交通运输系统工程与信息 ›› 2021, Vol. 21 ›› Issue (6): 153-159.DOI: 10.16097/j.cnki.1009-6744.2021.06.017

• 系统工程理论与方法 • 上一篇    下一篇

车辆跟驰的随机优化速度模型及其稳定性分析

刘中华*,舒思朝,吴子强,吴新烨   

  1. 厦门大学,建筑与土木工程学院,福建 厦门 361005
  • 收稿日期:2021-06-08 修回日期:2021-08-14 接受日期:2021-08-17 出版日期:2021-12-25 发布日期:2021-12-23
  • 作者简介:刘中华(1975- ),男,山东青岛人,教授,博士。
  • 基金资助:
    国家自然科学基金;厦门市交通基础设施智能管养工程技 术研究中心开放基金

Stochastic Optimal Velocity Model for Car Following and Its Stability Analysis

LIU Zhong-hua* , SHU Si-zhao, WU Zi-qiang, WU Xin-ye   

  1. School of Architecture and Civil Engineering, Xiamen University, Xiamen 361005, Fujian, China
  • Received:2021-06-08 Revised:2021-08-14 Accepted:2021-08-17 Online:2021-12-25 Published:2021-12-23
  • Supported by:
    National Natural Science Foundation of China(11772277);The Open Fund Project of Transportation Infrastructure Intelligent Management and Maintenance Engineering Technology Center of Xiamen City(TCIMI201803)。

摘要: 传统优化速度模型(OV)中把驾驶员的灵敏度系数设定为相同的常数值,而在真实驾驶情 况下,驾驶员的灵敏度系数会在跟驰过程中发生随机性变化。为描述这个交通流的随机行为,将 驾驶员的灵敏度系数模型化为高斯白噪声过程,建立随机优化速度模型(Stochastic Optimal Velocity,SOV)。然后,运用随机动力学稳定性分析中的矩稳定性理论分析SOV模型的稳定性, 得到一阶和二阶矩稳定性条件的解析解,解析式表明:SOV模型的稳定域由灵敏度系数的均值和 噪声强度,以及车头间距共同决定。最后,应用蒙特卡洛法进行数值模拟,模拟结果验证了矩稳 定性条件的有效性。与确定性OV模型进行数值模拟对比,结果表明:SOV模型中灵敏度系数的 噪声强度会增加交通系统产生拥堵的可能性,在扰动传播过程中的影响体现在扰动演化的波动 振幅上。

关键词: 交通工程, 随机跟驰模型, 矩稳定性分析, 灵敏度系数, 高斯白噪声过程, 随机性

Abstract: In the traditional optimal velocity model (OV), the driver's sensitivity coefficient is set as a constant value, but in real situations, the driver's sensitivity coefficient is changing stochastically in car following maneuvers. To describe the stochastic behavior of the traffic flow, this study models the driver's sensitivity coefficient as a white Gaussian noise process and develops the stochastic optimal velocity model (SOV). The moment stability theory with stochastic dynamics is used to analyze the stability of the SOV model, and the analytical solutions are obtained for the first and second moment stability conditions. The analytical formula shows that the stability region of SOV model is determined by the mean value and noise intensity of sensitivity coefficient and the headway. The Monte Carlo method is used for numerical simulation to verify the effectiveness of the moment stability condition. Compared to the deterministic OV model, the simulation results show that the noise intensity of the sensitivity coefficient in the SOV model might increase the possibility of traffic congestion, which is reflected in the fluctuation amplitude of disturbance evolution in the process of disturbance propagation.

Key words: traffic engineering, stochastic car following model, moment stability analysis, sensitivity coefficient, white Gaussian noise process, stochasticity

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