Reduction of Potential-Based Flow Networks

Max Klimm (), Marc E. Pfetsch (), Rico Raber () and Martin Skutella ()
Additional contact information
Max Klimm: Institut für Mathematik, Technische Universität Berlin, 10623 Berlin, Germany
Marc E. Pfetsch: Department of Mathematics, Technische Universität Darmstadt, 64293 Darmstadt, Germany
Rico Raber: Institut für Mathematik, Technische Universität Berlin, 10623 Berlin, Germany
Martin Skutella: Institut für Mathematik, Technische Universität Berlin, 10623 Berlin, Germany

Mathematics of Operations Research, 2023, vol. 48, issue 4, 2287-2303

Abstract: We consider potential-based flow networks with terminal nodes at which flow can enter or leave the network and physical properties, such as voltages or pressures, are measured and controlled. We study conditions under which such a network can be reduced to a smaller, equivalent network with the same behavior at the terminal nodes. Potential-based flow networks are widely used to model infrastructure networks, such as electricity, gas, or water networks. In contrast to Kron’s reduction for electrical networks, we prove that, in general, potential-based flow networks with at least three terminals cannot be reduced to smaller networks whose size only depends on the number of terminals. On the other hand, we show that it is possible to represent a special class of potential-based flow networks by a complete graph on the terminals, and we establish a characterization of networks that can be reduced to a path network. Our results build on fundamental properties of effective resistances proved in this paper, including explicit formulae for their dependence on edge resistances of the network and their metric properties.

Keywords: Primary: 90C35; secondary: 76N25; potential-based flows; network reduction; effective resistances (search for similar items in EconPapers)
Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://dx.doi.org/10.1287/moor.2022.1338 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:48:y:2023:i:4:p:2287-2303

Access Statistics for this article

More articles in Mathematics of Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().