Stabilization and enhancement of traffic flow by the next-nearest-neighbor interaction

Analytical Solution of the Mixed Traffic Flow Cellular Automaton FI Model with the Next-Nearest-Neighbor Interaction

Based on a one-dimensional (1D) traffic flow cellular automaton (CA) FI model, a deterministic next-nearest-neighbor interaction FI model (NIFI model) is proposed. Using the mean-field analysis, the analytical solution of the NIFI model in one-dimensional traffic flow is derived under periodic boundary conditions. For the mixed traffic flow, the occupancy and the mixing ratio are introduced to describe the mixing effect. Similarly, using the mean-field method, the exact solution of the mixed traffic flow is derived from the long-time evolution to reach the steady state. The numerical simulations are carried out for the mixed traffic flow with different vehicle lengths, maximum velocities, and mixing ratios to verify the analytical solutions. The results show that the numerical simulation results agree well with the analytical solution.

Stability Analysis of Continuous Stochastic Linear Model

Many scholars have conducted research on the traffic oscillations and reproduced the growth pattern by establishing stochastic models and simulations. However, the growth pattern of oscillations caused by uncertainty have not been thoroughly studied. Recently, a frequency domain stability analysis method was proposed to analyze the discrete stochastic model. This paper extends this analysis to a continuous situation based on frequency domain tools (e.g., Laplace transform) by introducing a continuous bandlimited white noise. The analytical expression for the evolution of speed standard deviation has been derived. Our study of a homogeneous case reveals an interesting phenomenon: when |G(ω)|∞<1, the speed variance will converge to a constant value, which only depends on the self-disturbance of vehicles. The simulation results verified that the continuous models and corresponding discrete model tend to be consistent when the discrete time step tends to the infinitesimal. Overall, this paper makes up for the deficiency of previous studies on continuous oscillations in car-following theory and can potentially be used to develop new control strategies to help dampen traffic oscillations.

The Car-Following Model and Its Applications in the V2X Environment: A Historical Review

The application of vehicle-to-everything (V2X) technology has resulted in the traffic environment being different from how it was in the past. In the V2X environment, the information perception ability of the driver–vehicle unit is greatly enhanced. With V2X technology, the driver–vehicle unit can obtain a massive amount of traffic information and is able to form a connection and interaction relationship between multiple vehicles and themselves. In the traditional car-following models, only the dual-vehicle interaction relationship between the object vehicle and its preceding vehicle was considered, making these models unable to be employed to describe the car-following behavior in the V2X environment. As one of the core components of traffic flow theory, research on car-following behavior needs to be further developed. First, the development process of the traditional car-following models is briefly reviewed. Second, previous research on the impacts of V2X technology, car-following models in the V2X environment, and the applications of these models, such as the calibration of the model parameters, the analysis of traffic flow characteristics, and the methods that are used to estimate a vehicle’s energy consumption and emissions, are comprehensively reviewed. Finally, the achievements and shortcomings of these studies along with trends that require further exploration are discussed. The results that were determined here can provide a reference for the further development of traffic flow theory, personalized advanced driving assistance systems, and anthropopathic autonomous-driving vehicles.

Research on the Impacts of Generalized Preceding Vehicle Information on Traffic Flow in V2X Environment

With the application of vehicles to everything (V2X) technologies, drivers can obtain massive traffic information and adjust their car-following behavior according to the information. The macro-characteristics of traffic flow are essentially the overall expression of the micro-behavior of drivers. There are some shortcomings in the previous researches on traffic flow in the V2X environment, which result in difficulties to employ the related models or methods in exploring the characteristics of traffic flow affected by the information of generalized preceding vehicles (GPV). Aiming at this, a simulation framework based on the car-following model and the cellular automata (CA) is proposed in this work, then the traffic flow affected by the information of GPV is simulated and analyzed utilizing this framework. The research results suggest that the traffic flow, which is affected by the information of GPV in the V2X environment, would operate with a higher value of velocity, volume as well as jamming density and can maintain the free flow state with a much higher density of vehicles. The simulation framework constructed in this work can provide a reference for further research on the characteristics of traffic flow affected by various information in the V2X environment.

