Phase Transition Of Traffic Flow Research Articles

Phase transition in heterogeneous macro continuum model integrating the jerk effect with the mixed traffic flow involving human driving and ADAS vehicles

Vehicles equipped with advanced driving assistance systems (ADAS) can acquire information about preceding and following vehicles, which will have an undeniable impact on the phase transition of traffic flow. Therefore, we establish a new heterogeneous continuum model of traffic flow considering the jerk effect mixed with human driving (HD) and ADAS vehicles. The neutral stability condition associated with the permeability of ADAS vehicle is inferred via stability analysis. According to simulation, shock wave occurs, implying that our model can emerge correct wave propagation trend. Moreover, the simulation of density evolution and flow changes also suggests that an increase in ADAS vehicle penetration and jerk effect can enhance traffic system stability and reduce energy consumption.

Tipping points, multistability, and stochasticity in a two-dimensional traffic network dynamics

Mitigating traffic jams is a critical step for the betterment of the urban transportation system, which comprises a large number of interconnected routes to form an intricate network. To understand distinct features of vehicular traffic flow on a network, a macroscopic two-dimensional traffic network model is proposed incorporating intra-nodal and inter-nodal vehicular interaction. Utilizing the popular techniques of nonlinear dynamics, we investigate the impact of different parameters like occupancy, entry rates, and exit rates of vehicles. The existence of saddle-node, Hopf, homoclinic, Bogdanov–Takens, and cusp bifurcations have been shown using single or biparametric bifurcation diagrams. The occurrences of different multistability (bistability/tristability) phenomena, stochastic switching, and critical transitions are explored in detail. Further, we calculate the possibility of achieving each alternative state using the basin stability metric to characterize multistability. In addition, critical transitions from free flow to congestion are identified at different magnitudes of stochastic fluctuations. The applicability of critical slowing down based generic indicators, e.g., variance, lag-1 autocorrelation, skewness, kurtosis, and conditional heteroskedasticity are investigated to forewarn the critical transition from free flow to traffic congestion. It is demonstrated through the use of simulated data that not all of the measures exhibit sensitivity to rapid phase transitions in traffic flow. Our study reveals that traffic congestion emerges because of either bifurcation or stochasticity. The result provided in this study may serve as a paradigm to understand the qualitative behavior of traffic jams and to explore the tipping mechanisms occurring in transport phenomena.

Analyses of a two-lane lattice hydrodynamic model incorporating predictive effect and self-delayed flux integral

To explore the mechanism among disturbance, spatiotemporal evolution characteristics and stability for traffic flow, this paper presents an improved lattice hydrodynamic model with lane change into consideration and investigates the influence of three influencing factors, namely, lane change effect, predictive effect, and self-delayed flux integral effect on traffic flow. Moreover, theoretical analyses containing linear and nonlinear analysis are further developed. By linear stability analysis, we obtain the model’s neutral stability curve. Moreover, the Burgers equation and modified Korteweg–de Vries equation are derived in nonlinear stability analysis section. The phase transition of traffic flow and its propagation behavior of congestion near the critical point are described. In addition, under the influence of disturbance, the spatiotemporal evolution characteristics of density wave and energy consumption are intuitively shown by numerical simulations. The results reveal that appropriate lane change behavior, predictive effect and self-delayed flux integral effect are conducive to improve traffic stability and reduce energy consumption.

The research of traffic flow in LaoTieshan channel based on AIS data

In order to study the ship traffic flow in LaoTieshan channel, this paper rewrites the rules of NS (Nagel-Schreckenberg) model of Cellular Automata (CA) based on AIS（Automatic Identification System） data. By referring to the idea of synchronous flow in three-phase traffic flow theory and introducing the speed adaptation mechanism into the simulation, the new model reproduces the traffic flow of LaoTieshan channel and gets the relevant fundamental diagrams. Compared with the actual flow-density diagram drawn from AIS data, it is found that the simulated flow generated by the improved model is more in line with the actual condition, and also conforms to the phase transition of traffic flow in LaoTieshan channel. The method and idea of the simulation are helpful to explain and investigate some complex situations in LaoTieshan channel.

