Traffic Flow Instability Research Articles

Response time of mixed platoons with traditional and autonomous vehicles in field trials: impact assessment on flow stability and safety

This study investigates the response times of autonomous vehicles (AVs) equipped with adaptive cruise control (ACC) and traditional human-driven vehicles (TVs) in mixed traffic scenarios. The primary objective is to assess how these response times impact the stability and safety of mixed traffic flow, considering the growing prevalence of ACC technology in vehicles worldwide. Utilising a trajectory dataset from OpenACC totalling 3389.70 s, this research introduces a response time estimation framework that combines cross-correlation and partial autocorrelation techniques. The study calibrates Gazis, Herman, and Rothery's (GHR) car-following model to evaluate mixed traffic flow stability and employs a modified time-to-collision (MTTC) surrogate for safety analysis. The study also delves into the influence of vehicle manufacturer diversity on study outcomes. Key findings reveal that the AVs exhibit significantly longer response times, ranging from 1.10–3.20 s, compared to the 0.30–1.90-second range of traditional vehicles (p value < 0.005). These extended response times in AVs contribute to prolonged traffic flow instability and increased traffic conflicts. Moreover, the type of lead vehicle does not significantly affect the response times of either AVs or TVs (p value > 0.005). The study also highlights that vehicle manufacturer diversity does not substantially affect these response times. Additionally, the examination of fitted GHR parameters underscores AVs’ heightened sensitivity to spacing and relative speed, providing insights into AV dynamics in the presence of mixed traffic.

Reducing strategic uncertainty in transportation networks by personalized routing advice: A route-choice laboratory experiment

One fundamental reason causing traffic flow instability and the difficulties in predicting traffic conditions is strategic uncertainty. This paper experimentally investigated how routing advice influenced strategic uncertainty and analyzed compliance behavior and decision time that might affect strategic uncertainty. Subjects participated in a route-choice game in which they were required to choose among three routes from one origin to one destination. Two routing advice strategies, user-optimal recommendation (UOR) and system-optimal recommendation (SOR), taking into account subjects’ choice inertia, were investigated. The experimental results indicated that (i) UOR could reduce strategic uncertainty and stabilize traffic flow, whereas SOR was counterproductive, (ii) subjects were more likely to comply with UOR compared with SOR and preferred to follow the advice with the same choices as the previous round rather than the route switching advice, (iii) the subjects with faster decisions (intuition) had higher compliance rates and lower travel costs than those with slower decisions (deliberation). Our experimental findings suggest that fairness and psychological factors are crucial in route choice, providing valuable guidance in designing personalized advanced traveler information systems.

Stability Analysis in Mixed-Autonomous Traffic With Deep Reinforcement Learning

The emergence of autonomous driving vehicles on roads has increased the importance of research on autonomous driving in mixed-autonomous traffic. In mixed-autonomous traffic scenarios, it is necessary to comprehend the instability of autonomous vehicles and traffic flow corresponding to the uncertainty level in human-driven behaviors. However, studies of stability analysis in deep reinforcement learning are limited. This study focuses on the impact of deep reinforcement learning based autonomous vehicles in mixed-autonomous traffic from the stability perspective. We define the policy instability and traffic flow instabilities using the entropy of the velocity distributions to quantitatively measure the instability of an autonomous vehicle. Subsequently, we provide mathematical analyses to explain logarithmic growth patterns of instability. Moreover, we propose a novel deep reinforcement learning approach that jointly determines discrete and continuous actions under partial observation. To verify the proposed solution, we perform extensive simulations of various traffic scenarios (e.g., increasing traffic volumes, increasing the number of autonomous vehicles on the road, and setting the multiple uncertainty levels for human-driven behaviors) with ablation studies on reward function. Moreover, we analyze instabilities when human-driven vehicles are modeled using the human-like noisy controller and a policy that imitates actual human-driving data based on imitation learning. The simulation results support the theoretical analysis and confirm that the proposed method is stabler compared to a conventional control-theoretic approach.

Statistical physics of the development of Kerner's synchronized-to-free-flow instability at a moving bottleneck in vehicular traffic.

