Kink–antikink density wave of an extended car-following model in a cooperative driving system |
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Authors: | Lei Yu Zhongke Shi Bingchang Zhou |
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Institution: | aCollege of Automation, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, China;bDepartment of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, China |
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Abstract: | We propose an extended optimal velocity model applicable to cooperative driving control system by considering the headway of arbitrary number of cars that precede and the relative velocity. The stability condition of the extended model is obtained by using the linear stability theory. The modified Korteweg-de Vries (mKdV) equation is derived to describe the traffic behavior near the critical point by applying the nonlinear analysis. Thus the traffic jams can be described by the kink–antikink density wave which is the solution of the mKdV equation. The simulation results confirm the analytical results and show that the traffic jams are suppressed more efficiently with considering not only the headway of more vehicles ahead but also the relative velocity. |
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Keywords: | Traffic flow Cooperative driving system Kink– antikink soliton Density wave |
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