A variational formulation for higher order macroscopic traffic flow models of the GSOM family |
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| Affiliation: | 1. Institute of Systems Engineering, College of Management and Economics, Tianjin University, Tianjin 300072, China;2. MOE Key Laboratory for Urban Transportation Complex Systems Theory and Technology, Beijing Jiaotong University, Beijing 100044, China;1. Institute of Systems Engineering, College of Management and Economics, Tianjin University, No. 92 Weijin Road, Nankai District, Tianjin 300072, China;2. Department of Civil and Environmental Engineering, University of California Davis, Davis, CA 95616, United States;3. Technische Universität Dresden, Institute for Transport & Economics, Würzburger Str. 35, D-01062 Dresden, Germany;4. Key Laboratory of Transport Industry of Big Data Application Technologies for Comprehensive Transport, Ministry of Transport, Beijing Jiaotong University, Beijing 100044, China |
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| Abstract: | The GSOM (Generic second order modelling) family of traffic flow models combines the LWR model with dynamics of driver-specific attributes and can be expressed as a system of conservation laws. The object of the paper is to show that a proper Lagrangian formulation of the GSOM model can be recast as a Hamilton–Jacobi equation, the solution of which can be expressed as the value function of an optimal control problem. This value function is interpreted as the position of vehicles, and the optimal trajectories of the optimal control formulation can be identified with the characteristics. Further the paper analyzes the initial and boundary conditions, proposes a generalization of the inf-morphism and the Lax–Hopf formulas to the GSOM model, and considers numerical aspects. |
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| Keywords: | Traffic flow models Lagrangian model Hamilton–Jacobi Lax–Hopf formula Inf-morphism GSOM models |
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