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International Theoretical Science Journal
Volume 60 >>> № 1 JANUARY — FEBRUARY 2024
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DOI: 10.34229/KCA2522-9664.24.1.8
UDC 519.168; 519.854.3
V.A. Vasyanin1, O.M. Trofymchuk2, L.P. Ushakova3


1 Institute of Telecommunications and Global Information Space, National Academy of Sciences of Ukraine, Kyiv, Ukraine

 archukr@meta.ua

2 Institute of Telecommunications and Global Information Space, National Academy of Sciences of Ukraine, Kyiv, Ukraine

 itgis@nas.gov.ua

3 Institute of Telecommunications and Global Information Space, National Academy of Sciences of Ukraine, Kyiv, Ukraine

 archukr@ukr.net

METHODOLOGY OF THE MATHEMATICAL MODELING FOR PERSPECTIVE
DEVELOPMENT OF NODES AND TRANSPORT ROUTES IN A MULTICOMMODITY
HIERARCHICAL NETWORK. I. OPTIMIZATION PROBLEMS

Abstract. The paper proposes a methodology for mathematical modeling of the step-by-step development of nodes and transport routes in a hierarchical network with multicommodity discrete flows of correspondence based on solving the problems of optimizing its structure and distribution of flows. As a rule, such networks consist of a decentralized trunk network and networks in the internal service areas of trunk nodes. In a multicommodity network, each node can exchange correspondence (products, goods, cargo, messages) with other nodes. Correspondence is characterized by a source node, a sink node, and a quantity, which for data transmission networks is given by the number of bytes, kilobytes, etc., and for transport networks by the number of cargo units in a package of uniform size. In the trunk network, all correspondence is transmitted via communication channels or transported in vehicles in transport blocks of a given size (capacity, volume). The authors considered the main postulates of generating a mathematical model of the perspective development of the trunk network and gave a method of mathematical modeling of the step-by-step development of nodes and transport routes, which includes, for each stage of development, the forecasting of data and network parameters, solving the problem of packing correspondence and choosing the structure of the network, solving the problem of distribution and routing of flows of transport blocks.

Keywords: multicommodity hierarchical networks, discrete flows, combinatorial optimization problems, mathematical models, computer simulation.


full text

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