Traffic Instability Research Articles

A novel stochastic second-order macroscopic continuum traffic flow model for traffic instability

Dispersion of vehicle speed often causes traffic instability, which affects traffic efficiency and safety. Previous studies have demonstrated that fluctuations near the steady-state equilibrium of traffic flow can be attributed to the stochasticity of traffic system leading by large vehicle speed dispersion. However, the intrinsic mechanisms between fluctuations of traffic flow and vehicle speed dispersion need further discussion. Therefore, a novel stochastic extended speed gradient model based on the fast-and-low speed vehicles is proposed to describe their relationships in this paper. Firstly, a speed-dependent stochastic process is characterized for the stochastic deviation of velocity dispersion, and a stochastic high-order macroscopic traffic flow model is constructed for fast and low speed vehicles. Secondly, using Lyapunov stability theorem and its derivatives, the linear stability criterion of the proposed model is derived. The theoretical results also indicate that the steady-state equilibrium of traffic flow is profoundly affected by the traffic flow initial density, penetration rate of fast and low speed vehicles, and noise intensity. Hence, simulations are implemented from the above three parameters. It can be found that the critical values of initial density affecting traffic flow stability are pursued, and some detailed tendencies of traffic flow are explored for different parameters. Finally, the model is also calibrated and validated through real data, and the impact of fast-and-low-speed vehicles on traffic instability at ramp-merging area is analyzed. Numerical experiments show that the stochastic traffic flow model proposed in this paper well reproduces the traffic oscillations occurring in real traffic.

A learning optimization for resilience enhancement of risk-informed traffic control system with hazardous materials transportation under uncertainty

A learning optimization is proposed to enhance overall resilience of interdependent traffic systems with hazardous materials (hazmat) transportation under uncertainty. To this end, three interconnected systems are proposed against traffic dynamics and congestion in a complex environment of regular traffic and hazmat carriers incurred with time-varying travel cost. In order to increase control resilience against traffic instability, a reinforcement learning hazmat network is proposed. In order to efficiently improve computation resilience against disruption of risk uncertainty, a resilience-aware learning optimization is proposed to obtain optimal solutions. In order to demonstrate computational performance of proposed approach, numerical experiments are performed at a real-world city under various kinds of traffic conditions. Computational comparisons are numerically made with stochastic and robust optimization at large-scale traffic control systems. As it reported, the proposed learning-based optimization can better greatly enhance overall traffic system resilience, control resilience and computation resilience compared to other models under mixed risk of hazmat transportation and uncertain demand.

Nonlinear Analysis of an Extended Heterogeneous Lattice Hydrodynamic Model Considering on/off-Ramps

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.

A Deep Reinforcement Learning Approach for Efficient, Safe and Comfortable Driving

Sensing, computing, and communication advancements allow vehicles to generate and collect massive amounts of data on their state and surroundings. Such richness of information fosters data-driven decision-making model development that considers the vehicle’s environmental context. We propose a data-centric application of Adaptive Cruise Control employing Deep Reinforcement Learning (DRL). Our DRL approach considers multiple objectives, including safety, passengers’ comfort, and efficient road capacity usage. We compare the proposed framework’s performance to traditional ACC approaches by incorporating such schemes into the CoMoVe framework, which realistically models communication, traffic, and vehicle dynamics. Our solution offers excellent performance concerning stability, comfort, and efficient traffic flow in diverse real-world driving conditions. Notably, our DRL scheme can meet the desired values of road usage efficiency most of the time during the lead vehicle’s speed-variation phases, with less than 40% surpassing the desirable headway. In contrast, its alternatives increase headway during such transient phases, exceeding the desired range 85% of the time, thus degrading performance by over 300% and potentially contributing to traffic instability. Furthermore, our results emphasize the importance of vehicle connectivity in collecting more data to enhance the ACC’s performance.

