Link-based day-to-day network traffic dynamics and equilibria |
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Institution: | 1. School of Economics and Management, Beihang University, Beijing 100191, China;2. Key Lab of Complex System Analysis and Management Decision, Ministry of Education, China;3. Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong;1. NEXTRANS Center, Purdue University, 3000 Kent Avenue, West Lafayette, IN 47906, United States\n;2. School of Civil Engineering, Purdue University, 550 Stadium Mall Drive, West Lafayette, IN 47907, United States\n |
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Abstract: | A general dynamical system model with link-based variables is formulated to characterize the processes of achieving equilibria from a non-equilibrium state in traffic networks. Several desirable properties of the dynamical system model are established, including the equivalence between its stationary state and user equilibrium, the invariance of its evolutionary trajectories, and the uniqueness and stability of its stationary points. Moreover, it is shown that not only a link-based version of two existing day-to-day traffic dynamics models but also two existing link-based dynamical system models of traffic flow are the special cases of the proposed model. The stabilities of stationary states of these special cases are also analyzed and discussed. In addition, an extension is made to the case with elastic demand. The study is helpful for better understanding the day-to-day adjustment mechanism of traffic flows in networks. |
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Keywords: | Traffic assignment Day-to-day dynamics User equilibrium Stability |
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