Open AccessFlows in strongly regular periodic dynamic resource networks
Author(s) -
V.A. Skorokhodov,
Дмитрий Олегович Свиридкин
Publication year - 2021
Publication title -
vestnik udmurtskogo universiteta. matematika, mehanika, kompʹûternye nauki
Language(s) - English
Resource type - Journals
eISSN - 2076-5959
pISSN - 1994-9197
DOI - 10.35634/vm210308
Subject(s) - computer science , resource allocation , resource (disambiguation) , limit (mathematics) , shortest path problem , path (computing) , vertex (graph theory) , graph , mathematical optimization , distributed computing , topology (electrical circuits) , theoretical computer science , mathematics , computer network , combinatorics , mathematical analysis
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.