Dahlmanns, Matthias, Kaiser, Franz and Witthaut, Dirk (2022). Branching in flow networks with linear congestion. Phys. Rev. Res., 4 (4). COLLEGE PK: AMER PHYSICAL SOC. ISSN 2643-1564

Full text not available from this repository.

Abstract

In our modern world, we rely on the proper functioning of a variety of networks with complex dynamics. Many of them are prone to congestion due to high loads, which determines their operation and resilience to failures. In this article, we propose a fundamental model of congestion where travel times increase linearly with the load. We show that this model interpolates between shortest path and Ohmic flow dynamics, which both have a broad range of applications. We formulate the model as a quadratic programme and derive a generalization of Ohm's law, where the flow of every link is determined by a potential gradient in a nonlinear way. We provide analytic solutions for fundamental network topologies that elucidate the transition from localized flow to a branched flow. Furthermore, we discuss how to solve the model efficiently for large networks and investigate the resilience to structural damages.

Item Type: Journal Article
Creators:
CreatorsEmailORCIDORCID Put Code
Dahlmanns, MatthiasUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Kaiser, FranzUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Witthaut, DirkUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
URN: urn:nbn:de:hbz:38-669067
DOI: 10.1103/PhysRevResearch.4.043208
Journal or Publication Title: Phys. Rev. Res.
Volume: 4
Number: 4
Date: 2022
Publisher: AMER PHYSICAL SOC
Place of Publication: COLLEGE PK
ISSN: 2643-1564
Language: English
Faculty: Unspecified
Divisions: Unspecified
Subjects: no entry
Uncontrolled Keywords:
KeywordsLanguage
PUBLIC TRANSPORT; TRAFFIC FLOW; COSTS; MODELMultiple languages
Physics, MultidisciplinaryMultiple languages
URI: http://kups.ub.uni-koeln.de/id/eprint/66906

Downloads

Downloads per month over past year

Altmetric

Export

Actions (login required)

View Item View Item