## 5 Conclusions  
Based on the IDM model, this paper has proposed a car-following model suitable for MTF composed of RVs and CAVs. With consideration of the influences of headway, speed difference, and acceleration difference, the car-following model has focused on the effect of RV drivers with distinct response characteristics on the stability of MTF.  
Through analysis of the stability of homogeneous traffic flows, the criteria for the stability of CACC and ACC vehicles and RVs have been derived. It has been found that, in the case of a homogeneous traffic flow, CACC vehicles can improve the stability of the traffic flow to a great extent. The traffic flow composed of RVs with Type IV drivers is more stable. In other words, a longer headway and a lower speed are more conducive to drivers responding to sudden disturbances. It should be noted that this paper has given mere consideration to the stability of a traffic flow, without considering whether the traffic flow is reduced.  
The stability analysis of the MTF has demonstrated the relationship among the penetration rate, the equilibrium speed, and the stability of CAVs. When the equilibrium speed is below 0.72 m/s or above 5.424 m/s, the MTF is stable regardless of the penetration rate of CAVs; when the penetration rate of CAVs exceeds 10.4%, the MTF can reach stability at any equilibrium speed.  
Figure 8: The averages of acceleration differences of fleets at distinct penetration rates and different distribution degrees of CAVs in the braking scenario.  
The numerical simulation results have shown that under the two typical disturbances of starting and braking, the acceleration fluctuation of CACCs is steadier than that of ACC vehicles and RVs. With the increase in the penetration rate of CAVs, the average of acceleration differences of the whole fleet can be effectively reduced. When the penetration rate of CAVs is below 70%, the centralized arrangement of CAVs can alleviate the fluctuation of traffic flow acceleration to a greater extent than the decentralized arrangement of CAVs. When the penetration rate of CAVs is above 70%, the positive impact of CAVs on the fleet is the same regardless of the distribution degree of CAVs. For RVs, higher stability coincides with the Type VI response characteristics of drivers in the starting scenario, and deceleration fluctuation is less significant for the Type II response characteristics of drivers in the braking scenario.  
In the future management and control of MTF, the penetration rate of CAVs can be increased by promoting CAV to improve the stability of traffic flow. Besides, adjusting the distribution degree of CAVs according to the penetration rate is also a way to improve the stability of MTF. The influence of RV drivers also cannot be neglected, so related departments can improve the comprehensive quality of drivers through publicity and training.  
Conceptualization, K.Z.; Funding acquisition, Y.W. and K.Z.; Investigation, Y.W. and R.X. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Hebei Natural Science Foundation (No. E2019210247), S&T Program of Hebei (No. 21550802D), Science and technology project of Hebei Education Department (No. QN2018238), Key project of Natural Science Research of Anhui Province of Educational (KJ2020A1214), Quality Engineering Project of Colleges and Universities in Anhui Province (2021 jyxm1116), Key Project of Excellent Youth Talent Program in Anhui Universities (gxyqZD2022101), Quality Engineering Project of Fuyang Normal University (College of Information Engineering) (2020 FXJY02), Provincial Natural Science Foundation of Anhui (1908085 QE217). The authors gratefully acknowledge their financial support.  
Not applicable.  
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.  
The authors declared that they have no conflict of interest to this work.