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Continuous and discrete flows over time: A general model based on measure theory

Please always quote using this URN:urn:nbn:de:0296-matheon-8188
  • Network flows over time form a fascinating area of research. They model the temporal dynamics of network flow problems occurring in a wide variety of applications. Research in this area has been pursued in two different and mainly independent directions with respect to time modeling: discrete and continuous time models. In this paper we deploy measure theory in order to introduce a general model of network flows over time combining both discrete and continuous aspects into a single model. Here, the flow on each arc is modeled as a Borel measure on the real line (time axis) which assigns to each suitable subset a real value, interpreted as the amount of flow entering the arc over the subset. We focus on the maximum flow problem formulated in a network where capacities on arcs are also given as Borel measures and storage might be allowed at the nodes of the network. We generalize the concept of cuts to the case of these Borel Flows and extend the famous MaxFlow-MinCut Theorem.

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Metadaten
Author:Ronald Koch, Ebrahim Nasrabadi, Martin Skutella
URN:urn:nbn:de:0296-matheon-8188
Referee:Martin Skutella
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2011/04/27
Release Date:2011/04/27
Tag:
Institute:Research Center Matheon
Technische Universität Berlin
MSC-Classification:05-XX COMBINATORICS (For finite fields, see 11Txx) / 05Cxx Graph theory (For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15) / 05C21 Flows in graphs
05-XX COMBINATORICS (For finite fields, see 11Txx) / 05Cxx Graph theory (For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15) / 05C35 Extremal problems [See also 90C35]
05-XX COMBINATORICS (For finite fields, see 11Txx) / 05Cxx Graph theory (For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15) / 05C85 Graph algorithms [See also 68R10, 68W05]
28-XX MEASURE AND INTEGRATION (For analysis on manifolds, see 58-XX) / 28Axx Classical measure theory / 28A33 Spaces of measures, convergence of measures [See also 46E27, 60Bxx]
Preprint Number:783
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