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In the real traffic, drivers often perceive traffic information with delay time, while presenting asynchronous reactions that form non-constant delay time. Meanwhile, on-ramps are very common in the real traffic network environment, especially on highway sections. Traffic flow merging from the on-ramps has a significant impact on the traffic stability of the main road. Given these facts, we develop an extended lattice hydrodynamic model with drivers' continuous delay time and on-ramp. Based on the linear and nonlinear stability analysis, we derive the stability criterion and modified Korteweg–de Vries (mKdV) equation of the proposed lattice model; the kink-antikink soliton wave solution obtained by solving the above mKdV equation can be used to describe the propagation and evolution characteristics of density waves near the neutral stable curve. Results show that the ramp inflow ratio and delay time have a significant impact on the stability of traffic flow on the freeway main lane. [ABSTRACT FROM AUTHOR]

Vehicular honk behavior is not uncommon in real traffic. Meanwhile, with the advent of sensors and communication technology, the real-time traffic state can be readily available to drivers. With such information, drivers can estimate the future traffic status and take countermeasures in advance. In this study, we propose a new lattice hydrodynamic model by jointly considering the vehicular honk and driver's predictive effect. In the linear stability analysis section, neutral stability curve of the model is given, and the modified Korteweg de Vries (mKdV) equation is obtained in nonlinear stability analysis. The kink–antikink soliton solution is obtained by solving the above mKdV equation, which can be used to describe the phase transition of the traffic flow near the critical point. Results show that the honk and the driver's predictive effect contribute to the traffic flow stability. [ABSTRACT FROM AUTHOR]

The rapid adoption of sensor technology has upgraded the vehicular communication capacity, which enables the drivers to predict the traffic state (e.g. headway variation tendency (HVT)) based on the current traffic information. Meanwhile, in practice, the drivers would exhibit bounded rationality behavior in that they often perceive and respond to acceleration/deceleration only when the headway variation exceeds a certain threshold. The collective effect may greatly affect the driving behavior and traffic flow performance. In this study, we innovatively model the traffic flow macroscopically considering HVT and bounded rationality effect in the context of continuum model. Based on the linear stability theory, the stability condition of the above model is obtained. The KdV-Burgers equation of the model is derived to describe traffic jam propagation mechanism near the neutral stability line by applying the reductive perturbation method in nonlinear stability analysis. Results show that the HVT and bounded rationality behavior have a great impact on the traffic congestion and energy consumption. [ABSTRACT FROM AUTHOR]

This paper presents a new lattice hydrodynamic model with vehicle overtaking and the continuous self-delayed traffic flux integral. The linear stability condition of the model is derived through the linear stability analysis, which shows that the stable region can be enlarged by increasing the step of delay time. The modified Korteweg–de Vries (mKdV) equation is formulated through nonlinear analysis to describe the propagating behavior of traffic density wave near the critical point. The kink–anti-kink solution under different passing constants is also obtained. Results show that when the passing constant is lower than a threshold (Case I) that is associated with the delay time step, uniform flow and kink jam phase exhibits, and jamming transition occurs between the uniform flow and kink jam. When the passing constant exceeds the threshold (Case II), jamming transitions occur from uniform traffic flow to kink-Bando traffic wave through chaotic phase with decreasing sensitivity. Simulation examples verify that when the delay time increases from 0 to 0.6, the fluctuation amplitude of the traffic density is reduced from 0.07 to 0 even with exogenous initial disturbance, whereas under Case II, chaotic traffic flow appears when the density ranges from 0.18 to 0.31 and the delay time is 0.6. [ABSTRACT FROM AUTHOR]

Connected vehicles are expected to become commercially available by the next decade. In this work, we propose a delay feedback control method for car-following model on a gyroidal road. By using the Hurwitz criteria and the condition for transfer function in terms of H ∞ -norm, the impact of controller gain coefficient and the delay time on the performance of traffic flow is investigated. Based on the bode curve, we verify that the designed delay feedback controller is effective in suppressing traffic congestion and reducing energy consumption. The enhanced traffic flow model is more sensitive to the controller gain coefficient and delay time at downhill situation compared to the uphill situation. The conclusion obtained from the simulation example is consistent with the theoretical analysis. [ABSTRACT FROM AUTHOR]

Connected vehicles are expected to become commercially available by the next decade, while traffic interruption is not uncommon in the real traffic environment. In this paper, we propose a feedback control method for lattice hydrodynamic model considering the traffic interruption probability effect. The stability criterion of the new model is explored through linear stability analysis of transfer function. When the stability conditions are not satisfied, a delay feedback controller is used to control the discharging flow to suppress traffic congestion. The impact of gain coefficient and delay time on the performance is discussed. We verify the effectiveness of the devised delay feedback controller by simulations. Results show that the traffic interruption probability effect has a considerable impact on the stability of traffic flow, while the controller is effective in suppressing traffic congestion. [ABSTRACT FROM AUTHOR]

