Classical Car-following Model Research Articles

Car-following traffic model based on PID control: modelling and simulation

PurposeThe performance of the classical car-following system is easily affected by external disturbances. To enhance the performance of the classical car-following model under sudden external disturbances, a novel car-following model is established to smooth traffic flow.Design/methodology/approachThis paper proposed a Proportion Integration Differentiation (PID) control strategy based on classical control theory and developed a novel car-following model. The linear system theory and Laplace transform are used to derive a closed-loop transfer function. Then, the stability condition is obtained by using the Routh stability criterion and the small gain theorem. Finally, the validity and feasibility of the PID control strategy is proved by numerical simulations.FindingsThe analytic results and the numerical simulation results show that both the integration part and the differential part have the positive effect to suppress traffic oscillation efficiently; the collaboration of these two parts has more power to improve the stability of traffic flow. It means that the proposed model integrated with the PID control strategy has the ability of anti-interference and smooth traffic compared with the classical car-following model.Originality/valueThis paper introduces the PID control strategy into the classical car-following system, which enhances the stability of the system and also provides an efficient method for optimizing the traffic flow system.

Hierarchical predictive control for electric vehicles with hybrid energy storage system under vehicle-following scenarios

For electric vehicles with hybrid energy storage system, driving economy depends not only on novel energy management strategies but also on load power demand. In order to optimize the power demand and energy management simultaneously, this paper proposes a hierarchical model predictive control framework for electric vehicles with a Li-ion battery/supercapacitor hybrid energy storage system under vehicle-following scenarios. In the vehicle-following level, based on vehicle-to-vehicle and vehicle-to-infrastructure communications, the following vehicle can acquire the real-time velocity and position of the preceding vehicle, optimize the motor electricity consumption, and ensure driving safety through velocity planning. Such cost-effective power demand is further allocated in the energy management level, in order to minimize battery degradation and power losses. Urban, suburban, and highway driving conditions are tested to evaluate the effectiveness and robustness of the proposed method. Determination of prediction horizon and detailed comparison with existing methods are investigated. Simulation results show that compared with optimizing energy management alone under a classical car-following model, the proposed method can reduce the total operation cost by 4.69–14.55% and yield results closer to offline dynamic programming, which provides the globally optimal results.

Driving strategy of connected and autonomous vehicles based on multiple preceding vehicles state estimation in mixed vehicular traffic

In the near future, connected and autonomous vehicles (CAVs) will share road space with human-driven vehicles (HVs). In this mixed vehicular traffic, effective following cooperation among multiple vehicles is an important basis for improving traffic efficiency and safety. However, CAVs are unable to communicate with HVs to acquire information. Therefore, how to obtain HV information and realize cooperative car-following has become an urgent problem for CAVs. This paper proposes a CAV driving strategy that considers multiple preceding vehicles, including HVs. The strategy first uses a large amount of real car-following data to build an upgraded Elman neural network (ENN) model optimized with the sparrow search algorithm (SSA), which is utilized to obtain HV information. Then, we combine the SSA-ENN with the classical car-following model and use a time-varying weighting model to analyze the impact of the different states of multiple preceding cars at various moments on the host car, so as to achieve car-following driving control. Numerical simulations are carried out, and the results show that the driving strategy can improve road capacity and suppress traffic oscillations. With the increase in CAV penetration, traffic efficiency, safety, and driving comfort are improved accordingly.

A sequence to sequence learning based car-following model for multi-step predictions considering reaction delay

Car-following behavior modeling is of great importance for traffic simulation and analysis. Considering the multi-steps decision-making process in human driving, we propose a sequence to sequence (seq2seq) learning based car-following model incorporating not only memory effect but also reaction delay. Since the seq2seq architecture has the advantage of handling variable lengths of input and output sequences, in this paper, it is applied to car-following behavior modeling to memorize historical information and make multi-step predictions. We further compare the seq2seq model with a classical car-following model (IDM) and a deep learning car-following model (LSTM). The evaluation results indicate that the proposed model outperforms others for reproducing trajectory and capturing heterogeneous driving behaviors. Moreover, the platoon simulation demonstrates that the proposed model can well reproduce different levels of hysteresis phenomenon. The proposed model is further extended with spatial anticipation, which improves platoon simulation accuracy and traffic flow stability.

Impact of delayed acceleration feedback on the classical car-following model

Abstract Delayed acceleration feedback (DAF) is known to have a positive impact on the stability properties of dynamical models in several applications. Motivated by this, we study the impact of DAF on the classical car-following model (CCFM). First, we show that DAF shrinks the locally stable region. We then show that the resulting model, similar to the CCFM, loses local stability via a Hopf bifurcation. However, DAF decreases the amplitude and increases the frequency of the resulting limit cycles. Additionally, we show that DAF is detrimental to the CCFM due to $(i)$ destruction of the non-oscillatory property of its solutions, $(ii)$ increased risk of string instability and $(iii)$ reduced resilience towards parametric uncertainty. Thus, we report a relevant application wherein DAF degrades the performance across several metrics of practical interest. Thus, our work motivates a systematic study of controllers that can guarantee performance enhancement. We complement our analytical results with stability charts and a bifurcation diagram.

