Stochastic Car-following Model Research Articles

An internal stochastic car-following model: Stochasticity analysis of mixed traffic environment

This paper investigates the impact of adaptive cruise control(ACC) vehicles on the stochasticity of human driving behavior by constructing a stochastic car-following model of human-driven vehicles (HDVs). Utilizing NGSIM dataset, the relationship between acceleration variance and space headway is analyzed, and a novel stochastic car-following model with headway is proposed to capture the internal stochasticity of drivers. Furthermore, the interaction between HDVs and AVs is explored by discussing stochasticity and stability in mixed traffic flow, using the proposed HDV model. The model parameters are calibrated based on NGSIM dataset and the simulation results indicate that the proposed stochastic car-following model can effectively reproduce the generation and propagation of traffic shocks without lane changes. Additionally, the simulations reveal that as the penetration rate of AVs increases in a lower range (0%–50%), the stochasticity of HDVs and stability in mixed traffic flow is substantially reduced. However, at higher penetration rates, increases in the AV penetration rate have a limited effect on the stochasticity of human driving behavior and the stability of mixed traffic flow. Concurrently, under conditions of low penetration rates, a smaller AV platoon size contributes more effectively to enhancing the stability of traffic flow and suppressing the stochastic behavior of HDVs. This research provides new insights for optimizing traffic flow control with automated vehicles.

Application of dynamic desired headway based adaptive backstepping sliding mode control design to mixed traffic system

To optimize the mixed car-following behavior of connected autonomous vehicles (CAVs) and human-driven vehicles (HDVs), an adaptive backstepping sliding mode control (ABSMC) strategy for longitudinal velocity and distance control model (namely, MCF-ABSMCM) is put forth. First, the variable desired headway model (VDHM) is designed based on the vehicle-to-vehicle and vehicle-to-infrastructure information. Also, an asymmetric stochastic car-following model (ASCM) is designed to realistically describe the stochastic factor as well as vehicle acceleration and braking behaviors in mixed car-following. Second, an adaptive cruise sliding mode control law with a backstepping approach is devised to precisely track the desired following distance based on the VDHM. After creating the basic diagram of the two-model traffic flow, the intelligent driver model (IDM) is used as a baseline to compare and analyze the traffic capacity. Lastly, the effectiveness of the MCF-ABSMCM approach is confirmed in terms of both the mixed traffic flow density wave evolution and the vehicle control strategy, and the MCF-ABSMCM is validated under various adversary inputs. The simulation results demonstrate that the mixed-flow queue can finish headway tracking and keep a safe distance when using the MCF-ABSMCM described. This control strategy has been validated in VISSIM to significantly improve the efficiency of traffic operations compared to IDM and ASCM.

An improved stochastic car-following model considering the complete state information of multiple preceding vehicles under connected vehicles environment

Studying the car-following model contributes to improving vehicle driving efficiency and traffic flow stability within the context of connected automated vehicles (CAVs). Therefore, an improved stochastic car-following model (SMLVM) is proposed in this paper, building upon the traditional FVD model and BLVD model. This new model comprehensively considers four deterministic factors: acceleration, velocity, headway, and optimal speed memory of multiple preceding vehicles, as well as the comprehensive influence of stochastic factors on car-following behavior during the traveling process. Meanwhile, weight functions are utilized to represent the varying strengths of influence from vehicles ahead with different positions and speeds on the following vehicle. The SMLVM model is categorized and discussed based on practical application scenarios in this paper. When the focus is primarily on fundamental traffic flow behavior, relative motion between vehicles, and other basic principles, the SMLVM model degenerates into the MLVM model. Through stability analysis and simulation experiments on MLVM model, critical stability conditions are derived. Comparisons with other classical models demonstrate that the MLVM model exhibits stronger stability and resistance to disturbances. When the focus is primarily on various realistic driving scenarios, through simulation experiments on SMLVM models in different scenarios, it is found that the influence of stochastic factors on SMLVM models mainly depends on the magnitude of the intensity of stochastic fluctuations, which is rarely affected by the specific functional expressions of the stochastic terms. Finally, empirical analysis is conducted by selecting five sets of processed data from the next-generation simulation (NGSIM) dataset. Based on parameter estimation using the SMLVM model, and a comparison is made with the FVD model and BLVD model. The results confirm that the model proposed in this paper fits vehicle speeds better and absorbs disturbances more effectively, and exhibiting greater stability in traffic flow.