We present a multi-phase lattice model by considering the optimal current change with memory effect, in which traffic congestion could possibly take place in the cases of both high density and low density. The linear stability condition of the model is obtained by applying the linear stability theory. A modified Korteweg-de Vries (mKdV) equation is also derived through nonlinear analysis to examine the traffic density wave propagation near the critical point. Numerical simulation verified that not only the sensitivity of the optimal velocity change with memory of drivers but also the memory time step could effectively stabilize the traffic flow. The stability of traffic flow could be strengthened by increasing the memory step size of optimal current changes and the intensity of drivers' memory. In addition, the phase transitions and the deviation between the analytical and simulation model is highly dependent on the sensitivity. [ABSTRACT FROM AUTHOR]

Drivers would adjust the speeds in response to not only the external environment, but also the anticipated traffic condition. In this paper, we propose a new continuum model considering the driver's self-anticipative effect. Such effect is mainly reflected by the difference between the current speed and optimal speed within the anticipation time step. By applying the linear stability theory, the stability condition of the new model is obtained. Through the nonlinear analysis method, the KdV–Burgers equation of the model is provided. The solution describes the evolution of density waves near the neutral stability region. The simulation example verifies that the self-anticipative effect of the driver contributes to suppressing traffic congestion and reducing exhaust emissions effectively. We thus suggest that the traffic flow stability could be improved in an ad hoc manner. [ABSTRACT FROM AUTHOR]

As communication and perception technologies develop, connected vehicles (CVs) advance rapidly. In the process of popularization of CVs, it is bound to lead to the coexistence of CVs and human-driven vehicles (HDVs) on the road network for some time to come, and the previous study assumes that road vehicle is homogeneous, which could not quantify the difference between mixed vehicular flow, based on this, we consider the differences between CAVs and CVs in the way of information acquisition, a heterogeneous lattice hydrodynamics model mixing the HDVs and CVs are presented. Subsequently, by using the small perturbation method, we analyze the linear stability of the proposed model and derive the corresponding stability criteria; when the above stability norm does not hold, in order to investigate the nonlinear phenomenon, nonlinear stability analysis is performed and a modified Korteweg–de Vries equation (mKdV) corresponding to the proposed model is derived. By solving the mKdV equation, we obtain the kink–antikink solitary wave solution which can be used to explain how traffic jams form and propagate. At last, several numerical simulations were conducted to test the impact of the penetration rate of CVs and the bi-directional visual field for both forward-looking and backward-looking on the heterogeneous traffic flow stability, i.e., the first two are positive, while the last is negligible, this conclusion is consistent with the conclusion of theoretical derivation. • A generic lattice hydrodynamic model synthesizing the human-driven vehicles and connected vehicles. • In the linear stability analysis, the stability criterion of proposed heterogeneous lattice model is obtained. • In the linear stability analysis, the mKdV equation of proposed model is derived. • Numerical results demonstrate that the heterogeneity of vehicles exert great influence on the traffic jam. [ABSTRACT FROM AUTHOR]

Gradient roads are not uncommon in mountainous areas and freeways. The driving field of vision will be limited under such a complex road environment, which hinders the drivers from accurately perceiving the speed of the preceding vehicle. Accurate modeling of traffic flow in such an environment is therefore paramount to make accurate predictions and to effectively control the system. To this end, we present a modified continuum model accounting for the uncertain velocity of preceding vehicles on gradient highways. We derive the stability criterion and the KdV–Burgers equation of the proposed model via linear and nonlinear stability analysis. The density wave solution obtained by solving the above KdV–Burgers equation can explain the propagation mechanism of traffic jams near the stability curve. Numerical examples reveal that the slope information and uncertainty term exert great influence on traffic jams and energy consumption. Specifically, the effect of the slope information is positive, whereas the effect of the uncertainty term is negative. • A new continuum model considering the velocity uncertainty of preceding vehicle on gradient highways. • Stability condition and KdV–Burgers equation of the proposed continuous traffic flow model. • The complex traffic phenomena such as shock waves, rarefaction waves and local cluster effects are reproduced. • The simulation results are in good agreement with theoretical analysis. [ABSTRACT FROM AUTHOR]

The car taillights in the deceleration process of preceding vehicle may greatly affect the acceleration and deceleration processes of the following vehicle. Additionally, the driver can predict the headway at the next time period from surrounding traffic information, and adjust the vehicle acceleration based on the difference between the predicted headway and the current headway information. To analyze these combined effects, we propose a new continuous traffic flow model taking into account the predictive headway variation and preceding vehicle's taillight. The stability condition and KdV–Burgers equation of the continuum model are derived in linear and nonlinear stability analysis. The density wave solution obtained by solving the KdV–Burgers equation can be used to describe the formation and propagation mechanism of traffic jams near stable conditions. The complex traffic phenomena such as shock waves, rarefaction waves and local cluster effects are reproduced by simulation. Results show that the taillight information of preceding vehicle and the driver's prediction time step both contribute greatly to the stability of the traffic flow and energy consumption. • A new continuous traffic flow model taking into account the predictive headway variation and preceding vehicle's taillight. • Stability condition and KdV–Burgers equation of the proposed continuous traffic flow model. • The complex traffic phenomena such as shock waves, rarefaction waves and local cluster effects are reproduced • The simulation results are in good agreement with theoretical analysis. [ABSTRACT FROM AUTHOR]