МЕТОДОЛОГІЯ МАТЕМАТИЧНОГО МОДЕЛЮВАННЯ ПЕРСПЕКТИВНОГО РОЗВИТКУ ВУЗЛІВ І ТРАНСПОРТНИХ МАРШРУТІВ У БАГАТОПРОДУКТОВІЙ ІЄРАРХІЧНІЙ МЕРЕЖІ. І. ЗАДАЧІ ОПТИМІЗАЦІЇ.

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. [ABSTRACT FROM AUTHOR]