连续随机跟驰模型的Langevin方法及其稳定性条件
Langevin method for a continuous stochastic car-following model and its stability conditions
摘要：
在跟车模型中，驾驶员根据他的身体和心理能力做出反应，这些能力可能会随着时间的推移而变化。然而，大多数跟车模型是确定性的，并没有捕捉到人类感知的随机性。由于驾驶员的随机驾驶行为，纯确定性交通模型可能会产生不切实际的结果。本文致力于开发一个独特的跟车模型，其中采用随机过程来描述随时间变化的随机加速度，这基本上反映了随机个人感知的驾驶员行为相对于领先的车辆随着时间的推移。特别是，我们应用耦合朗之万方程来模拟复杂的人类驾驶员行为。在该模型中，一个扩展的Cox-Ingersoll-Ross（CIR）随机过程将被用来描述随机速度的追随者响应于刺激的领导者。扩展的CIR过程的一个重要属性是增强随机交通变量（例如，非负速度）的非负属性，对于任何任意的模型参数。基于随机过程理论，我们推导出随机线性稳定性条件，第一次，从理论上捕捉的随机参数对交通不稳定性的影响。我们的稳定性结果符合经验的结果，交通不稳定性是有关的交通流的随机性在低速条件下，即使交通被认为是稳定的确定性模型。
英文摘要：
In car-following models, the driver reacts according to his physical and psychological abilities which may change over time. However, most car-following models are deterministic and do not capture the stochastic nature of human perception. It is expected that purely deterministic traffic models may produce unrealistic results due to the stochastic driving behaviors of drivers. This paper is devoted to the development of a distinct car-following model where a stochastic process is adopted to describe the time-varying random acceleration which essentially reflects the random individual perception of driver behavior with respect to the leading vehicle over time. In particular, we apply coupled Langevin equations to model complex human driver behavior. In the proposed model, an extended Cox-Ingersoll-Ross (CIR) stochastic process will be used to describe the stochastic speed of the follower in response to the stimulus of the leader. An important property of the extended CIR process is to enhance the non-negative properties of the stochastic traffic variables (e.g. non-negative speed) for any arbitrary model parameters. Based on stochastic process theories, we derive stochastic linear stability conditions which, for the first time, theoretically capture the effect of the random parameter on traffic instabilities. Our stability results conform to the empirical results that the traffic instability is related to the stochastic nature of traffic flow at the low speed conditions, even when traffic is deemed to be stable from deterministic models.
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