{"title":"Local Control of In-Flows in Regular Resource Networks with\nLow Resource","authors":"A. V. Evseenko, V. A. Skorokhodov","doi":"10.1134/S1990478925020048","DOIUrl":null,"url":null,"abstract":"<p> The paper is devoted to solving the problem of local control of in-flows in regular resource\nnetworks with low resource. For such networks, a set of controlled vertices is specified. The local\ncontrol problem is to determine such capacities of arcs entering the controlled vertices that the\nunique limit state\n<span>\\( Q^* \\)</span> of regular resource network is the closest to a given state\n<span>\\( Q^{\\prime } \\)</span>. Conditions for the unreachability of the limit state that coincides with the\nstate\n<span>\\( Q^{\\prime } \\)</span> are obtained. Various configurations of resource networks with respect to the\ndistribution of controlled vertices in them are considered. It is shown that if the conditions for the\nunreachability of the limit state are not satisfied, then there exists a set of capacities of arcs\nentering the controlled vertices for which the limit state\n<span>\\( Q^* \\)</span> is equal to the given state\n<span>\\( Q^{\\prime } \\)</span>.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"19 2","pages":"240 - 254"},"PeriodicalIF":0.5800,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478925020048","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
The paper is devoted to solving the problem of local control of in-flows in regular resource
networks with low resource. For such networks, a set of controlled vertices is specified. The local
control problem is to determine such capacities of arcs entering the controlled vertices that the
unique limit state
\( Q^* \) of regular resource network is the closest to a given state
\( Q^{\prime } \). Conditions for the unreachability of the limit state that coincides with the
state
\( Q^{\prime } \) are obtained. Various configurations of resource networks with respect to the
distribution of controlled vertices in them are considered. It is shown that if the conditions for the
unreachability of the limit state are not satisfied, then there exists a set of capacities of arcs
entering the controlled vertices for which the limit state
\( Q^* \) is equal to the given state
\( Q^{\prime } \).
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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