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The paper proposes a solution to the problem of selecting the bandwidth capabilities of digital communication channels of a transport communication network taking into account the imbalance of data traffic by priorities. The algorithm for selecting bandwidth guarantees the minimum costs associated with renting digital communication channels with optimal bandwidth, provided that the requirements for quality of service of protocol data blocks of the first, second, and k-th priority in an unbalanced in terms of priorities transport communication network are met. At the first stage of solving the problem, using the method of Lagrange multipliers, an algorithm for selecting the capacities of digital communication channels for a balanced in terms of priorities transport network was developed. High performance of this algorithm was ensured by applying algebraic operations on matrices (addition, multiplication, etc.). At the second stage of solving the problem, using the generalized Lagrange multipliers method, we compared the conditional extrema of the cost function for renting digital communication channels for single active quality of service requirements for protocol data blocks, for all possible pairs of active quality of service requirements for protocol data blocks, for all possible triples of active requirements for the quality of service of protocol data units, and so on up to the case when all the requirements for quality of service maintenance of protocol data units are active simultaniously. At the third stage of solving the problem, an example of selecting the bandwidth capabilities of digital communication channels of the unbalanced by priorities transport network consisting of eight routers serving protocol data blocks of three priorities was considered. At the fourth stage of the solution of the problem of the choice of carrying capacities the estimation of efficiency of the developed algorithm by a method of simulation modeling was carried out. To this end, in the environment of the network simulator OMNet ++, the unbalanced in terms of priority transport communication network consisting of eight routers connected by twelve digital communication channels with optimal bandwidth was investigated.

Аннотация. В работе предлагается оригинальный алгоритм решения прикладной задачи теории графов о нахождении k максимальных потоков между двумя заданными верши-нами графа. Описываемый подход представляет собой комплексное применение в еди-ном оптимизационном цикле алгоритма Форда-Фалкерсона (Эдмондса-Карпа или Дини-ца) и алгоритма построения усеченного дерева состояний в ширину. Ключевые слова: сеть связи с коммутацией пакетов, пропускная способность соедине-ния, задача о максимальном потоке.Tregubov R.B., Lazarev S. N., Andreev S. Ju. The algorithm of finding of k maximum flows. Abstract. In the paper the original algorithm of solution of an applied task of the graph theory on finding of k maximum flows between the two set count's tops is proposed. The approach described represents a complex application of Ford-Fulkerson (Edmonds-Karp or Dinitz) algorithm and the algorithm of creation of a truncated tree of states in width in an indivisible optimizing cycle. Keywords: a communication network with packet switching, connection capacity, the maximum flow task.

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