With the use of simulations of a stochastic microscopic traffic model in the framework of the three-phase traffic theory, we have revealed the statistical physics of a traffic flow instability with respect to a transition from synchronized flow (S) to free flow (F) (Kerner's S→F instability) at a moving bottleneck (MB) occurring through a slow-moving vehicle in vehicular traffic. We have found that the S→F instability can occur at the MB more frequently than at an on-ramp bottleneck. From a comparison of the occurrence of the S→F instability at the MB and on-ramp bottleneck at the same probability of traffic breakdown and the same flow rate it has been found that, whereas the frequency of the S→F instability at the on-ramp bottleneck barely changes, the larger the velocity of the MB, the more frequently the S→F instability occurs at the MB. Contrarily, when the MB velocity decreases considerably, then rather than the S→F instability, in synchronized flow at the MB the classical traffic flow instability leading to the emergence of wide-moving jams (S→J instability) occurs. It has been found that the physics of the intensification of the S→F instability at the MB with the increase in the MB velocity is associated with the increase in the mean space gap (mean time headway) between vehicles in synchronized flow. For this reason, when the MB velocity increases, there is an MB velocity at which the S→F instability dominates the S→J instability: The MB velocity influences considerably on the competition between the S→F and classical traffic flow instabilities in synchronized flow.

Improved STCA Model for Multi-Lane Using Driving Guidance under CVIS

In a multi-lane area, the increasing randomness of lane changes contributes to traffic insecurity and local traffic flow instability. A study on safe lane shifting activity that focuses on threat assessment under real-time knowledge is necessary to enhance smooth vehicle flow. This paper proposed a more comprehensive lane changing guidance rule to investigate the status of surrounding vehicles to accommodate future vehicle-on-road collaborative environments based on these parameters 1) lane change demand and 2) treat assessment function. The collaborative relationships between vehicles are analyzed using a cellular automata model based on their location, velocity, and acceleration. We analyze and examine the relationship between the number of lanes and traffic flow when the road capacity is heavily mined via intelligent lane changing. Our analysis can further provide theoretical guidance for the selection of road expansion mode. Our proposed STCA-L is compared based on the average speed, average flow, lane changing frequency, spatial and temporal pattern of STCA, STCA-I, and STCA-S, and STCA-M under different vehicle densities. The numerical simulation results show that our proposed STCA-L provides the most flexible lane changing guidance in the multi-lanes road. Moreover, the simulated results show that the exponential growth of physical space cannot provide the corresponding increase in the average flow of vehicles.

A Vehicle Control Model to Alleviate Traffic Instability

While bringing convenience to people, the growing number of vehicles on road already cause inevitable traffic congestion. Some traffic congestion happen with observable reasons, but others occur without apparent reasons or bottlenecks, which referred to as phantom jams, are caused by traditional vehicle following model. In order to alleviate the traffic instability caused by phantom jam, several models have been proposed with the development of intelligent transportation system (ITS). these have been proved to be able to suppress traffic instability in the ideal situation. But in road scenarios, uncertainties of vehicle state measurements and time delay caused by on-board sensors, inter-vehicle communications and control system of vehicles will affect the performance of the existing models severely, and cannot be ignored. In this paper, a novel predictable bilateral control model-PBCM, which consists of best estimation and state prediction is proposed to determine accurate acceleration values of the host vehicle in traffic flow to alleviate traffic instability. Theoretical analysis and simulation results show that our model could reduce the influence of the measurement errors and the delay caused by communication and control system effectively, control the state of the vehicles in traffic flow accurately, thus achieve the goal of restrain the instability of traffic flow.

