Bidirectional resource networks: A new flow model (Q600769)

The classical model of flows in networks [\textit{L. R. Ford} and \textit{D. R. Fulkerson}, Flows in networks. Moskau: Verlag `Mir' (1966; Zbl 0139.13701); \textit{R. K. Ahuja, T. L. Magnanti} and \textit{J. B. Orlin}, Network flows. Theory, algorithms, and applications. Englewood Cliffs, NJ: Prentice Hall (1993; Zbl 1201.90001)] and its dynamic modifications (see, e.g., [\textit{L. Fleischer} and \textit{M. Skutella}, in: Proceedings of the fourteenth annual ACM-SIAM symposium on discrete algorithms (SODA 2003), Baltimore, MD, USA. New York, NY: Association for Computing Machinery; Philadelphia, PA: Society for Industrial and Applied Mathematics. 66--75 (2003; Zbl 1094.90511)]) are characterized by two properties: (a) the network is open: it includes sources from which resources flow into the network and sinks that consume resources; and (b) the intermediate vertices serve as a transfer medium between the sources and the sinks. In static problems, the delay of resources at intermediate vertices is prohibited [Ford and Fulkerson (loc. cit.)], while, in dynamic problems, it is generally undesirable [Fleischer and Skutella (loc. cit.)]. In this paper, we consider a dynamic model of a closed system in which no resources are supplied or consumed. Resources are contained at vertices and can be exchanged between them. The basic problem is to analyze the exchange processes and their stabilization.