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Abstract <p> The paper is devoted to solving the problem of local control of in-flows in regular resourcenetworks with low resource. For such networks, a set of controlled vertices is specified. The localcontrol problem is to determine such capacities of arcs entering the controlled vertices that theunique limit state<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(Q^*\)</EquationSource> </InlineEquation> of regular resource network is the closest to a given state<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(Q^{\prime }\)</EquationSource> </InlineEquation>. Conditions for the unreachability of the limit state that coincides with thestate<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(Q^{\prime }\)</EquationSource> </InlineEquation> are obtained. Various configurations of resource networks with respect to thedistribution of controlled vertices in them are considered. It is shown that if the conditions for theunreachability of the limit state are not satisfied, then there exists a set of capacities of arcsentering the controlled vertices for which the limit state<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(Q^*\)</EquationSource> </InlineEquation> is equal to the given state<InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(Q^{\prime }\)</EquationSource> </InlineEquation>.</p>

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Local Control of In-Flows in Regular Resource Networks with Low Resource

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • A. V. Evseenko,
  • V. A. Skorokhodov

摘要

Abstract

The paper is devoted to solving the problem of local control of in-flows in regular resourcenetworks with low resource. For such networks, a set of controlled vertices is specified. The localcontrol problem is to determine such capacities of arcs entering the controlled vertices that theunique 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 thestate \(Q^{\prime }\) are obtained. Various configurations of resource networks with respect to thedistribution of controlled vertices in them are considered. It is shown that if the conditions for theunreachability of the limit state are not satisfied, then there exists a set of capacities of arcsentering the controlled vertices for which the limit state \(Q^*\) is equal to the given state \(Q^{\prime }\) .