Integrated optimal control strategies for freeway traffic mixed with connected automated vehicles: A model-based reinforcement learning approach

This paper proposes an integrated freeway traffic flow control framework that aims to minimize the total travel cost, improve greenness and safety for freeway traffic mixed with connected automated vehicles (CAVs) and regular human-piloted vehicles (RHVs). The proposed framework devises an integrated action of several control strategies such as ramp metering, lane changing control (LCC) for CAVs and lane changing recommendation (LCR) for RHVs, variable speed limit control (VSLC) for CAVs and variable speed limit recommendation (VSLR) for RHVs with minimum safety gap control measures for lane changing and merging maneuvers. The CAVs are assumed to follow the system control instructions fully and immediately. In contrast, the RHVs would make decisions in response to the recommendations disseminated and also the behaviors of CAVs. The compliance rate of drivers to the LCR is captured by the underlying traffic flow model. A set of constraints is imposed to restrict VSLC/VSLR and LCC/LCR measures from changing too frequently or too sharply on both temporal and spatial dimensions to avoid excessive nuisance to passengers and traffic flow instability. A reinforcement learning based solution algorithm is proposed. First, a control parameterization technique is adopted to reduce the dimension of the original optimal control problem to increase computational efficiency. Then, a gradient-free Cross-Entropy-Method based algorithm is used to search the optimal parameters to circumvent the non-differentiability of the traffic flow model. The feasibility and effectiveness of the proposed framework are illustrated via numerical examples for a variety of penetration rates of CAVs under various traffic conditions. A sensitivity analysis is conducted to demonstrate the impacts of several important parameters such as the reaction time of the CAVs. It is found that the integrated control strategy can reduce the total travel cost by reducing the lane changing maneuvers and vehicles queuing at the bottleneck meanwhile smooth the traffic flow and suppress the adverse impact of shockwaves. The effect of ramp metering is not significant when the penetration rate of CAVs is high enough. Speed harmonization (with minimum gap control) in conjunction with LCC/LCR would be a better integrated control strategy under high penetration rate of CAVs.

Effects of static bottlenecks on traffic flow in urban road network

Existing traffic flow models do not consider the effects of road static bottlenecks on traffic flow. In this paper, a modified macroscopic continuum model for traffic flow on urban road network with static bottlenecks is presented. The model takes into account the fluctuations of traffic flow considering static bottlenecks during the morning peak period. The model results show that existence of static road bottlenecks with various configurations cause traffic flow instabilities. This phenomenon lead into stop-and-go traffic flow conditions under the moderate density and reduction of the traffic system’s efficiency. Furthermore, results show that an increase in traffic density is accompanied by a significant decrease of speed which adversely influences performance of roadway and decrease the traffic system’s efficiency and thus resulting to the occurrence of congestions. The methodological aspects of the study and results will enable traffic engineers and planners to assess and improve existing urbanroad networks.&#x0D; Keywords: Traffic flow, Bottlenecks, stability, Stop-and-go traffic, System’s efficiency, Congestion.

Coordinated management and control of autonomous traffic systems

The rapid development of autonomous driving technology in the past decade has brought unprecedented opportunities and challenges to the coordinated management and control of traffic systems. Compared to human drivers, autonomous vehicles (AV) are equipped with shorter reaction time and better situational awareness, promising to increase the throughput of existing road networks, dramatically improve safety and robustness, and reduce the instability of vehicular traffic flow. Moreover, controlling the route, lane and even trajectory of every AV in a network could effectively eliminate excessive congestion caused by “selfish” human travel and driving behaviors. This ability to coordinate the entire AV fleet thus has important implications for planning the next-generation “smart” road systems. In this paper we consider the coordinated management and control of AV fleets from both macroscopic and microscopic perspectives. The former focuses on how coordinating macroscopic travel decisions, such as route, departure time and mode (e.g., ridesharing vs. micro-transit), might help reduce traffic congestion caused by what is widely known as the price of anarchy in transportation. While the underlying idea is simply moving the system from a user equilibrium state to a system optimal one, the challenge is to model the complex interactions between autonomous and human-driven vehicles, to anticipate how human drivers would behave in such an environment, and to design effective, fair and practical schemes to achieve the goal. What we learn from these efforts could potentially impact infrastructure planning, especially in terms of whether and how AVs should be separated from human-driven vehicles on road. On the other hand, because AVs can be programmed to remember and execute all maneuvers in a journey, much like the auto pilot for airplanes and high-speed trains, the entire trajectory of their journey, not just the aforementioned macroscopic travel decisions, may be targeted for the purpose of traffic management. Here, the focus is to manage the microscopic maneuvers (e.g., lane changing and gap-keeping behaviors) of a fleet of AVs to improve the performance of the road network. An interesting analogy can be drawn between this task and the task of managing a railway network in which many fast moving trains operate. Accordingly, the lanes on highways may be viewed as “virtual tracks” in an imaginary railway network. There is an extensive literature on railway operations from which one can draw useful mathematical tools and empirical results. A primary challenge to operationalize this analogy is the enormous computational requirement caused by both the sheer size of the problem, as well as the short time framework (seconds or shorter) within which such a coordinated management and control decision must be made.