Revealing the impact of stochastic driving characteristics on car-following behavior with locally collected vehicle trajectory data

This study investigates the impact of Chinese drivers’ stochastic behaviour on local car-following situations using localized trajectory data. An extended stochastic car-following model (S-IDM) is established, which considers both internal and external stochasticity. External stochasticity is characterized by different driver types, while internal stochasticity is characterized by the standard deviation of acceleration under different headway and velocity differences for the same driver. The proposed model shows advantages in terms of single-vehicle simulation accuracy and traffic shock reproduction ability, compared to traditional and existing car-following models. The model can also be extended to the evolution analysis of mixed traffic flow models, where reducing the stochasticity of human-driven vehicles is critical for optimizing and controlling traffic flow.

Trajectory planning at a signalized road section in a mixed traffic environment considering lane-changing of CAVs and stochasticity of HDVs

Connected and automated vehicles (CAVs) are projected to bring significant benefits to traffic efficiency and driving comfort. However, the realization of full CAV penetration rate will take a long time. In this paper, a framework is proposed for planning the trajectories of vehicles at a signalized road section in a mixed traffic environment consisting of CAVs, human-driven vehicles (HDVs) and connected and automated buses (CABs). In the proposed trajectory planning framework (TPF), both the lane-changing (LC) behavior of CAVs and the stochasticity of HDVs are considered. The whole TPF is composed of a planning module, a running module, and a switching module. In the planning module, the mixed integer programming (MIP) models for trajectory planning with/without LCs are formulated to optimize the trajectories of CAVs/CABs. A parsimonious algorithm is designed to determine a suitable planning time horizon for the MIP models. The running module and the switching module are designed to ensure the driving safety of vehicles. To consider the stochasticity of HDVs, the concept of α-trajectory is employed in simulations to produce predicted trajectories of HDVs, while the actual trajectories of HDVs are generated by a stochastic car-following model. Here, α is a parameter between 0 and 1 related to one randomly changing parameter of HDVs, and α-trajectory is a series of predicted trajectories generated for HDVs based on the value of α. A rolling time horizon scheme is applied for TPF to account for the time-varying traffic situations. Numerical experiments under different traffic states and market penetration rates (MPRs) of CAVs/CABs are conducted to validate the performance of the proposed TPF. The average improvement in travel time and fuel consumption can reach up to 28.9 %, 17.8 % and 52.2 %, 35.3 % under medium and heavy traffic, respectively, and the average improvement in driving comfort is over 20 % in most traffic scenarios. The comparison experiment without fixed rolling time window (FTW) shows the advantage of setting FTW in adapting to the time-varying traffic situations, especially under heavy traffic. The sensitivity analysis shows that the values of α1 and α2 associated with α-trajectory can affect the performance of the proposed TPF in varying degrees. Finally, the length of the control zone is suggested to be set to 300–500 m.

Managing merging from a CAV lane to a human-driven vehicle lane considering the uncertainty of human driving

This paper proposes a control strategy for a freeway merging bottleneck consisting of a Connected and Automated Vehicle (CAV) exclusive lane and a human-driven vehicle (HDV) lane, aiming to achieve fuel economy and increase traffic efficiency. The trajectories of CAVs are optimized to enable them to smoothly merge into the gaps in the HDV lane. We utilize a stochastic car-following model to incorporate the uncertainty of HDVs and adopt the concept of α-percentile trajectory proposed in our earlier work (Xiong and Jiang, 2021) to estimate the trajectories of HDVs. Based on these, an optimization model is constructed to optimize the merging sequence and the merging trajectories of CAVs simultaneously. We use dynamic programming to solve the optimization model. Dividing RECTangles algorithm and Hamiltonian analysis are imbedded as a subroutine to obtain the energy efficient merging trajectory of each CAV. Simulation results show that the proposed control strategy is capable of reducing average fuel consumption and travel time under a wide range of inflow rates. The benefits depend on the inflow rate and the trajectory percentile α. When the total inflow rate is low, the impact of α is insignificant. If the total inflow rate increases to a high level, the impact of α becomes remarkable and the maximum benefits would be achieved at an intermediate range of α. Moreover, the computation efficiency of the proposed system is fast enough and can be implemented in real-time in the near future.

