Stability analysis of heterogeneous traffic flow influenced by memory feedback control signal

This paper is aimed at building a framework for string stability analysis of traffic flow mixed with different cooperative adaptive cruise control (CACC) market penetration rates. In addition to the string stability, the fundamental diagram of the mixed flow is also taken into consideration for evaluating the effect of CACC vehicles on capacity. In order to describe the car-following dynamics of real CACC vehicles, the CACC model proposed by PATH is employed, which is validated by real experimental data. The intelligent driver model (IDM) is used as a surrogate car-following model for traditional manual driven vehicles. Based on the guidelines proposed by Ward[Ward J A 2009 Ph. D. Dissertation (Bristol:University of Bristol)], a framework is developed for the analytical investigation of heterogeneous traffic flow string stability. The framework presented considers the instability condition of traffic flow as a linear function of CACC market penetration rate. Following the framework, the string stabilities of the mixed traffic flow under different CACC market penetration rates and equilibrium velocities are analyzed. For fundamental diagram of the heterogeneous traffic flow, the equilibrium velocity-spacing functions of manual vehicles and CACC vehicles are obtained respectively based on car-following model. Then, the fundamental diagram of the density-velocity relationship of the heterogeneous traffic flow is derived based on the definition of traffic flow density. In addition, the theoretical fundamental diagram is plotted to show the property of traffic throughput. The numerical simulations are also carried out in order to investigate the effect of CACC vehicle on the characteristics of fundamental diagram. Besides, sensitivity analyses on CACC desired time gap are conducted for both string stability and fundamental diagram. Analytical studies and simulation results are as follows. 1) The heterogeneous traffic flow is stable for different equilibrium velocities and CACC market penetration rates, if manual driven vehicles are stable. Otherwise, the instability of traditional traffic flow is improved gradually with the increase of the CACC market penetration rate. Additionally, the stability will become better when equilibrium velocity is away from the velocity range of 9.6-18.6 m/s. 2) Because CACC vehicles can travel at free-flow speed in a relatively small headway, CACC vehicles can improve the capacity of heterogeneous traffic flow. 3) The results of sensitivity analysis indicate that with the increase of the CACC desired time gap, the stable region of heterogeneous traffic flow increases. However, the capacity of the fundamental diagram drops. Therefore, the value of the desired time gap should be determined with considering the effects of the two aspects on the heterogeneous traffic flow. It is noted that the CACC model used in this paper is based on the current state-of-the-art real CACC vehicle experiments. In the future, more experimental observations will yield new CACC models. However, the framework presented in this paper can still be used for the analytical investigation of string stability of the heterogeneous traffic flow at that time.

Mixed traffic system with multiple vehicle types and autonomous vehicle platoon: Modeling, stability analysis and control strategy

Modeling and simulation of the car-truck heterogeneous traffic flow based on a nonlinear car-following model

Potential field-based modeling and stability analysis of heterogeneous traffic flow

ABSTRACTThe Cooperative Adaptive Cruise Control (CACC) system is beneficial to the traffic flow stability. However, the CACC mode will degrade to the ACC mode if a CACC vehicle following right behind a manual vehicle. This paper presents a framework for the analytical studies on the stability of the CACC-manual heterogeneous flow. ACC and CACC car-following models validated by the PATH program are used as surrogate models for degraded ACC vehicles and CACC vehicles respectively. The Intelligent Driver Model (IDM) is used as the manual driven car-following model. The stability of heterogeneous traffic flow is investigated theoretically under various CACC market penetration rates. It is found that the degradation of the CACC system leads to the deterioration of flow stability remarkably, which can be avoided by building a complete vehicle-to-vehicle communication environment. Parametric sensitivity analysis is conducted to give some suggestions for the enhancements of the stability of heterogeneous flow.