Model of vehicle interactions with autonomous cars and its properties

<p style='text-indent:20px;'>We study a hierarchy of models based on kinetic equations for the descriptions of traffic flow in presence of autonomous and human–driven vehicles. The autonomous cars considered in this paper are thought of as vehicles endowed with some degree of autonomous driving which decreases the stochasticity of the drivers' behavior. Compared to the existing literature, we do not model autonomous cars as externally controlled vehicles. We investigate whether this feature is enough to provide a stabilization of traffic instabilities such as stop and go waves. We propose two indicators to quantify traffic instability and we find, with analytical and numerical tools, that traffic instabilities are damped as the penetration rate of the autonomous vehicles increases.</p>

A Statistical Simulation Model for the Analysis of the Traffic Flow Reliability and the Probabilistic Assessment of the Circulation Quality on a Freeway Segment

Measuring the traffic quality and congestion level is fundamental in highway engineering, and several decades of studies and research have pursued this specific objective, especially for freeways. Nowadays, smart technologies on personal devices and information shared by users have made available various online information platforms that provide dynamic representations of the use of the road network. If, on the one hand, these tools provide a simple and direct representation of the quality of circulation, on the other hand, their aggregated information is only partial for those dealing with traffic and highway engineering. This branch of engineering relies on multidimensional knowledge of traffic flow phenomena, and only through their in-depth knowledge, we can assess traffic quality and congestion risk. After identifying the different approaches for analyzing in quantitative terms the traffic quality on the freeway, the paper deepens the reliability approach. From this point of view, the paper aims to unite the two perspectives in the literature, namely, the probabilistic analysis of traffic instability with the characterization of speed random processes and the analysis of breakdowns with the survival analysis. For this purpose, the work outlines a procedure based on the estimation and simulation of ARIMA models for speed random processes in a freeway section, particularly on the leftmost lane, to assess the traffic reliability function. Applying the Product Limit Method to the Monte Carlo simulation results makes it possible to obtain probabilistic assessments of congestion, considering the Level of Service density limits defined in the Highway Capacity Manual. Its application to a case study makes it possible to illustrate the application of the method, which can be easily applied to historical and near-real-time data using a continuous flow of information.

Stochastic factors and string stability of traffic flow: Analytical investigation and numerical study based on car-following models

The emergence dynamics of traffic instability has always attracted particular attention. For several decades, researchers have studied the stability of traffic flow using deterministic traffic models, with less emphasis on the presence of stochastic factors. However, recent empirical and theoretical findings have demonstrated that the stochastic factors tend to destabilize traffic flow and stimulate the concave growth pattern of traffic oscillations. In this paper, we derive a string stability condition of a general stochastic continuous car-following model by the mean of the generalized Lyapunov equation. We have found, indeed, that the presence of stochasticity destabilizes the traffic flow. The impact of stochasticity depends on both the sensitivity to the gap and the sensitivity to the velocity difference. Numerical simulations of three typical car-following models have been carried out to validate our theoretical analysis. Finally, we have calibrated and validated the stochastic car-following models against empirical data. It is found that the stochastic car-following models reproduce the observed traffic instability and capture the concave growth pattern of traffic oscillations. Our results further highlight theoretically and numerically that the stochastic factors have a significant impact on traffic dynamics.

System-size dependence of a jam-absorption driving strategy to remove traffic jam caused by a sag under the presence of traffic instability

Sag is a road section where a downhill changes into an uphill, and is a highway bottleneck. We consider a system in which all vehicles are connected, and run on a single-lane road with a sag. We propose a simple strategy for removing each traffic jam caused by the sag. Our strategy assigns a vehicle upstream of the jam front to perform the jam-absorption driving (JAD): running toward the predicted goal, and finally removing the jam. We use a microscopic car-following model possessing the traffic instability, an acceleration model against the road gradient of a sag, and an instantaneous fuel consumption model. Our main goal is to elucidate the influence of the system size (the number of vehicles in the system) on our strategy. By increasing the system size from 500 to 10000 vehicles, we have found the following results for the average total travel time per vehicle, and the average total fuel consumption per vehicle. Our strategy can reduce the former with a slightly increasing rate of reduction. Our strategy can reduce the latter with a rate of reduction which decreases and becomes roughly constant. Optimal spatiotemporal scales of JAD for the former and the latter become roughly constant, respectively. Minimizing the former and the latter simultaneously is not possible. Not only vehicular traffic flow, but also the collective dynamics of other self-driven particles (such as ships, swarm robots, and pedestrians) lined up in a single column, and passing through a bottleneck can be modeled using our strategy.

