TY - JOUR
T1 - Physics of day-to-day network flow dynamics
AU - Xiao, Feng
AU - Yang, Hai
AU - Ye, Hongbo
N1 - Funding Information:
The research is supported by the National Natural Science Foundation of China ( 71201135 , 71431003 ) and Hong Kong's Research Grants Council (Project no. HKUST16211114 ).
Publisher Copyright:
© 2016 Elsevier Ltd.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2016/4/1
Y1 - 2016/4/1
N2 - 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.
AB - 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.
KW - Day-to-day dynamics
KW - Kinetic energy
KW - Network flow
KW - Potential energy
KW - User learning
UR - http://www.scopus.com/inward/record.url?scp=84958213170&partnerID=8YFLogxK
U2 - 10.1016/j.trb.2016.01.016
DO - 10.1016/j.trb.2016.01.016
M3 - Journal article
AN - SCOPUS:84958213170
SN - 0191-2615
VL - 86
SP - 86
EP - 103
JO - Transportation Research, Series B: Methodological
JF - Transportation Research, Series B: Methodological
ER -