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A traffic system can be interpreted as a multiagent system, wherein vehicles choose the most efficient driving approaches guided by interconnected goals or strategies. This paper aims to develop a family of mean field games (MFG) for generic second-order traffic flow models (GSOM), in which cars control individual velocity to optimize their objective functions. GSOMs do not generally assume that cars optimize self-interested objectives, so such a game-theoretic reinterpretation offers insights into the agents’ underlying behaviors. In general, an MFG allows one to model individuals on a microscopic level as rational utility-optimizing agents while translating rich microscopic behaviors to macroscopic models. Building on the MFG framework, we devise a new class of second-order traffic flow MFGs (i.e., GSOM-MFG), which control cars’ acceleration to ensure smooth velocity change. A fixed-point algorithm with fictitious play technique is developed to solve GSOM-MFG numerically. In numerical examples, different traffic patterns are presented under different cost functions. For real-world validation, we further use an inverse reinforcement learning approach (IRL) to uncover the underlying cost function on the next-generation simulation (NGSIM) data set. We formulate the problem of inferring cost functions as a min-max game and use an apprenticeship learning algorithm to solve for cost function coefficients. The results show that our proposed GSOM-MFG is a generic framework that can accommodate various cost functions. The Aw Rascle and Zhang (ARZ) and Light-Whitham-Richards (LWR) fundamental diagrams in traffic flow models belong to our GSOM-MFG when costs are specified. History: This paper has been accepted for the Transportation Science Special Issue on ISTTT25 Conference. Funding: X. Di is supported by the National Science Foundation [CAREER Award CMMI-1943998]. E. Iacomini is partially supported by the Italian Research Center on High-Performance Computing, Big Data and Quantum Computing (ICSC) funded by MUR Missione 4-Next Generation EU (NGEU) [Spoke 1 “FutureHPC & BigData”]. C. Segala and M. Herty thank the Deutsche Forschungsgemeinschaft (DFG) for financial support [Grants 320021702/GRK2326, 333849990/IRTG-2379, B04, B05, and B06 of 442047500/SFB1481, HE5386/18-1,19-2,22-1,23-1,25-1, ERS SFDdM035; Germany’s Excellence Strategy EXC-2023 Internet of Production 390621612; and Excellence Strategy of the Federal Government and the Länder]. Support through the EU DATAHYKING is also acknowledged. This work was also funded by the DFG [TRR 154, Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks, Projects C03 and C05, Project No. 239904186]. Moreover, E. Iacomini and C. Segala are members of the Indam GNCS (Italian National Group of Scientific Calculus).
A traffic system can be interpreted as a multiagent system, wherein vehicles choose the most efficient driving approaches guided by interconnected goals or strategies. This paper aims to develop a family of mean field games (MFG) for generic second-order traffic flow models (GSOM), in which cars control individual velocity to optimize their objective functions. GSOMs do not generally assume that cars optimize self-interested objectives, so such a game-theoretic reinterpretation offers insights into the agents’ underlying behaviors. In general, an MFG allows one to model individuals on a microscopic level as rational utility-optimizing agents while translating rich microscopic behaviors to macroscopic models. Building on the MFG framework, we devise a new class of second-order traffic flow MFGs (i.e., GSOM-MFG), which control cars’ acceleration to ensure smooth velocity change. A fixed-point algorithm with fictitious play technique is developed to solve GSOM-MFG numerically. In numerical examples, different traffic patterns are presented under different cost functions. For real-world validation, we further use an inverse reinforcement learning approach (IRL) to uncover the underlying cost function on the next-generation simulation (NGSIM) data set. We formulate the problem of inferring cost functions as a min-max game and use an apprenticeship learning algorithm to solve for cost function coefficients. The results show that our proposed GSOM-MFG is a generic framework that can accommodate various cost functions. The Aw Rascle and Zhang (ARZ) and Light-Whitham-Richards (LWR) fundamental diagrams in traffic flow models belong to our GSOM-MFG when costs are specified. History: This paper has been accepted for the Transportation Science Special Issue on ISTTT25 Conference. Funding: X. Di is supported by the National Science Foundation [CAREER Award CMMI-1943998]. E. Iacomini is partially supported by the Italian Research Center on High-Performance Computing, Big Data and Quantum Computing (ICSC) funded by MUR Missione 4-Next Generation EU (NGEU) [Spoke 1 “FutureHPC & BigData”]. C. Segala and M. Herty thank the Deutsche Forschungsgemeinschaft (DFG) for financial support [Grants 320021702/GRK2326, 333849990/IRTG-2379, B04, B05, and B06 of 442047500/SFB1481, HE5386/18-1,19-2,22-1,23-1,25-1, ERS SFDdM035; Germany’s Excellence Strategy EXC-2023 Internet of Production 390621612; and Excellence Strategy of the Federal Government and the Länder]. Support through the EU DATAHYKING is also acknowledged. This work was also funded by the DFG [TRR 154, Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks, Projects C03 and C05, Project No. 239904186]. Moreover, E. Iacomini and C. Segala are members of the Indam GNCS (Italian National Group of Scientific Calculus).
In recent years, traffic density forecasting has been playing an important role in developing and improving the performance of intelligent traffic systems. Traffic density forecasting to optimize traffic management, urban management of vehicular traffic have the ability to coordinate traffic, optimize traffic light signals and apply intelligent regulation based on forecasts, thereby improving the handling of the road segment and reducing travel time. Therefore, the construction of predictive algorithms along with integration into traffic management systems is essential to promote the sustainable development of intelligent transportation systems in the future. In this research, an algorithm has been developed to predict traffic density on the delayed Lighthill - Whitham - Richards (LWR) model, in which a regularization difference method has been proposed as the basis for the algorithm. This article mainly focus on building an algorithm and performing experimental calculations to verify the correctness of the algorithm on a mathematical model.
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