Network traffic instability with automated driving and cooperative merging

Connected and/or automated vehicles (CAVs or AVs) have been shown to dampen stop-and-go waves in mixed autonomy traffic, thus improving string stability. However, their effects on network traffic instability due to turning and merging maneuvers are less known. In this paper, we characterize such effects using the macroscopic or network fundamental diagram (MFD or NFD). We first revisit and extend the theoretical two-ring network, and then develop an integrated modeling and simulation framework that explicitly accounts for different microscopic traffic models of human-driven vehicles (HVs), AVs, and CAVs. Results suggest that network traffic instability resulting from turning and merging maneuvers persists even if vehicles become automated and cooperative. When the turning probability is low, the presence of CAVs does not induce a significant change in the bifurcation point of the NFD. Scatter in both link fundamental diagrams (FDs) and NFDs, however, reduces resulting in higher and more stable network flows. When the turning probability is high, AVs without cooperation turn out to worsen network traffic stability, giving rise to an NFD that undergoes bifurcation long before the theoretical critical network density is reached. This is in contrast to the case with CAVs that perform cooperative merging. Results also suggest that, whenever the penetration rate of CAVs is too low or too high, making HVs connected is not as effective in delaying the bifurcation of the NFD as when the penetration rate is moderate. We further compare cooperative merging with adaptive signal control and adaptive driver routing to demonstrate its benefits in improving network flows. Simulation experiments on a real motorway segment in Sydney, Australia are also performed to confirm our findings.

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.

Understanding the effects of vehicle platoons on crash type and severity

Crash type is an informative indicator to infer driving behaviors and conditions that cause a crash. For example, rear-end and side-swipe crashes are typically caused by improper vehicle interaction such as sudden lane-changing or speed control while hit-object crashes are likely the result of a single driver’s mistake. This study investigated the impact of vehicles travelling as a group (platoon) and its configuration (i.e., types of vehicles consisting of the platoon) on crash type and severity since the vehicles could affect each other when travelling in close proximity. This study applied Generalized Structure Equation Modeling (GSEM) to capture the complex relationships among the various crash factors such as traffic condition, driver characteristics, environmental conditions, and vehicle interaction to the crash attributes including type and severity.This study collected over 3 million individual vehicle data from 39 traffic count sites in California to estimate the vehicle interactions and driving behaviors. The microscopic traffic data are matched to 1417 crash reports. Results showed that vehicles traveling in platoons are associated with more rear-end and side-swipe crashes. Speed difference in the platoon had a positive effect on hit-object crashes if the platoon comprises vehicles of homogeneous type – either trucks or non-trucks. In addition, human factors such as age and gender were identified as significant influential factors in all type of crashes, however truck involvement particularly played an important role amongst side-swipe crashes. Crash severity was negatively affected by total flow, and rear-end crashes were more likely to be severe compared with hit-object crashes. Based on findings, this study suggests practical operational strategies to reduce traffic instability associated with platooned vehicle patterns. Understanding the high-risk factors for different crash types and severities would provide valuable insights for decision-makers and transportation engineers to develop targeted intervention strategies in consideration of road users and traffic conditions such as fleet mix and speed.

Hopf bifurcation structure of a generic car-following model with multiple time delays

This paper establishes a general bifurcation structure of a car-following model with multiple time delays. By applying the Hopf theorem, analytical calculation and numerical simulation are carried out for some typical car-following models. Our results allow a discussion of the impact of multiple time delays and other model parameters on Hopf bifurcation in various existing car-following models with delays, from elementary car-following models such as the optimal velocity model, the full velocity difference model and the intelligent driver model, to Cooperative Adaptive Cruise Control car-following models. It is particularly interesting to observe that the multiple time delays cancel out the impact of each other on the traffic instability.

