoi seti”, Upravlenie bolshimi sistemami., 2016, no. 63, 6–23

[11] Skorokhodov V. A., Abdulrakhman Kh., “Dinamicheskie resursnye seti. Sluchai malogo resursa”, Vestn. VGU. Fiz. Mat., 2018, no. 4, 186–194

[12] Skorokhodov V. A., Sviridkin D. O., “Potoki v silno regulyarnykh periodicheskikh dinamicheskikh resursnykh setyakh”, Vestn. Udmurt. un-ta. Mat. Mekh. Kompyut. nauki., 31:3 (2021), 458–470 | MR | Zbl

[13] Chaplinskaya N. V., “Issledovanie polnykh odnorodnykh resursnykh setei s «zhadnymi» vershinami: zona «dostatochno bolshogo resursa»”, Upravlenie bolshimi sistemami., 2021, no. 90, 49–66

[14] Chaplinskaya N. V., “Issledovanie ergodicheskikh neodnorodnykh resursnykh setei s «zhadnymi» vershinami”, Upravlenie bolshimi sistemami., 2021, no. 93, 5–50 | MR

[15] Aronson J. E., “A survey of dynamic network flows”, Ann. Oper. Res., 1989, no. 20, 1–66 | DOI | MR | Zbl

[16] Fonoberova M., Lozovanu D., “The maximum flow in dynamic networks”, Comp. Sci. J. Moldova., 2004, no. 3 (36), 387–396 | MR | Zbl

[17] Fonoberova M., Lozovanu D., “The minimum cost multicommodity flow problem in dynamic networks and an algorithm for its solving”, Comp. Sci. J. Moldova., 2005, no. 1 (37), 29–36 | MR | Zbl

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

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

[20] Skorokhodov V. A., “Generalization of the reachability problem on directed graphs”, Math. Stat., 8:6 (2020), 699–704 | DOI

[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 | DOI | MR | Zbl