Stabilization strategy of a car-following model with multiple time delays of the drivers* *Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant No. LY20G010004), the Program of Humanities and Social Scienceof Education Ministry of China (Grant No. 20YJA630008), the National Key Research and Development Program of China – Traffic Modeling, Surveillance and Control with Connected & Automated

Abstract

An extended car-following model with multiple delays is constructed to describe driver’s driving behavior. Through stability analysis, the stability condition of this uncontrolled model is given. To dampen the negative impact of the driver’s multiple delays (i.e., stability condition is not satisfied), a novel control strategy is proposed to assist the driver in adjusting vehicle operation. The control strategy consists of two parts: the design of control term as well as the design of the parameters in the term. Bifurcation analysis is performed to illustrate the necessity of the design of parameters in control terms. In the course of the design of parameters in the control term, we improve the definite integral stability method to reduce the iterations by incorporating the characteristics of bifurcation, which can determine the appropriate parameters in the control terms more quickly. Finally, in the case study, we validate the control strategy by utilizing measured data and configuring scenario, which is closer to the actual traffic. The results of validation show that the control strategy can effectively stabilize the unstable traffic flow caused by driver’s delays.