ON THE REALIZABILITY OF STATIONARY FLOWS IN RESOURCE NETWORKS BY FLOWS IN CLASSICAL NETWORKS

This paper considers the problem of constructing a classical Ford—Fulkerson network whose flow matches a stationary flow in an original resource network. We show that this problem has a solution. Some properties of stationary flows in resource networks are studied. We defined the concept of disengagement of a resource network at an arbitrary vertex to a classical Ford–Fulkerson network. This allows us to prove that the problem of constructing a classical network implementing a stationary flow in a resource network by a flow in a classical network has a solution, but it is not unique. We use the original definition of the functioning of the resource network, which is different from that used by Kuznetsov and Zhilyakova (2010), Doklady Mathematics 82(1):643-646, but equivalent to it. It has the advantage of being simpler and more precise. The necessary and sufficient conditions for the initial resource distribution to be stable at infinity are obtained. The examples illustrating both the definitions and the results are presented.