Journal Article

FZJ-2023-01636

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Branching in flow networks with linear congestion

Dahlmanns, M. ; Kaiser, F. ; Witthaut, D. (Corresponding author)FZJ*

2022
APS College Park, MD

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Please use a persistent id in citations: http://hdl.handle.net/2128/34251  doi:10.1103/PhysRevResearch.4.043208

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.

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Contributing Institute(s):

1. Systemforschung und Technologische Entwicklung (IEK-STE)

Research Program(s):

1. 1112 - Societally Feasible Transformation Pathways (POF4-111) (POF4-111)

Appears in the scientific report 2023

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Database coverage:
; ; ; ; Article Processing Charges ; Clarivate Analytics Master Journal List ; DOAJ Seal ; Emerging Sources Citation Index ; Fees ; SCOPUS ; Web of Science Core Collection

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