Linear stability analysis of heterogeneous traffic flow considering degradations of connected automated vehicles and reaction time

With the development of connected automated vehicles (CAVs) technologies, traffic flow on the road is converting into the heterogeneous traffic flow, which consists of CAVs and human-driven vehicles (HDVs). Considering the function of CAVs would degrade when following HDVs in heterogeneous traffic flow. Moreover, the reaction time of degraded CAVs would be different with CAVs or HDVs. This paper deduces and analyzes the linear stability of such heterogeneous traffic flow based on CAVs degradations and reaction time diversity. Firstly, considering the degradations of CAVs, the vehicle types and their ratios in heterogeneous traffic flow are analyzed. Secondly, the car-following model and the reaction time of three types of vehicles are discussed. Then, the linear stability condition of heterogeneous traffic flow is proposed. Finally, the impact factors on the stability condition are illustrated through numerical analysis. The results show that the high penetration rate of CAVs and the short reaction time can improve the linear stability of heterogeneous traffic flow. Besides, when the penetration rate of CAVs increases to 65%, the stability of heterogeneous traffic flow is not affected by speed. Furthermore, the analysis shows that CAVs degradations also has a negative effect on linear stability. •The linear stability condition based on three types of vehicles and reaction time is derived.•The impacts of CAVs’ penetration rate and reaction time on stability are analyzed.•The critical penetration rate of CAVs independent of speed is obtained under the impact of DCAVs.