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The Hamilton–Jacobi partial differential equation and the three representations of traffic flow |
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| Institution: | 1. School of Transportation and Logistics, Southwest Jiaotong University, No. 111, Erhuanlu Beiyiduan, Chengdu 610031, PR China;2. Division of Engineering, New York University Abu Dhabi, Saadiyat Island, Abu Dhabi, P.O. Box 129188, United Arab Emirates;3. Department of Civil and Environmental Engineering, University of Michigan Ann Arbor, 2350 Hayward, 2116 GG Brown, Ann Arbor, Michigan 48109-2125, USA;4. Tandon School of Engineering, New York University, Brooklyn, New York, USA |
| Abstract: | This paper applies the theory of Hamilton–Jacobi partial differential equations to the case of first-order traffic flow models. The traffic flow surface is analyzed with respect to the three 2-dimensional coordinate systems arising in the space of vehicle number, time and distance. In each case, the solution to the initial and boundary value problems are presented. Explicit solution methods and examples are shown for the triangular flow-density diagram case. This unveils new models and shows how a number of existing models are cast as special cases. |
| Keywords: | Hamilton–Jacobi partial differential equation Stochastic traffic flow Kinematic wave model |
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