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.