Xiao, F, Yang, H and Ye, H (2016) Physics of day-to-day network flow dynamics. Transportation Research Part B: Methodological, 86. pp. 86-103. ISSN 0191-2615
Abstract
This paper offers a new look at the network flow dynamics from the viewpoint of physics by demonstrating that the traffic system, in terms of the aggregate effects of human behaviors, may exhibit like a physical system. Specifically, we look into the day-to-day evolution of network flows that arises from travelers’ route choices and their learning behavior on perceived travel costs. We show that the flow dynamics is analogous to a damped oscillatory system. The concepts of energies are introduced, including the potential energy and the kinetic energy. The potential energy, stored in each link, increases with the traffic flow on that link; the kinetic energy, generated by travelers’ day-to-day route swapping, is proportional to the square of the path flow changing speed. The potential and kinetic energies are converted to each other throughout the whole flow evolution, and the total system energy keeps decreasing owing to travelers’ tendency to stay on their current routes, which is analogous to the damping of a physical system. Finally, the system will approach the equilibrium state with minimum total potential energy and zero kinetic energy. We prove the stability of the day-to-day dynamics and provide numerical experiments to elucidate the interesting findings.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016, Elsevier. This is an author produced version of a paper published in Transportation Research Part B: Methodological. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Day-to-day dynamics; Network flow; User learning; Potential energy; Kinetic energy |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Environment (Leeds) > Institute for Transport Studies (Leeds) > ITS: Spatial Modelling and Dynamics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 19 Feb 2016 16:03 |
Last Modified: | 21 Aug 2017 22:15 |
Published Version: | http://dx.doi.org/10.1016/j.trb.2016.01.016 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.trb.2016.01.016 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:95278 |