An Extended Car-Following Model Considering Generalized Preceding Vehicles in V2X Environment

Vehicle-to-everything (V2X) technology will significantly enhance the information perception ability of drivers and assist them in optimizing car-following behavior. Utilizing V2X technology, drivers could obtain motion state information of the front vehicle, non-neighboring front vehicle, and front vehicles in the adjacent lanes (these vehicles are collectively referred to as generalized preceding vehicles in this research). However, understanding of the impact exerted by the above information on car-following behavior and traffic flow is limited. In this paper, a car-following model considering the average velocity of generalized preceding vehicles (GPV) is proposed to explore the impact and then calibrated with the next generation simulation (NGSIM) data utilizing the genetic algorithm. The neutral stability condition of the model is derived via linear stability analysis. Numerical simulation on the starting, braking and disturbance propagation process is implemented to further study features of the established model and traffic flow stability. Research results suggest that the fitting accuracy of the GPV model is 40.497% higher than the full velocity difference (FVD) model. Good agreement between the theoretical analysis and the numerical simulation reveals that motion state information of GPV can stabilize traffic flow of following vehicles and thus alleviate traffic congestion.

An extended car-following model at un-signalized intersections under V2V communication environment

An extended car-following model is proposed in this paper to analyze the impacts of V2V (vehicle to vehicle) communication on the micro driving behavior at the un-signalized intersection. A four-leg un-signalized intersection with twelve streams (left-turn, through movement, and right turn from each leg) is used. The effect of the guidance strategy on the reduction of the rate of stops and total delay is explored by comparing the proposed model and the traditional FVD car-following model. The numerical results illustrate that potential conflicts between vehicles can be predicted and some stops can be avoided by decelerating in advance. The driving comfort and traffic efficiency can be improved accordingly. More benefits could be obtained under the long communication range, low to medium traffic density, and simple traffic pattern conditions.

Collision-free nonuniform dynamics within continuous optimal velocity models

Optimal velocity (OV) car-following models give with few parameters stable stop-and -go waves propagating like in empirical data. Unfortunately, classical OV models locally oscillate with vehicles colliding and moving backward. In order to solve this problem, the models have to be completed with additional parameters. This leads to an increase of the complexity. In this paper, a new OV model with no additional parameters is defined. For any value of the inputs, the model is intrinsically asymmetric and collision-free. This is achieved by using a first-order ordinary model with two predecessors in interaction, instead of the usual inertial delayed first-order or second-order models coupled with the predecessor. The model has stable uniform solutions as well as various stable stop-and -go patterns with bimodal distribution of the speed. As observable in real data, the modal speed values in congested states are not restricted to the free flow speed and zero. They depend on the form of the OV function. Properties of linear, concave, convex, or sigmoid speed functions are explored with no limitation due to collisions.

Kinetic Monte Carlo simulations of one-dimensional and two-dimensional traffic flows: comparison of two look-ahead rules

We employ an efficient list-based kinetic Monte Carlo (KMC) method to study traffic flow models on one-dimensional (1D) and two-dimensional (2D) lattices based on the exclusion principle and Arrhenius microscopic dynamics. This model implements stochastic rules for cars' movements based on the configuration of the traffic ahead of each car. In particular, we compare two different look-ahead rules: one is based on the distance from the car under consideration to the car in front of it, and the other one is based on the density of cars ahead. The 1D numerical results of these two rules suggest different coarse-grained macroscopic limits in the form of integro-differential Burgers equations. The 2D results of both rules exhibit a sharp phase transition from freely flowing to fully jammed, as a function of the initial density of cars. However, the look-ahead rule based on the density of the traffic produces more realistic results. The KMC simulations reported in this paper are compared with those from other well-known traffic flow models and the corresponding empirical results from real traffic.

Stability of the car-following model on two lanes

In the case of two-lane traffic, vehicle drivers always worry about the lane changing actions from neighbor lane. This paper studies the stability of a car-following model on two lanes which incorporates the lateral effects in traffic. The stability condition of the model is obtained by using the linear stability theory. The modified Korteweg-de Vries equation is constructed and solved, and three types of traffic flows in the headway-sensitivity space--stable, metastable, and unstable--are classified. Both analytical and simulation results show that the anxiousness about lane changing from neighbor lane indeed has influence upon people's driving behavior and the consideration of lateral effects could stabilize the traffic flows on both lanes.

Stabilization analysis and modified Korteweg-de Vries equation in a cooperative driving system

Two lattice traffic models are proposed by incorporating a cooperative driving system. The lattice versions of the hydrodynamic model of traffic flow are described by the differential-difference equation and difference-difference equation, respectively. The stability conditions for the two models are obtained using the linear stability theory. The results show that considering more than one site ahead in vehicle motion leads to the stabilization of the system. The modified Korteweg-de Vries equation (the mKdV equation, for short) near the critical point is derived by using the reductive perturbation method to show the traffic jam which is proved to be described by kink-anti-kink soliton solutions obtained from the mKdV equations.