Driver Reactions to Uphill Grades: Inference from a Stochastic Car-Following Model

This paper analyzes the impact of uphill grades on the acceleration drivers choose to impose on their vehicles. Statistical inference is made based on the maximum likelihood estimation of a two-regime stochastic car-following model using Next Generation SIMulation (NGSIM) data. Previous models assume that the loss in acceleration on uphill grades is given by the effects of gravity. We find evidence that this is not the case for car drivers, who tend to overcome half of the gravitational effects by using more engine power. Truck drivers only compensate for 5% of the loss, possibly because of limited engine power. This indicates not only that current models are severely overestimating the operational impacts that uphill grades have on regular vehicles, but also underestimating their environmental impacts. We also find that car-following model parameters are significantly different among shoulder, median and middle lanes but more data is needed to understand clearly why this happens.

Stability Analysis of Stochastic Linear Car-Following Models

Recent scholars have developed a number of stochastic car-following models that have successfully captured driver behavior uncertainties and reproduced stochastic traffic oscillation propagation. Whereas elegant frequency domain analytical methods are available for stability analysis of classic deterministic linear car-following models, there lacks an analytical method for quantifying the stability performance of their peer stochastic models and theoretically proving oscillation features observed in the real world. To fill this methodological gap, this study proposes a novel analytical method that measures traffic oscillation magnitudes and reveals oscillation characteristics of stochastic linear car-following models. We investigate a general class of stochastic linear car-following models that contain a linear car-following model and a stochastic noise term. Based on frequency domain analysis tools (e.g., Z-transform) and stochastic process theories, we propose analytical formulations for quantifying the expected speed variances of a stream of vehicles following one another according to one such stochastic car-following model, where the lead vehicle is subject to certain random perturbations. Our analysis on the homogeneous case (where all vehicles are identical) reveals two significant phenomena consistent with recent observations of traffic oscillation growth patterns from field experimental data: A linear stochastic car-following model with common parameter settings yields (i) concave growth of the speed oscillation magnitudes and (ii) reduction of oscillation frequency as oscillation propagates upstream. Numerical studies verify the universal soundness of the proposed analytical approach for both homogeneous and heterogeneous traffic scenarios, and both asymptotically stable and unstable underlying systems, as well as draw insights into traffic oscillation properties of a number of commonly used car-following models. Overall, the proposed method, as a stochastic peer, complements the traditional frequency-domain analysis method for deterministic car-following models and can be potentially used to investigate stability responses and mitigate traffic oscillation for various car-following behaviors with stochastic components.

Dissipation of traffic congestion using autonomous-based car-following model with modified optimal velocity

We investigate dynamical properties of traffic flow using the stochastic car-following model with modified optimal velocity on circular road. The safety distance following the two-second rule and autonomous vehicles obeying simple requirements are incorporated into the model. The dynamic safety distance increases in a light traffic condition where the average driving velocity is high, while decreases in a dense traffic condition in anticipation of slower traffic motion. The results show that the presence of the autonomous vehicles can enhance overall velocity and traffic current of the system, and postpone the traffic congestion. In a particular phase region, imposing a speed limit enables the system to leave the congested flow phase. The density-dependent speed limit in autonomous-free condition is obtained to achieve the optimal traffic flow.

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.

Integrated deep learning and stochastic car-following model for traffic dynamics on multi-lane freeways

The current paper proposes a novel stochastic procedure for modelling car-following behaviours on a multi-lane motorway. We develop an integrated multi-lane stochastic continuous car-following model where a deep learning architecture is used to estimate a probability of lane-changing (LC) manoeuvres. To the best of our knowledge, this work is among the very few papers which exploit deep learning to model driving behaviour on a multi-lane road. The objective of this study is to establish a coupled stochastic continuous multi-lane car-following model using Langevin equations to cope with probabilistic characteristics of LC manoeuvres. In particular, a stochastic volatility, derived from LC manoeuvres is introduced in a multi-lane stochastic optimal velocity model (SOVM). In additions, Convolutional Neural Network (CNN) is applied to estimate a probability of LC manoeuvres in the integrated multi-lane car-following model. Furthermore, imaged second-based trajectories of the lane-changer and surrounding vehicles are used to identify whether LC manoeuvres occur by using the CNN. Finally, the proposed method is validated using a real-world high-resolution vehicle trajectory dataset. The results indicate that the prediction of the integrated SOVM is almost identical to the observed trajectories of the lane-changers and the following vehicles in the initial and the target lane. It has been found that the proposed multi-lane SOVM can tackle the unpredictable fluctuations in the velocity of the vehicles in the acceleration/deceleration zone.