Combined effects of drivers’ disturbance risk preference heterogeneity and the nearest following vehicle headway on traffic flow instability: Analytical studies

Driver’s disturbance risk preference is defined as the driver’s reaction degree to the disturbance, which is a kind of the driver’s attributes and can be expressed by the disturbance risk preference coefficient. This paper proposes a new car-following model and firstly attempts to analytically investigate the combined effects of drivers’ disturbance risk preference heterogeneity and the nearest following vehicle headway on traffic flow instability under some specific traffic scenarios. Solution of the model yields many insights including the following: (1) when drivers’ disturbance risk preference increases from the following driver to the preceding driver, traffic flow instability increases, and the bigger the disturbance risk preference coefficient ratio of the preceding driver’s coefficient to the following driver’s coefficient, the bigger the increasing effect and vice versa; at this scenario, the nearest following vehicle headway increases traffic flow instability; (2) when drivers’ disturbance risk preference is homogeneous, drivers’ disturbance risk preference and the nearest following vehicle headway have no effects on traffic flow instability; (3) when drivers’ disturbance risk preference reduces from the following driver to the preceding driver, for the general traffic situation, traffic flow instability reduces, and the smaller the disturbance risk preference coefficient ratio of the preceding driver’s coefficient to the following driver’s coefficient, the bigger the reducing effect and vice versa; at this scenario, if the coefficient ratio reduces from the following to the preceding or is homogeneous, the nearest following vehicle headway increases traffic flow instability, otherwise, the effects of the nearest following vehicle headway on traffic flow instability cannot be confirmed.

Macroscopic model for multi-anticipation self-driving cars

Self-driving cars technology and vehicle connectivity enable self-driving cars to precisely receive information of many cars leading them. By multi-anticipation, a flow of self-driving car is proved to be more stable than without multi-anticipation. The instability of traffic flow can cause a traffic jam as a little velocity fluctuation is amplified. In this work, we discuss the macroscopic effect of parameters in the microscopic model for a self-driving car. Those parameters are the number of the vehicle the car anticipate (field size) and weight for anticipation with the leadings (strength factor). The macroscopic model is derived from the microscopic model. We obtained a partial derivative equation that describe how the velocity fluctuation change through time. According to our model, these two variables play a crucial role in the traffic flow harmonization. Comparison between each model was carried out and discussed.

On the Chain Stability of Bilateral Control Model

In this paper, we study the chain stability of vehicles under bilateral control (BCM), and prove that vehicles under bilateral control are chain stable, i.e., all input perturbations to the chain decay exponentially (with the length of the chain). Chain stability analysis tells us how vehicles under bilateral control will act in traffic when mixed with cars driven by human drivers. It shows that self-driving cars using bilateral control can reduce traffic flow instabilities in mixed traffic. Indeed, chains of BCM vehicles become perturbation-consuming dampers when inserted in traffic, since they split chains of human-driven vehicles and prevent perturbations from being transmitted from one chain of car-following cars to the next. Thus, today's traffic can be improved greatly by the insertion of BCM vehicles. The simulation results validate the theoretical analysis.

Multinode Bilateral Control Model

Bilateral control can suppress traffic flow instabilities. The simplest form of bilateral control uses information about the relative positions and relative velocities of leading and trailing vehicles. In this paper, we provide a multinode version of bilateral control, in which information about the state of more than just the immediately leading and trailing cars is used. In this mode of control, the question arises: “How much weight should information about vehicles at different positions be given?” Two different methods—a Taylor series approach and a least-squares approach—are explored. We show that the least-squares approach generates sets of coefficients that can damp out low-frequency components of perturbations faster. This means that traffic under multinode bilateral control will approach an equilibrium state more rapidly than under the traditional version of bilateral control. Simulation results confirm our analysis.

