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As one key basis of traffic flow theory, the fundamental diagram (FD) has wide application in traffic management and control. However, the FD of mixed human-driven vehicles (HVs) and cooperative adaptive cruise control (CACC) vehicles remains unclear. The deterministic and stochastic FD of mixed traffic was obtained. First, the longitudinal control model (LCM) and connected LCM (CLCM) were selected as the car-following model of HVs and CACCs. Next, in deterministic simulation, the mathematical expression of mixed-traffic FD was conducted considering the CACC penetration rate and platooning intensity. Then, the stochastic distribution of perception and response time calibrated by the vehicle trajectory data set NGSIM was introduced to derive the stochastic FD. After that, in stochastic simulation, taking the variance and computation effort into account, the optimal number of simulated vehicles to obtain steady-state FD was obtained. The impact of CACC penetration rates and platooning intensity was also explored. It revealed that the optimal number of simulated vehicles is 400. CACC can improve the capacity and critical density of highways. In mixed traffic, due to the large variance of HV driver response time, scattering remains unchanged regardless of CACC penetration when there are enough vehicles. Pure CACC traffic has minimum scattering. More importantly, the proposed framework is applicable to other CACC, adaptive cruise control (ACC), and HV car-following models, including further experimental models. [ABSTRACT FROM AUTHOR]

String stability is important for understanding traffic flow dynamics, while its analytical study for mixed traffic is deficient. We focus on an analytical framework on string stability of mixed traffic consisting of cooperative adaptive cruise control (CACC), adaptive cruise control (ACC), and human vehicles. The analytical framework was conducted based on generalized car-following model formulations of the three vehicular types. Then string stability criterions of one-class traffic flow, mixed traffic flow, and local CACC/ACC platoons were derived. Taking into account the mixed flow with partial degenerations of CACC and three concrete car-following models, an example application was studied. The example application analyzed the string stability from the perspectives of the homogeneous flow, the mixed traffic flow, and the local CACC/ACC platoon, respectively. The example application also studied balance between stability and capacity for the mixed traffic with CACC vehicles. Results show the usefulness of the proposed analytical framework, in term of not only analyzing string stability but also providing suggestions for dynamic regulations of CACC/ACC management strategy to balance string stability and traffic capacity for the mixed CACC-human flow. [ABSTRACT FROM AUTHOR]

In the environment of intelligent connected vehicles, the mixed traffic flow consisting of human-driven vehicles (HDVs), connected and automated vehicles (CAVs), and their platoons will coexist for a long time. Exploring and discovering the operational rules of mixed traffic flow is the foundation for its management and control. This study delves into the distinct characteristics of various vehicles within a mixed traffic environment, particularly focusing on HDVs, CAVs, and CAV platoons. Drawing on the psychological predisposition of HDVs to maintain a prudent following distance, we introduce a discrete motion safety distance model to establish the longitudinal movement rule for HDVs. Furthermore, a longitudinal movement rule for CAVs is established based on their ability to keep a constant headway using Adaptive Cruise Control (ACC) and Cooperative Adaptive Cruise Control (CACC), alongside meeting specific speed and spacing criteria for platoon movement. On this basis, the paper proposes a cellular automaton model for single-lane mixed traffic flow that accounts for CAV platoon length and the decision-time disparity between HDVs and CAVs. The simulation results show that an increased proportion of CAVs can enhance the traffic capacity, elevate average speed, extend average platoon length, and reduce the congestion ratio and CACC degradation rate. Notably, in scenarios where the CAV proportion p > 0.7, the flow-density graph shows a trapezoidal shape, with the majority of CAVs in the traffic flow synchronizing their movements in CACC mode. Even when vehicular density surpasses the optimum threshold, the traffic flow maintains high-speed operation until reaching a critical congestion point, whereupon velocities precipitously decline. Through sensitivity analysis aimed at understanding the impact of maximum platoon length, it has been observed that, for CAV proportions below 0.7, variations in maximum platoon length negligibly impact traffic capacity, velocity, CACC degradation, and congestion levels. Only in scenarios dominated by CAVs does extending platoon length restrictions significantly enhance performance. However, as the maximum platoon length increases, the gains in traffic capacity, speed, CACC degradation rate, and congestion ratio diminish. When the platoon length of CACC exceeds a certain threshold, there will not be a significant improvement in traffic capacity or speed. [ABSTRACT FROM AUTHOR]

With the emerging application of low-level driving automation technology, heterogeneous traffic flow mixed with human-driven vehicles and low-level autonomous vehicles is dawning. In this context, it is imperative to investigate its effect on mixed traffic flow. As a key component for adaptive cruise control (ACC) which is a practical low-level application of driving automation, the time gap policy determines the dynamic of ACC-equipped vehicles and plays a crucial role in traffic flow stability and efficiency. There are two main time gap policies used for ACC at present, namely, constant time gap (CTG) policy and variable time gap (VTG) policy. In this study, we carried out a detailed comparison between these time gap policies to investigate their potential effect on mixed traffic flow, where the analytical- and simulation-based approaches are both considered. Analytical results show that VTG policy is superior to CTG policy in stabilizing the mixed traffic flow. In addition, numerical simulations are also conducted and simulation results further support the analytical results. As for throughput, there is no difference between CTG policy and VTG policy in analytical progress when the same time gap is set at the equilibrium. However, simulation results based on an on-ramp scenario show that the throughput of mixed traffic flow with VTG policy is slightly higher than that of CTG policy. Meanwhile, the scatter of mixed traffic flow with VTG policy in the flow-density diagram gradually clusters in the middle range of density (i.e., 20–40 veh/km) with the increase of the penetration rates of ACC vehicles, where the traffic flow operates more efficiently. These results indicate that VTG policy is better than CTG policy when designing controllers for ACC in the context of traffic flow operation and control. [ABSTRACT FROM AUTHOR]

