论文标题
随机二阶宏观连续体模型和数值模拟的稳定性分析
Stability analysis of stochastic second-order macroscopic continuum models and numerical simulations
论文作者
论文摘要
数十年来，二阶宏观连续体模型一直在不断改善，以重现经验观察。最近，一系列实验研究表明，随机因素有助于破坏交通流动。然而，随机二阶宏观连续体模型的交通流量稳定性尚未在过去的研究中受到应有的关注。更重要的是，我们发现在现有的理论稳定性分析中仍未正确验证随机性的不稳定方面。在本文中，我们通过使用直接的Lyapunov方法分析研究了随机性二阶宏观模型对交通流量稳定性的影响。已经针对不同典型的随机二阶宏观模型进行了数值模拟。我们的分析稳定性分析已得到验证，我们的方法也被证明更有效。从理论上讲，我们的研究表明，随机性的存在在随机宏观模型中具有不稳定的作用。
Second-order macroscopic continuum models have been constantly improving for decades to reproduce the empirical observations. Recently, a series of experimental studies have suggested that the stochastic factors contribute significantly to destabilizing traffic flow. Nevertheless, the traffic flow stability of the stochastic second-order macroscopic continuum model hasn't received the attention it deserves in past studies. More importantly, we have found that the destabilizing aspect of stochasticity is still not correctly validated in the existing theoretical stability analysis. In this paper, we analytically study the impact of stochasticity on traffic flow stability for a general stochastic second-order macroscopic model by using the direct Lyapunov method. Numerical simulations have been carried out for different typical stochastic second-order macroscopic models. Our analytical stability analysis has been validated, and our methodology has been proved more efficient. Our study has theoretically revealed that the presence of stochasticity has a destabilizing effect in stochastic macroscopic models.