Stability of heterogeneous traffic considering impacts of platoon management with multiple time delays

Stability analysis of the mixed traffic flow of cars and trucks using heterogeneous optimal velocity car-following model

Modeling and analysis of car-following models incorporating multiple lead vehicles and acceleration information in heterogeneous traffic flow

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

Fundamental diagram and stability analysis for heterogeneous traffic flow considering human-driven vehicle driver’s acceptance of cooperative adaptive cruise control vehicles

Enhancing stability of traffic flow mixed with connected automated vehicles via enabling partial regular vehicles with vehicle-to-vehicle communication function

Analysis on traffic stability and capacity for mixed traffic flow with platoons of intelligent connected vehicles

The introduction of connected autonomous vehicles (CAVs) gives rise to mixed traffic flow on the roadway, and the coexistence of human-driven vehicles (HVs) and CAVs may last for several decades. CAVs are expected to improve the efficiency of mixed traffic flow. In this paper, the car-following behavior of HVs is modeled by the intelligent driver model (IDM) based on actual trajectory data. The cooperative adaptive cruise control (CACC) model from the PATH laboratory is adopted for the car-following model of CAVs. The string stability of mixed traffic flow is analyzed for different market penetration rates of CAVs, showing that CAVs can effectively prevent stop-and-go waves from forming and propagating. In addition, the fundamental diagram is obtained from the equilibrium state, and the flow-density chart indicates that CAVs can improve the capacity of mixed traffic flow. Furthermore, the periodic boundary condition is designed for numerical simulation according to the infinite length platoon assumption in the analytical approach. The simulation results are consistent with the analytical solutions, suggesting the validity of the string stability and fundamental diagram analysis of mixed traffic flow.

Autonomous driving technology and vehicle-to-vehicle communication technology make the hybrid driving of connected and automated vehicles (CAVs) and regular vehicles (RVs) a long-existing phenomenon in the coming future. Among the existing studies, IDM models are mostly used to study the performance of homogeneous traffic flow. To explore the stability of mixed traffic flow, an extended intelligent driver model (IDM) based car-following model was proposed for mixed traffic flow (MTF) with both CAVs and RVs, considering the headway, the speed and acceleration of multiple front vehicles, as well as the response characteristics of RV drivers. Through the linear stability analysis, the criterion for the stability of MTFs was derived, and the relationship among the penetration rate of CAVs, equilibrium velocity and traffic stability in MTF are discussed. Based on the above theoretical model, a numerical simulation was conducted in two typical scenarios of starting and braking. The results showed that, at the microscopic scale, the vehicle in the Cooperative Adaptive Cruise Control (CACC) mode could significantly decelerate in response to the interference from other vehicles in the same traffic environment. At the macroscopic scale, as the penetration rate of CAVs increased, the overall acceleration fluctuation of the traffic flow decreased. At the same penetration rate of CAVs, the higher density of CAVs coincided with the higher stability of the MTF. When the penetration rate of CAVs was 50%, the degree of distribution had the greatest impact on the MTF. When the penetration rate of CAVs exceeded 70%, the degree of distribution had little impact on the MTF. This research can provide basic theoretical support for the management and control of MTF in the future.

To study the impact of on/off-ramps on traffic stability in heterogeneous traffic flow, a novel lattice hydrodynamic model was presented. The new model’s stability condition was determined using the linear stability analysis method. The theoretical results reveal that traffic flow stability is influenced by the proportion of vehicles with different maximum speeds and safe headway, as well as the presence of on-ramps and off-ramps to a certain degree. Through the approximate perturbation method, the mKdV equation and the kink–antikink solution of the traffic density at the jam area are obtained. In order to verify the effectiveness and feasibility of the new model, numerical simulations were conducted to demonstrate on/off ramp effect and different proportions of vehicles which possess bigger maximum velocity or safe space headway affect the traffic stability. The numerical results indicate that in heterogeneous traffic flow scenarios, increasing the ratio of vehicles which possess bigger maximum velocity or bigger safe space headway can lead to a deterioration of traffic stability. The effect of on-ramp could cause traffic instability, while the effect of off-ramp is beneficial for easing traffic congestion.