INVESTIGATION OF THE PROBLEM OF OPTIMIZATION OF THE HIERARCHICAL STRUCTURE OF A SPARSE AND DENSE COMMUNICATION NETWORK

Abstract

The article is devoted to the study of the optimization problem for the hierarchical structure of a multicommodity communication network with discrete flows and parameters when its density changes (the ratio of the number of network arcs to the maximum possible number of arcs for a given number of nodes in the network). The network has three levels of hierarchy — a backbone, a zonal and a internal and four types of nodes — backbone nodes of the first, second and third types, forming the backbone and zonal levels of the network, and nodes of the fourth type, which subordinate to each backbone node and form the internal levels of the network. The types of nodes different from one another in functionality. The main task of the study is to establish how the structure of the backbone network changes (the number and location of backbone nodes of the first, second and third types), the scheme of processing and distribution of flows and technical and economic indicators of the network's functioning for various degrees of its density. The principles of organizing the sorting and distribution of flows in a three-level network and its mathematical model are given. A mathematical model of the problem of optimizing the structure of the backbone network and the schemes of sorting and distribution of flows is formulated. The algorithms for solving the problem are based on the discrete analogue of the local descent method proposed earlier by the authors, when the neighborhoods of the metric space of possible solutions are chosen from heuristic considerations, taking into account the peculiarities of the problem being solved. Computer modeling of the problem on a homogeneous network containing 100 nodes with a change in the degree of nodes from 2 to 99 is carried out. The modeling was carried out on the example of a road transport network for the transportation of cargo using a computer program, which is part of the instrumental software of the Information and Analytical Decision Support System (IA DSS), which is being developed at the Institute of Telecommunications and Global Information Space of the National Academy of Sciences of Ukraine. An experimental study of the solution to the problem showed that the best technical, economic and operational indicators of its functioning are achieved with a degree nodes from 9 to 14, when high network connectivity is ensured, and is significantly reduced the average and maximum time of delivery of cargos to recipients. The proposed computer technology for solving problem with changing network density allows you to interactively modeling various options of a network , changing the topology, hierarchical structure, flows, parameters and constraints of the model and from the family of the resived results choose the best option, taking into account the selected a goal function and the accepted constraints; calculate preliminary technical and economic indicators of the network's functioning, estimate the cost of additional resources and plan the amount of investment required for the modernization and construction of its structural elements, which ultimately makes it possible to increase the efficiency functioning of the network by optimizing use of its resources and reducing the operating costs for the processing and transportation of flows.