Continuous and Discrete Flows Over Time: A General Model Based on Measure Theory

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dc.contributor.authorKoch, Ronald
dc.contributor.authorNasrabadi, Ebrahim
dc.contributor.authorSkutella, Martin
dc.date.accessioned2021-12-17T10:08:25Z
dc.date.available2021-12-17T10:08:25Z
dc.date.issued2009
dc.description.abstractNetwork 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.en
dc.identifier.issn2197-8085
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/15664
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-14437
dc.language.isoenen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.ddc510 Mathematiken
dc.subject.othernetwork flowsen
dc.subject.otherflows over timeen
dc.subject.othermeasure theoryen
dc.subject.otherMaxFlow-MinCuten
dc.subject.otherdiscrete flowsen
dc.titleContinuous and Discrete Flows Over Time: A General Model Based on Measure Theoryen
dc.typeResearch Paperen
dc.type.versionsubmittedVersionen
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften::Inst. Mathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
tub.series.issuenumber2009, 16en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
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