Combined effects of drivers’ disturbance risk preference heterogeneity and the nearest following vehicle headway on traffic flow instability: Analytical studies

Driver's disturbance risk preference is defined as the driver's reaction degree to the disturbance, which is a kind of the driver's attributes and can be expressed by the disturbance risk preference coefficient. This paper proposes a new car-following model and firstly attempts to analytically investigate the combined effects of drivers’ disturbance risk preference heterogeneity and the nearest following vehicle headway on traffic flow instability under some specific traffic scenarios. Solution of the model yields many insights including the following: (1) when drivers’ disturbance risk preference increases from the following driver to the preceding driver, traffic flow instability increases, and the bigger the disturbance risk preference coefficient ratio of the preceding driver's coefficient to the following driver's coefficient, the bigger the increasing effect and vice versa; at this scenario, the nearest following vehicle headway increases traffic flow instability; (2) when drivers’ disturbance risk preference is homogeneous, drivers’ disturbance risk preference and the nearest following vehicle headway have no effects on traffic flow instability; (3) when drivers’ disturbance risk preference reduces from the following driver to the preceding driver, for the general traffic situation, traffic flow instability reduces, and the smaller the disturbance risk preference coefficient ratio of the preceding driver's coefficient to the following driver's coefficient, the bigger the reducing effect and vice versa; at this scenario, if the coefficient ratio reduces from the following to the preceding or is homogeneous, the nearest following vehicle headway increases traffic flow instability, otherwise, the effects of the nearest following vehicle headway on traffic flow instability cannot be confirmed.