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Linear and Weakly Nonlinear Stability Analyses of Cooperative Car-Following Models

机译：协同跟随模型的线性和弱非线性稳定性分析

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摘要

Stability analyses have been widely used to better understand the mechanism of traffic jam formation. In this paper, we consider the impact of cooperative systems (a.k.a. connected vehicles) on traffic dynamics and, more precisely, on flow stability. Cooperative systems are emerging technologies enabling communication between vehicles and/or with the infrastructure. In a distributed communication framework, equipped vehicles are able to send and receive information to/from other equipped vehicles. Here, the effects of cooperative traffic are modeled through a general bilateral multianticipative car-following law that improves cooperative drivers' perception of their surrounding traffic conditions within a given communication range. Linear stability analyses are performed for a broad class of car-following models. They point out different stability conditions in both multianticipative and nonmultianticipative situations. To better understand what happens in unstable conditions, information on the shock wave structure is studied in the weakly nonlinear regime by the mean of the reductive perturbation method. The shock wave equation is obtained for generic car-following models by deriving the Korteweg de Vries equations. We then derive traffic-state-dependent conditions for the sign of the solitary wave (soliton) amplitude. This analytical result is verified through simulations. Simulation results confirm the validity of the speed estimate. The variation of the soliton amplitude as a function of the communication range is provided. The performed linear and weakly nonlinear analyses help justify the potential benefits of vehicle-integrated communication systems and provide new insights supporting the future implementation of cooperative systems.
机译：稳定性分析已被广泛用于更好地了解交通拥堵形成的机制。在本文中，我们考虑了协作系统（也称为互联车辆）对交通动力学的影响，更确切地说，对流量稳定性的影响。协作系统是新兴技术，可实现车辆之间和/或与基础设施之间的通信。在分布式通信框架中，配备的车辆能够与其他配备的车辆之间收发信息。在这里，合作交通的影响是通过通用的双边多预期汽车跟随法律来建模的，该法律改善了合作驾驶员在给定通信范围内对其周围交通状况的感知。线性稳定性分析针对多种汽车跟踪模型进行。他们指出了在多预期和非多预期情况下的不同稳定性条件。为了更好地理解在不稳定条件下会发生什么，通过还原摄动方法研究了在弱非线性状态下冲击波结构的信息。通过推导Korteweg de Vries方程，可以得到通用汽车跟随模型的冲击波方程。然后，我们得出与交通状态有关的孤立波（孤子）幅度的符号。通过模拟验证了该分析结果。仿真结果证实了速度估计的有效性。提供了孤子振幅随通信范围的变化。进行的线性和弱非线性分析有助于证明车辆集成通信系统的潜在优势，并提供新的见解来支持未来合作系统的实施。

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