An extended macroscopic model for traffic flow on curved road and its numerical simulation

In this paper, we propose a full angular velocity difference model by introducing the angular velocity and displacement on curved road. The relation of transformation of microscopic model in form of angular variables into macroscopic one is deduced. Consequently, a corresponding continuum traffic flow model on curved road is derived. The critical condition for the steady traffic flow is obtained. Meanwhile, the stability condition of this continuum traffic model is compared with one of the microscopic model and lattice hydrodynamic traffic model on curved road. By nonlinear analysis, the KdV–Burgers equation which describes the density wave near the neutral stability line is derived. Furthermore, the numerical simulations are carried out to verify the validity of this macroscopic traffic. Results indicate the radius of curved road have a great impact on the formation of traffic jams. Local clustering effects in the state of instability of traffic flow give rise to the stop&go traffic jams. Numerical simulation also indicates the unstable region is shrunken under the increasing strength of the angular velocity difference.

Effects of the Driver’s Disturbance Risk Preference Heterogeneity and its System Thresholds on Traffic Flow Instability

Driver’s disturbance risk preference is defined as the driver’s reaction degree to the disturbance, which is one kind of driver’s attributes and can be expressed by the disturbance risk preference coefficient. This paper first attempts to investigate the effects of the driver’s disturbance risk preference heterogeneity and its system thresholds on traffic flow instability based on a car-following model. An analytical analysis is conducted to obtain the calculation formulas of traffic system unstable threshold and traffic system instability eliminated threshold and traffic flow unstable region headway range, and the calculation method of the probability of traffic congestion caused by a small disturbance under some traffic scenarios, and then, the numerical analysis is carried out to present the main contributions and findings of this paper. It is shown that: 1) when the disturbance risk preference coefficient ratio between the preceding vehicle driver and the following vehicle driver is not less than the traffic system unstable threshold, the traffic flow is always unstable; 2) when the disturbance risk preference coefficient ratio between the preceding vehicle driver and the following vehicle driver is not bigger than the traffic system instability eliminated threshold, the traffic flow instability is completely eliminated; and 3) when the disturbance risk preference coefficient ratio between the preceding vehicle driver and the following vehicle driver is bigger than the traffic system instability eliminated threshold and less than the traffic system unstable threshold, such as for the general traffic situation, the smaller the coefficient ratio, the traffic flow instability is smaller, and vice versa.

Wave Equation of Suppressed Traffic Flow Instabilities

Traffic congestion wastes fuel and commuters’ time, and adds to CO2 emissions. Stop-and-go traffic instabilities can be suppresses using bilateral control—which differs from “car following” and adaptive cruise control in that, counter-intuitively, it uses information about the following vehicle (as well as about the leading vehicle). Stability can be proven mathematically, and can be demonstrated in simulation. A physical analog of a sequence of vehicles using bilateral control is a chain of masses connected by springs and dampers—a system which is inherently stable, since it lacks an external energy source. Here, in order to further understand bilateral control and its capacity to suppress instabilities, we move from a microscopic view (interaction of individual vehicles) to a macroscopic view (densities and flow rates). This leads us to the damped wave equation governing traffic under bilateral control. That equation allows us to determine the speed of propagation of disturbances, as well as their rate of decay. The equation is also useful in fine tuning parameters of bilateral control systems.

An extended continuum traffic model with the consideration of the optimal velocity difference

In this letter, we derived an extended continuum model from a car-following model with consideration of the optimal velocity difference called the relative optimal velocity via employing the transformation relation from microscopic variables to macroscopic ones. The stability condition of this continuum traffic model is obtained by performing linear stability analysis. Results show that the optimal velocity difference helps to improve the stability of traffic flow. We make use of the upwind finite difference scheme for simulation. The effects of the optimal velocity difference (the relative optimal velocity) and the velocity difference (the optimal velocity) on local clustering effect and instability are studied and compared each other, respectively. The spatiotemporal evolution patterns of traffic flow for the different initial density, strength of the optimal velocity difference and the velocity-difference are obtained. Their space–time diagrams reveal the local clustering effect induced by the instability of traffic flow and generate the stop&go traffic jams. Numerical simulation result indicates the unstable region is shrunken under the effect of the optimal velocity difference (the relative optimal velocity) and/or the velocity difference (the optimal velocity).

