车辆跟驰的随机优化速度模型及其稳定性分析

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。

Stochastic Optimal Velocity Model for Car Following and Its Stability Analysis

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.