Considering the influence of slope sections and random degradation of the communication function of cooperative adaptive cruise control vehicles and the effect of the cooperative adaptive cruise control vehicle group driving, a linear stability criterion for heterogeneous traffic flow composed of cooperative adaptive cruise control vehicles and humanly-driven vehicles on slopes is derived, and a parameter sensitivity analysis is carried out. On this foundation, the safety of traffic flow on two-lane roads up and down hills is simulated while considering the lane-changing behavior of automobiles. The stability study shows increased cooperative adaptive cruise control vehicle penetration and uphill gradient will help improve traffic flow stability. In contrast, the increase in the downhill slope will intensify the transmission amplitude of the disturbance. When vehicle starting sensitivity is 2.5, and the gradient is 60, the minimum cooperative adaptive cruise control vehicle penetration required for mixed traffic flow to maintain stability on a downhill at any initial equilibrium speed is 85%, and the minimum penetration required on an uphill is 73%, and this proportion decreases with the increase in the uphill gradient and increases with the rise in the downhill slope. According to the safety study, increasing cooperative adaptive cruise control vehicle penetration and implementing lane-changing rules will improve traffic flow safety. Compared with the straight section, under the same conditions, the traffic flow safety of the uphill section is the best, and the safety of the downhill section is poor, which is consistent with the stability analysis results. This study is of great significance for future traffic control strategies for mountain roads. [ABSTRACT FROM AUTHOR]

The emergence of automated vehicles may have significant impacts on traffic flow. While many studies suggest that fully automated vehicles can improve traffic flow by changing their macroscopic characteristics at different market penetration rates, recent studies show that partially automated vehicles (e.g., adaptive cruise control vehicles) commercially available on the market may negatively impact the traffic flow. With this in mind, existing traffic control strategies, such as ramp metering, may require further modification due to the change of macroscopic traffic flow characteristics in the presence of mixed autonomy traffic. However, the extent to which the ramp metering control algorithm will have to change in response to mixed autonomy traffic is still an open question. In this study, we first formulate the fundamental diagram analytically for mixed autonomy traffic, which is dependent on the market penetration rates of automated vehicles. Next, we model and simulate the composite traffic flow with a mixed autonomy macroscopic traffic flow model, and modify a standard ramp metering control strategy to optimize operations under the new flow conditions. The simulation results show that the total time spent is reduced by 4% compared to the scenario controlled with a standard ramp metering control strategy, suggesting a higher highway throughput is obtained at a merge section when leveraging the modified ramp metering controller. The results also show that the system-wide total delay is reduced by 11% compared to the scenario controlled with a standard ramp metering control strategy, implying the proposed ramp metering control strategy is efficient. • Traffic fundamental diagram depends on the fraction of automated vehicles. • Traffic makeup has potential to degrade traditional ramp metering control. • Ramp metering designed to consider automated vehicles in the flow. [ABSTRACT FROM AUTHOR]

Stop-and-go waves are easily caused by unstable traffic due to the collective behavior of human drivers, resulting in higher vehicle fuel consumption and emissions. In this article, we develop a general approach to synthesizing feedback controllers of autonomous vehicles (AVs) for smoothing unstable nonlinear mixed traffic flow, consisting of AVs and human-driven vehicles (HVs). In the context of traffic smoothing and stabilization, prior studies have mainly focused on analyzing string stability of specific car-following models linearized at flow equilibrium points. By contrast, we are interested to analytically synthesize appropriate feedback controllers of AVs for smoothing nonlinear mixed traffic in its general functional forms, covering a broad class of deterministic car-following models commonly seen in the literature. Specifically, by leveraging feedback control theory AVs are controlled to operate in such a way that they closely track a virtual speed profile, i.e., a subtler version of the disturbance resulting from the immediate preceding vehicle. Thus, traffic waves are reduced when propagating backward across controlled AVs. Based on the general functional form of car-following dynamics, we derive a class of effective additive AV controllers that are proven to be able to ensure convergence in tracking desired speed profiles, leading to smoother traffic. In addition, a set of sufficient conditions is devised for guaranteeing car-following safety. More importantly, head-to-tail string stability of the mixed traffic is likely to be achieved with a sufficient market penetration rate (MPR) of AVs. Notably, unlike many existing studies the feedback controllers synthesized for AVs require only local traffic information without having to rely on high degrees of vehicle connectivity, and the rate of smoothing mixed traffic is readily tunable, which is useful for practical implementations. The proposed approach is further illustrated with a theoretical intelligent driver model (IDM) and commercially available adaptive cruise control (ACC) vehicles represented by a well calibrated IDM. Extensive numerical results are presented to show the effectiveness and robustness of the feedback controllers synthesized for AVs on smoothing nonlinear mixed traffic. • Virtual tracking for autonomous vehicles to smooth nonlinear traffic • Applicable to a broad class of deterministic car-following dynamics • Only local traffic information is required for controller synthesis of autonomous vehicles [ABSTRACT FROM AUTHOR]