Effect of speed deviation and anticipation effect of flux difference in the lattice hydrodynamic model

To ease traffic pressure and reduce congestion, an extended lattice hydrodynamic model by considering speed deviation and anticipation effect of flux difference is presented. The linear stability condition of this model is derived by control method. The results reveal that these two factors can enhance traffic flow stability. Through nonlinear analysis, the mKdV equation near the critical point is obtained, which describes the phase transition of traffic flow. Numerical simulations are applied to this paper to prove the result of theoretical analysis. Simulation results demonstrate that high estimate of speed and anticipation effect of flux difference play a positive role in relieving traffic jams, and the stability of traffic flow is impeded when the low estimate of speed is added.

A new lattice hydrodynamic model accounting for the traffic interruption probability on a gradient highway

In this paper, a novel lattice hydrodynamic model is presented by accounting for the traffic interruption probability on a gradient highway. The stability condition can be obtained by the use of linear analysis. Linear analysis demonstrates that the traffic interruption probability and the slope will affect the stability region. Through nonlinear analysis, the mKdV equation is derived to describe the phase transition of traffic flow. Furthermore, the numerical simulation is carried out, and the results are consistent with the analytical results. Numerical results demonstrate that the traffic flow can be efficiently improved by accounting for the traffic interruption probability on a gradient highway.

Relative velocity difference model for the car-following theory

To explore and evaluate the impacts of relative velocity difference (RVD) with memory on the dynamic characteristics and fuel economy of traffic flow in the intelligent transportation environment, we first analyze the linkage between RVD with different-step memory and the following car’s behaviors with the measured car-following (CF) data in cities by using the gray correlation analysis method and then present a RVD model based on the previous CF models in the literatures and calibrate it. Finally, we conduct several numerical simulations in the adaptive cruise control (ACC) strategy to explore how RVD with memory affects car’s velocity fluctuation and fuel consumptions, and find that the RVD model can describe the phase transition of traffic flow and estimate the evolution of traffic congestion, and that considering RVD with memory in modeling CF behaviors and designing the advanced ACC strategy can improve the stability and fuel economy of traffic flow.

An extended lattice model accounting for traffic jerk

In this paper, a flux difference lattice hydrodynamics model is extended by considering the traffic jerk effect which comes due to vehicular motion of non-motor automobiles. The effect of traffic jerk has been examined through linear stability analysis and shown that it can significantly enlarge the unstable region on the phase diagram. To describe the phase transition of traffic flow, mKdV equation near the critical point is derived through nonlinear stability analysis. The theoretical findings have been verified using numerical simulation which confirms that the jerk parameter plays an important role in stabilizing the traffic jam efficiently in sensing the flux difference of leading sites.

Stability analysis of a new lattice hydrodynamic model by considering lattice’s self-anticipative density effect

In this paper, a new lattice hydrodynamic model with consideration of the density difference of a lattice’s current density and its anticipative density is proposed. The influence of lattice’s self-anticipative density on traffic stability is revealed through linear stability theory and it shows that lattice’s self-anticipative density can improve the stability of traffic flow. To describe the phase transition of traffic flow, the mKdV equation near the critical point is derived by using nonlinear analysis method. The propagating behavior of density wave in the unstable region can be described by the kink–antikink soliton of the mKdV equation. Numerical simulation validates the analytical results, which shows that traffic jam can be suppressed efficiently by considering lattice’s self-anticipative density in the modified lattice hydrodynamic model.

The effects of velocity difference changes with memory on the dynamics characteristics and fuel economy of traffic flow

Abstract To evaluate the effects of velocity difference changes with memory in the intelligent transportation environment on the dynamics and fuel consumptions of traffic flow, we first investigate the linkage between velocity difference changes with memory and car-following behaviors with the measured data in cities, and then propose an improved cooperative car-following model considering multiple velocity difference changes with memory in the cooperative adaptive cruise control strategy, finally carry out several numerical simulations under the periodic boundary condition and at signalized intersections to explore how velocity difference changes with memory affect car’s velocity, velocity fluctuation, acceleration and fuel consumptions in the intelligent transportation environment. The results show that velocity difference changes with memory have obvious effects on car-following behaviors, that the improved cooperative car-following model can describe the phase transition of traffic flow and estimate the evolution of traffic congestion, that the stability and fuel economy of traffic flow simulated by the improved car-following model with velocity difference changes with memory is obviously superior to those without velocity difference changes, and that taking velocity difference changes with memory into account in designing the advanced adaptive cruise control strategy can significantly improve the stability and fuel economy of traffic flow.

