Geodesic
Flows in strongly regular periodic dynamic resource networks
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 31 (2021) no. 3, pp. 458-470

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This paper is devoted to studying the processes of resource allocation in dynamic resource networks. In such networks, the capacities of the arcs depend on time. Resource allocation in the network occurs in discrete time. The resource of each vertex is distributed only between adjacent vertices according to some rules. The study of the processes of resource redistribution in such networks is carried out. The main goal is to develop methods for finding the limit state (distribution) of a resource in a dynamic resource network. It is shown that the approach based on the construction of an auxiliary network is also applicable to reduce the problem of resource allocation in a dynamic network to a similar problem in an auxiliary network. Theorems on the existence of a limit state on an auxiliary graph are proved for strongly regular periodic dynamical networks. To find the limit states, one can use the approaches which are developed for the shortest path problem in dynamic networks.
Keywords: resource network, dynamic networks, threshold value, process of resources allocation, limit state in resource network. 
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     title = {Flows in strongly regular periodic dynamic resource networks},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {458--470},
     publisher = {mathdoc},
     volume = {31},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2021_31_3_a7/}
}
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V. A. Skorokhodov; D. O. Sviridkin. Flows in strongly regular periodic dynamic resource networks. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 31 (2021) no. 3, pp. 458-470. http://geodesic.mathdoc.fr/item/VUU_2021_31_3_a7/