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. 
@article{INTO_2023_226_a10,
     author = {V. A. Skorokhodov and I. M. Erusalimskyi and H. N. Abdulrahman},
     title = {Resource networks with dynamic arc durations},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {108--119},
     publisher = {mathdoc},
     volume = {226},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_226_a10/}
}
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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/