Stabilization effect of traffic flow in an extended car-following model based on an intelligent transportation system application

An extended car following model is proposed by incorporating an intelligent transportation system in traffic. The stability condition of this model is obtained by using the linear stability theory. The results show that anticipating the behavior of more vehicles ahead leads to the stabilization of traffic systems. The modified Korteweg-de Vries equation (the mKdV equation, for short) near the critical point is derived by applying the reductive perturbation method. The traffic jam could be thus described by the kink-antikink soliton solution for the mKdV equation. From the simulation of space-time evolution of the vehicle headway, it is shown that the traffic jam is suppressed efficiently with taking into account the information about the motion of more vehicles in front, and the analytical result is consonant with the simulation one.

Equivalence of linear response among extended optimal velocity models

We investigate the property of extended optimal velocity (OV) models of traffic flow, in which a driver looks at arbitrary number of vehicles that precede. We prove an equivalence of linear response among extended models. This equivalence provides a natural understanding of the improvement of the stability of traffic flow.

Dynamical model of a cooperative driving system for freeway traffic

We propose an extended optimal velocity model applicable to cooperative driving control system, which will be realized in the near future. In the model, a vehicle is controlled by the system using the information of arbitrary number of vehicles that precede or follow. We investigate the stability of uniform flow and the response to a disturbance in the linear approximation.

Towards a variational principle for motivated vehicle motion

We deal with the problem of deriving the microscopic equations governing individual car motion based on assumptions about the strategy of driver behavior. We presume the driver behavior to be a result of a certain compromise between the will to move at a speed that is comfortable for him under the surrounding external conditions, comprising the physical state of the road, the weather conditions, etc., and the necessity to keep a safe headway distance between the cars in front of him. Such a strategy implies that a driver can compare the possible ways of further motion and so choose the best one. To describe the driver preferences, we introduce the priority functional whose extremals specify the driver choice. For simplicity we consider a single-lane road. In this case solving the corresponding equations for the extremals we find the relationship between the current acceleration, velocity, and position of the car. As a special case we get a certain generalization of the optimal velocity model similar to the "intelligent driver model" proposed by Treiber and Helbing.

Effect of looking at the car that follows in an optimal velocity model of traffic flow

An extension of an optimal velocity model is proposed. In the new model, a driver looks at the following car as well as the preceding car. We introduce an additional optimal velocity function that depends on the headway of the following car. We investigate the effect of looking back at the car that follows and show that this extension effectively stabilizes the traffic flow.

Noise-assisted traffic of spikes through neuronal junctions

The presence of noise, i.e., random fluctuations, in the nervous system raises at least two different questions. First, is there a constructive role noise can play for signal transmission in a neuron channel? Second, what is the advantage of the power spectra observed for the neuron activity to be shaped like 1/f(k)? To address these questions a simple stochastic model for a junction in neural spike traffic channels is presented. Side channel traffic enters main channel traffic depending on the spike rate of the latter one. The main channel traffic itself is triggered by various noise processes such as Poissonian noise or the zero crossings of Gaussian 1/f(k) noise whereas the variation of the exponent k gives rise to a maximum of the overall traffic efficiency. It is shown that the colored noise is superior to the Poissonian and, in certain cases, to deterministic, periodically ordered traffic. Further, if this periodicity itself is modulated by Gaussian noise with different spectral exponents k, then such modulation can lead to noise-assisted traffic as well. The model presented can also be used to consider car traffic at a junction between a main and a side road and to show how randomness can enhance the traffic efficiency in a network. (c) 2001 American Institute of Physics.

Enhancement and stabilization of traffic flow by moving in groups

We study the traffic behavior of vehicles moving in groups analytically and numerically. A car-following model of traffic is extended to take into account a binary mixture of vehicles. It is shown that the movement in groups stabilizes the traffic flow. The jamming transition among the free traffic, the inhomogeneous traffic, and the homogeneous congested traffic occurs at a higher density than the threshold of the original model. The traffic current is highly enhanced at a high-density region by keeping a short headway without jam. The jamming transition is analyzed by using the linear stability method. It is found that the theoretical neutral stability curve agrees with the transition line obtained by the simulation.