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.

Analysis of a Two-Regime Stochastic Car-Following Model: Explaining Capacity Drop and Oscillation Instabilities

Analysis of a Two-Regime Stochastic Car-Following Model: Explaining Capacity Drop and Oscillation Instabilities

Wiedemann Revisited

A new data-driven stochastic car-following model based on the principles of psychospacing or action-point modeling is presented. It uses empirical or experimental trajectory data and mimics the main microscopic behavioral characteristics present in the data. In the action-point model, regions are defined in the relative speed–distance headway plane, in which the follower is likely to perform an action (increase or decrease acceleration) or not. These regions can be established empirically from vehicle trajectory data and thereby yield a joint cumulative probability distribution function of the action points. Furthermore, the conditional distribution of the actions (the size of the acceleration or deceleration given the current distance headway and relative speed or given the acceleration before the action) can be determined from these data as well. To assess the data correctly, a new filtering technique is proposed. The main hypothesis behind this idea is that the speed profile is a continuous piecewise linear function: accelerations are piecewise constant changing values at nonequidistant discrete time instants. The durations of these constant acceleration periods are not fixed but depend on the state of the follower in relation to its leader. The data analysis illustrates that driving behavior shows nonequidistant constant acceleration periods. The distributions of the action points and the conditional accelerations form the core of the presented data-driven stochastic model. The mathematical formalization that describes how these distributions can be used to simulate car-following behavior is presented. Empirical data collected on a Dutch motorway are used to illustrate the workings of the approach and the simulation results.

Longitudinal Driving Behavior under Adverse Conditions: A Close Look at Psycho-spacing Models

Adverse weather conditions have been shown to have a substantial impact on traffic flow operations following substantial adaptation effects in driving behavior. In quantifying these effects psycho-spacing models may be used. In this contribution it was examined to what extend adverse weather conditions influence the position of action points in the relative speed-spacing plane in these models, the relationship between speed of the lead vehicle and relative speed at the action points and acceleration as well as jumps in acceleration. In this regard a driving simulator experiment with a Repeated Measures design was performed in which fog was simulated in the experimental condition. Using a new data analysis technique followed from the results that substantial differences were present with regard to the position of action points. Furthermore a substantial influence of fog on the relationship between speed of the lead vehicle and relative speed at the action points was found. Finally, a substantial influence of this adverse weather condition on acceleration and jumps in acceleration was established. Furthermore, a large degree of driver heterogeneity was observed with regard to the position of action points as with regard to (jumps in) acceleration at the action points. It is recommended to develop a data driver stochastic car-following model based on psycho-spacing theory.

Probabilistic Traffic Flow Breakdown in Stochastic Car-Following Models

Whether traffic displays multiple phases (e.g., laminar, jammed, synchronized) has been much discussed. Computational evidence is presented that a stochastic car-following model can be moved from two phases (laminar and jammed) to one phase by changing one of its parameters. Models with two phases show three states. Two of them are homogeneous and correspond to the two phases. The third state consists of a mix of the two phases (phase coexistence). Although the gas–liquid analogy to traffic models has been widely discussed, no traffic-related model ever displayed a completely understood stochastic version of that transition. A stochastic model is important to the understanding of the potentially probabilistic nature of the transition. If indeed two-phase models describe certain aspects correctly, predictions for breakdown probabilities can be made. Alternatively, if one-phase models describe these aspects better, there is no breakdown. Interestingly, such one-phase models can still allow for jam formation on a small scale, which may give the impression of two-phase dynamics.

Optimization of congested traffic by controlling stop-and-go waves.

We propose a new optimization strategy based on inducing stop-and-go waves on the main road and controlling their wavelength. Using numerical simulations of a recent stochastic car-following model we show that this strategy yields optimization of traffic flow when implemented in systems with a localized periodic inhomogeneity, such as signalized intersections and entry ramps. The optimization process is explained by our finding of a generalized fundamental diagram (GFD) for traffic, namely a flux-density-wavelength relation. Projecting the GFD on the density-flux plane yields a two-dimensional region of stable states, qualitatively similar to that found empirically [Kerner, Phys. Rev. Lett. 81, 3797 (1998)] in synchronized traffic.