Experimental and empirical investigations of traffic flow instability

Traffic instability is an important but undesirable feature of traffic flow. This paper reports our experimental and empirical studies on traffic flow instability. We have carried out a large scale experiment to study the car-following behavior in a 51-car-platoon. The experiment has reproduced the phenomena and confirmed the findings in our previous 25-car-platoon experiment, i.e., standard deviation of vehicle speeds increases in a concave way along the platoon. Based on our experimental results, we argue that traffic speed rather than vehicle spacing (or density) might be a better indicator of traffic instability, because vehicles can have different spacing under the same speed. For these drivers, there exists a critical speed between 30km/h and 40km/h, above which the standard deviation of car velocity is almost saturated (flat) along the 51-car-platoon, indicating that the traffic flow is likely to be stable. In contrast, below this critical speed, traffic flow is unstable and can lead to the formation of traffic jams. Traffic data from the Nanjing Airport Highway support the experimental observation of existence of a critical speed. Based on these findings, we propose an alternative mechanism of traffic instability: the competition between stochastic factors and the so-called speed adaptation effect, which can better explain the concave growth of speed standard deviation in traffic flow.

The Intelligent Driver Model with stochasticity – New insights into traffic flow oscillations

Traffic flow oscillations, including traffic waves, are a common yet incompletely understood feature of congested traffic. Possible mechanisms include traffic flow instabilities, indifference regions or finite human perception thresholds (action points), and external acceleration noise. However, the relative importance of these factors in a given situation remains unclear. We bring light into this question by adding external noise and action points to the Intelligent Driver Model and other car-following models thereby obtaining a minimal model containing all three oscillation mechanisms. We show analytically that even in the subcritical regime of linearly stable flow (order parameter ϵ < 0), external white noise leads to spatiotemporal speed correlations “anticipating” the waves of the linearly unstable regime. Sufficiently far away from the threshold, the amplitude scales with (−ϵ)−0.5. By means of simulations and comparisons with experimental car platoons and bicycle traffic, we show that external noise and indifference regions with action points have essentially equivalent effects. Furthermore, flow instabilities dominate the oscillations on freeways while external noise or action points prevail at low desired speeds such as vehicular city or bicycle traffic. For bicycle traffic, noise can lead to fully developed waves even for single-file traffic in the subcritical regime.

Smart Driving System for Improving Traffic Flow

Traffic congestion on road networks is one of the most significant problems that is faced in almost all urban areas. Driving under traffic congestion compels frequent idling, acceleration, and braking, which increase energy consumption and wear and tear on vehicles. By efficiently maneuvering vehicles, traffic flow can be improved. An Adaptive Cruise Control (ACC) system in a car automatically detects its leading vehicle and adjusts the headway by using both the throttle and the brake. Conventional ACC systems are not suitable in congested traffic conditions due to their response delay. For this purpose, development of smart technologies that contribute to improved traffic flow, throughput and safety is needed. In today’s traffic, to achieve the safe inter-vehicle distance, improve safety, avoid congestion and the limited human perception of traffic conditions and human reaction characteristics constrains should be analyzed. In addition, erroneous human driving conditions may generate shockwaves in addition which causes traffic flow instabilities. In this paper to achieve inter-vehicle distance and improved throughput, we consider Cooperative Adaptive Cruise Control (CACC) system. CACC is then implemented in Smart Driving System. For better Performance, wireless communication is used to exchange Information of individual vehicle. By introducing vehicle to vehicle (V2V) communication and vehicle to roadside infrastructure (V2R) communications, the vehicle gets information not only from its previous and following vehicle but also from the vehicles in front of the previous Vehicle and following vehicle. This enables a vehicle to follow its predecessor at a closer distance under tighter control.