caa a22 4500 445839759 CHVBK 20180317145340.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s00186-011-0357-2 doi (NATIONALLICENCE)springer-10.1007/s00186-011-0357-2 Continuous and discrete flows over time [Elektronische Daten] A general model based on measure theory [Ronald Koch, Ebrahim Nasrabadi, Martin Skutella] 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. Springer-Verlag, 2011 Network flows nationallicence Flows over time nationallicence Measure theory nationallicence MaxFlow-MinCut nationallicence Koch Ronald Technische Universität Berlin, Institut für Mathematik, Straße des 17. Juni 136, 10623, Berlin, Germany aut Nasrabadi Ebrahim Technische Universität Berlin, Institut für Mathematik, Straße des 17. Juni 136, 10623, Berlin, Germany aut Skutella Martin Technische Universität Berlin, Institut für Mathematik, Straße des 17. Juni 136, 10623, Berlin, Germany aut Mathematical Methods of Operations Research Springer-Verlag 73/3(2011-06-01), 301-337 1432-2994 73:3<301 2011 73 186 https://doi.org/10.1007/s00186-011-0357-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00186-011-0357-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Koch Ronald Technische Universität Berlin, Institut für Mathematik, Straße des 17. Juni 136, 10623, Berlin, Germany aut NATIONALLICENCE 700 1- Nasrabadi Ebrahim Technische Universität Berlin, Institut für Mathematik, Straße des 17. Juni 136, 10623, Berlin, Germany aut NATIONALLICENCE 700 1- Skutella Martin Technische Universität Berlin, Institut für Mathematik, Straße des 17. Juni 136, 10623, Berlin, Germany aut NATIONALLICENCE 773 0- Mathematical Methods of Operations Research Springer-Verlag 73/3(2011-06-01), 301-337 1432-2994 73:3<301 2011 73 186 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer