Physics of day-to-day network flow dynamics

Feng Xiao, Hai Yang, Hongbo Ye

    Research output: Journal article publicationJournal articleAcademic researchpeer-review

    47 Citations (Scopus)


    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.

    Original languageEnglish
    Pages (from-to)86-103
    Number of pages18
    JournalTransportation Research Part B: Methodological
    Publication statusPublished - 1 Apr 2016


    • Day-to-day dynamics
    • Kinetic energy
    • Network flow
    • Potential energy
    • User learning

    ASJC Scopus subject areas

    • Civil and Structural Engineering
    • Transportation


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