Anomaly Detection for Cooperative Adaptive Cruise Control in Autonomous Vehicles Using Statistical Learning and Kinematic Model

This paper focuses on Cooperative Adaptive Cruise Control (CACC) in autonomous vehicles. In CACC, vehicles regulate their speed according to a preceding “leader” vehicle in the lane, forming a platoon. In a benign environment, CACC reduces fuel consumption, maximizes road capacity, and ensures traffic safety. However, CACC is vulnerable to various security threats. In this paper, we consider one of the critical threats, where the platoon leader is compromised, and forges acceleration information sent to platoon members. Such attack would lead to traffic instability and potential collisions. First, we propose information sharing in CACC model to allow vehicles and fixed infrastructure to sense and share information about platoon leaders, hence improves the reliability and supports the detection of anomalous behavior. Then, we propose a real-time anomaly detection mechanism that combines statistical learning with the physics laws of kinematics. Specifically, we propose Generalized Extreme Studentized Deviate with Sliding Chunks (GESD-SC) approach, which is applied at each vehicle in the platoon to detect anomalies in real-time based on the vehicle's own speeding decisions. Kinematic model is also utilized to detect unexpected deviations using the leader's information, communicated directly and observed by the leader's neighboring vehicle(s) and/or supporting infrastructure. Combining kinematic model with GESD-SC has shown to be effective in detecting falsification attacks in CACC. Furthermore, we analyze the time performance, and show that the proposed technique outperforms existing method in detection accuracy and processing time.

On the role of speed adaptation and spacing indifference in traffic instability: Evidence from car-following experiments and its stochastic model

Understanding the mechanisms responsible for the emergence and evolution of oscillations in traffic flow has been a subject of intensive research by numerous scholars. In our previous work, we proposed a new mechanism to explain the generation of traffic oscillations: traffic instability caused by the competition between speed adaptation and stochastic effects. By conducting a closer examination of car following data obtained in a 25-car platoon experiment, we discovered in this work that the speed difference plays a more important role on car-following dynamics than the spacing, and when its amplitude is small, the growth of oscillations is mainly determined by the stochastic factors that follow the mean reversion process; when its amplitude increases, the growth of the oscillations is determined by the competition between the stochastic factors and the speed difference. An explanation is then provided, based on the above findings, to why the speed variance in the oscillatory traffic grows in a concave way along the platoon. We also proposed a mode-switching stochastic car-following model that incorporates the speed adaptation and spacing indifference behavior of drivers, which captures the observed characteristics of oscillation and discharge rate. Finally, our sensitivity analysis shows that the influence on oscillation growth and discharge rate is small by the reaction delay but large by the indifference region boundary.

Langevin method for a continuous stochastic car-following model and its stability conditions

In car-following models, the driver reacts according to his physical and psychological abilities which may change over time. However, most car-following models are deterministic and do not capture the stochastic nature of human perception. It is expected that purely deterministic traffic models may produce unrealistic results due to the stochastic driving behaviors of drivers. This paper is devoted to the development of a distinct car-following model where a stochastic process is adopted to describe the time-varying random acceleration which essentially reflects the random individual perception of driver behavior with respect to the leading vehicle over time. In particular, we apply coupled Langevin equations to model complex human driver behavior. In the proposed model, an extended Cox-Ingersoll-Ross (CIR) stochastic process will be used to describe the stochastic speed of the follower in response to the stimulus of the leader. An important property of the extended CIR process is to enhance the non-negative properties of the stochastic traffic variables (e.g. non-negative speed) for any arbitrary model parameters. Based on stochastic process theories, we derive stochastic linear stability conditions which, for the first time, theoretically capture the effect of the random parameter on traffic instabilities. Our stability results conform to the empirical results that the traffic instability is related to the stochastic nature of traffic flow at the low speed conditions, even when traffic is deemed to be stable from deterministic models.

