DETERMINATION OF MAXIMUM FLOW IN A FUZZY PERIODIC GRAPH

Abstract

The article illustrates a method for finding the maximum value of a dynamic flow using periodic graphs, presented in the form of a generalized network. The interest in networks of this type is explained by their wide practical application in places where there is periodicity, for example, management of periodic passenger transportation on various types of transport, freight transportation, including goods with a short shelf life, management of road traffic flow, namely regulation traffic lights, taking into account frequency and workload. At the same time, the values of the bandwidth of the arcs of the networks under consideration may vary depending on the time of departure of the stream and possible cycles, so we turn to dynamic networks. Network parameters are presented in a fuzzy form due to the influence of environmental factors and human activity. And the choice of periodic graphs is due to the presence of cycles and the frequency of time intervals. The considered types of networks can be implemented on real roads during transportation. To solve the identified problem, within the framework of the presented work, a brief overview of literary sources is provided, which allows us to assess the current level of development of systems for such purposes. As a result of this review, it was found that the most effective methods of solving the problem posed are the use of fuzzy periodic graph methods. In this regard, it was decided to conduct a study of these methods. The novelty of this work is determined based on the use of periodic temporal fuzzy graphs in solving the problem of finding the maximum flow of a dynamic network.