Stability, convergence and Hopf bifurcation analyses of the classical car-following model

Reaction delays play an important role in determining the qualitative dynamical properties of a platoon of vehicles traversing a straight road. In this paper, we investigate the impact of delayed feedback on the dynamics of the Classical Car-Following Model (CCFM). Specifically, we analyze the CCFM in no delay, small delay and arbitrary delay regimes. First, we derive a sufficient condition for local stability of the CCFM in no-delay and small-delay regimes using. Next, we derive the necessary and sufficient condition for local stability of the CCFM for an arbitrary delay. We then demonstrate that the transition of traffic flow from the locally stable to the unstable regime occurs via a Hopf bifurcation, thus resulting in limit cycles in system dynamics. Physically, these limit cycles manifest as back-propagating congestion waves on highways. In the context of human-driven vehicles, our work provides phenomenological insight into the impact of reaction delays on the emergence and evolution of traffic congestion. In the context of self-driven vehicles, our work has the potential to provide design guidelines for control algorithms running in self-driven cars to avoid undesirable phenomena. Specifically, designing control algorithms that avoid jerky vehicular movements is essential. Hence, we derive the necessary and sufficient condition for non-oscillatory convergence of the CCFM. Next, we characterize the rate of convergence of the CCFM, and bring forth the interplay between local stability, non-oscillatory convergence and the rate of convergence of the CCFM. Further, to better understand the oscillations in the system dynamics, we characterize the type of the Hopf bifurcation and the asymptotic orbital stability of the limit cycles using Poincare normal forms and the center manifold theory. The analysis is complemented with stability charts, bifurcation diagrams and MATLAB simulations.

A Car-Following Model Considering Preceding Vehicle’s Lane-Changing Process

Car following and lane changing are two common driving behaviors in the traffic flow. Preceding vehicle's lane changing is affected by the surroundings and will have a greater influence on the followers' driving decision. The existing car-following theory does not fully take it into consideration that the followers' driving behavior may change during a lane-changing process. In order to reflect the driving decision in a complex traffic flow more precisely, the influence on the following vehicle during the preceding vehicle's lane-changing process is studied. First, the different types of stimulus during the preceding vehicle's lane-merging (LM) process and the space gain effect produced by the preceding vehicle's lane-passing (LP) behavior are analyzed. Then, the LM-FVDM and LP-FVDM are proposed based on the classical car-following model-FVD model. Finally, the linear stability theory, numerical simulation, and NGSIM data sets are used to analyze and validate the performance of the LM-FVDM and LP-FVDM. The numerical simulation results show that the model can reasonably reflect the driving decision of the following vehicle in various scenarios, and verification based on NGSIM shows that the $R$ -squared of vehicles' speed and distance is significantly better than the FVD model, which can more effectively reflect the speed adjustment process of the following vehicle during the preceding vehicle's lane-changing process in the real traffic flow.

String and robust stability of connected vehicle systems with delayed feedback

Two important characteristics of a connected vehicle system are string stability (i.e., disturbance in state variables should not propagate along the platoon) and robustness to parametric uncertainties. In this paper, we study these properties for a platoon of vehicles driving on a single-lane straight road. Specifically, we model individual vehicle’s dynamics by the Classical Car-Following Model (CCFM) and the Modified Optimal Velocity Model (MOVM). These models capture the reaction delays inherent in such a setting. First, we focus on string stability. For both models, we derive a sufficient condition for string stability. We then concentrate on the robustness to uncertainties in the parameters of the said models. For both models, we derive bounds on the reaction delay to ensure (a) pairwise robust stability, and (b) platoon robust stability, when the remaining model parameters lie in an interval. Finally, we compare our results with conditions for these models to be locally asymptotically stable. This brings forth the additional constraints imposed on the reaction delay to achieve string and robust stability. Our results may provide design guidelines for futuristic connected vehicle systems. Additionally, from a technological perspective, our results suggest the sufficiency of using only on-board sensors for all forms of local stability except platoon robust stability.

A Fuzzy Logic Approach for Car-Following Modelling

In this communication, the classical car-following theory, which is based on intuitiveness and behavioural representation, is revisited from the point of view of cybernetics theory. Then, a new approach, based on fuzzy modelling, is proposed to estimate the main parameters of the basic car following model. This approach, contrarily to earlier fuzzy logic approaches, maintains the structure of the classical car-following model, limits its complexity and provides means to take into account the main parameters influencing the behaviour of the driver and allows a formal verification of local and global stability of the simulated traffic flow.So, after introducing a new approach based on cybernetics concepts for the modelling of car-following, which provides a theoretical basis for the basic model, the main concepts of fuzzy logic theory and of fuzzy modelling are briefly presented. Then a fuzzy estimation approach is proposed for the main parameters of the basic car-following model. Finally, simulation results making use of the proposed modelling approach are presented.

Stability analysis of the classical car-following model

This paper investigates the stability of the classical car-following model (for example, Chandler et al., Operations Research, 6, 165–184, 1958; Herman et al., Operations Research, 7, 86–106, 1959; Wilhelm and Schmidt, Transportation Engineering Journal (ASCE) 99, 923–933, 1973). Conditions for local and asymptotic stability as defined in the references cited are established for the linear model. These differ from those in the literature in two ways. First, it will be shown that, in the autonomous model when the product of the coefficient of proportionality α and the reaction time τ is less than or equal to 1/e, there exist oscillatory solutions with higher frequencies than 2π, although there are none with lower frequencies. Secondly, asymptotic stability is considered along with local stability. The derived condition for asymptotic stability is both necessary and sufficient. In addition, the condition depends on the frequency of the forcing term, with the sufficient condition ατ < 1 2 for the asymptotic stability found in the literature being included as a special case. The nonlinear model is considered by linearization and numerical integrations. Some practical values of parameters are tested for the stability of the model. The analyses in this paper are extended to consider different values of α and τ for different drivers in the line.