Research on the Influence of District Opening of Urban Road Base on Multi-decision and Network Vulnerability Models

In order to relieve the increasing serious traffic pressure, the open of urban districts has been put on the agenda, and computer simulation is an effective method to evaluate the effect of openness. The influence of different types of districts on urban road capacity under different degrees of openness is discussed in this paper. Four evaluation index, including: the road capacity expansion degree, traffic instability variation coefficient, simplified origin and destination connectivity and path betweenness are established, simulation models of multi-objective decision making and traffic network vulnerability based on evaluation indexes are built. Make full use of the advantages of computer simulations with the big data of urban districts. Finally, the influence of three different types of typical residential areas on the capacity of the surrounding roads before and after the opening is analyzed and evaluated under computer simulation results, which illuminate the effectiveness of these models.

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.

Variable speed limit control at fixed freeway bottlenecks using connected vehicles

The connected vehicle (CV) technology is applied to develop VSL strategies to improve bottleneck discharge rates and reduce system delays. Three VSL control strategies are developed with different levels of complexity and capabilities to enhance traffic stability using: (i) only one CV (per lane) (Strategy 1), (ii) one CV (per lane) coupled with variable message signs (Strategy 2), and (iii) multiple CVs (Strategy 3). We further develop adaptive schemes for the three strategies to remedy potential control failures in real time. These strategies are designed to accommodate different queue detection schemes (by CVs or different sensors) and CV penetration rates. Finally, probability of control failure is formulated for each strategy based on the stochastic features of traffic instability to develop a general framework to (i) estimate expected delay savings, (ii) assess the stability of different VSL control strategies, and (iii) determine optimal control speeds under uncertainty. Compared to VMS-only strategies, the CV-based strategies can effectively impose dynamic control over continuous time and space, enabling (i) faster queue clearance around a bottleneck, (ii) less restrictive control with higher control speed (thus smoother transition), and (iii) simpler control via only one or a small number of CVs.

Including heavy vehicles in a car‐following model: modelling, calibrating and validating

SummaryHeavy vehicles influence general traffic in many different ways compared with passenger vehicles, and this may result in different levels of traffic instability. Increases in the number and proportion of heavy vehicles in the traffic stream will therefore result in different traffic flow conditions. This research initially outlines the different car‐following behaviour of drivers in congested heterogeneous traffic conditions indicating the necessity for developing a car‐following model, which includes these differences. A psychophysical car‐following model, similar in form to Weideman's car‐following model, was developed. Due to the complexity of the developed model, the calibration of the model was undertaken using a particle swarm optimisation algorithm with the data recorded under congested traffic conditions. This was then incorporated into a traffic microsimulation model. The results showed that the car‐following perceptual thresholds and thus action points of drivers differ based on their vehicle and the lead vehicle types. The inclusion of the heavy vehicles in the model showed significant impacts on the traffic dynamic and interactions amongst different vehicles. Copyright © 2016 John Wiley & Sons, Ltd.

An empirical study on the traffic state evolution and stop-and-go traffic development on freeways

Stop-and-go traffic, related to traffic breakdown and instability, is the core mechanism of traffic state transition to congestion. The purpose of this paper is to provide improved empirical understanding on the development of the stop-and-go traffic from asymmetric theory's viewpoint. We analyse traffic state transition before and after stop-and-go wave by observing platoon trajectories using NGSIM data. We observe that stop-and-go wave develops into growth (dissipation) in unstable (stable) traffic, which becomes stable (unstable) by passing the wave, respectively. Alternating patterns can explain recurring oscillatory traffic. Besides, we investigate the relationship between the evolution of stop-and-go wave and lane-changes. We can find that the growth region in the flow-density plane is located on the higher flow and density area above dissipation region. Also, as the number of lane-change increases (decreases), traffic will be developed to growth (dissipation), respectively. The findings of this research have potential for detailed traffic control over stop-and-go waves’ development.