An improved car-following model considering relative velocity fluctuation

To explore and evaluate the impacts of relative velocity fluctuation on the dynamic characteristics and fuel consumptions of traffic flow, we present an improved car-following model considering relative velocity fluctuation based on the full velocity difference model, then we carry out several numerical simulations to determine the optimal time window length and to explore how relative velocity fluctuation affects cars’ velocity and its fluctuation as well as fuel consumptions. It can be found that the improved car-following model can describe the phase transition of traffic flow and estimate the evolution of traffic congestion, and that taking relative velocity fluctuation into account in designing the advanced adaptive cruise control strategy can improve the traffic flow stability and reduce fuel consumptions.

Analysis of a novel two-lane lattice model on a gradient road with the consideration of relative current

In this paper, a novel hydrodynamic lattice model is proposed by considering of relative current for two-lane gradient road system. The stability condition is obtained by using linear stability theory and shown that the stability of traffic flow varies with three parameters, that is, the slope, the sensitivity of response to the relative current and the rate of lane changing. The stable region increases with the increasing of one of them when another two parameters are constant. By using nonlinear analysis, the Burgers, Korteweg–de Vries, and modified Korteweg–de Vries equations are derived to describe the phase transition of traffic flow. Their solutions present the density wave as the triangular shock wave, soliton wave, and kink–antikink wave in the stable, metastable, and unstable region, respectively, which can explain the phase transitions from free traffic to stop-and-go traffic, and finally to congested traffic. To verify the theoretical results, a series of numerical simulations are carried out. The numerical results are consistent with the analytical results. To check the novel model, calibration are taken based on the empirical traffic flow data. The theoretical results and numerical results show that the traffic flow on the gradient road becomes more stable and the traffic congestion can be efficiently suppressed by considering the relative current and lane changing, and the empirical analysis shows that the novel lattice model is reasonable.

Analysis of a modified two-lane lattice model by considering the density difference effect

In this paper, a modified lattice hydrodynamic model of traffic flow is proposed by considering the density difference between leading and following lattice for two-lane system. The effect of density difference on the stability of traffic flow is examined through linear stability analysis and shown that the density difference term can significantly enlarge the stability region on the phase diagram. To describe the phase transition of traffic flow, the Burgers equation and mKdV equation near the critical point are derived through nonlinear analysis. To verify the theoretical findings, numerical simulation is conducted which confirms that traffic jam can be suppressed efficiently by considering the density difference effect in the modified lattice model for two-lane traffic.

Analyses of driver’s anticipation effect in sensing relative flux in a new lattice model for two-lane traffic system

In this paper, a new lattice hydrodynamic traffic flow model is proposed by considering the driver’s anticipation effect in sensing relative flux (DAESRF) for two-lane system. The effect of anticipation parameter on the stability of traffic flow is examined through linear stability analysis and shown that the anticipation term can significantly enlarge the stability region on the phase diagram. To describe the phase transition of traffic flow, mKdV equation near the critical point is derived through nonlinear analysis. The theoretical findings have been verified using numerical simulation which confirms that traffic jam can be suppressed efficiently by considering the anticipation effect in the new lattice model for two-lane traffic.

Full velocity difference and acceleration model for a car-following theory

In order to describe the car-following behavior more actually in real traffic, a full velocity difference and acceleration model (for short, FVDAM) is proposed by synthetically taking into account headway, velocity difference and acceleration of the leading car on the basis of full velocity difference model. The analytical method and numerical simulation results show that the proposed model can describe the phase transition of traffic flow and estimate the evolution of traffic congestion, that incorporating the acceleration of the leading car into car-following model can stabilize traffic flow, suppress the traffic jam and increase capacity, and that the following car in FVDAM can accelerate more quickly than in FVDM.

Properties of Phase Transition of Traffic Flow on Urban Expressway Systems with Ramps and Accessory Roads

In this paper, we develop a cellular automaton model to describe the phase transition of traffic flow on urban expressway systems with on-off-ramps and accessory roads. The lane changing rules are given in detailed, the numerical results show that the main road and the accessory road both produce phase transitions. These phase transitions will often be influenced by the number of lanes, lane changing, the ramp flow, the input flow rate, and the geometry structure.

A NEW LATTICE MODEL OF TRAFFIC FLOW WITH THE CONSIDERATION OF THE HONK EFFECT

In this paper, a new lattice model is presented with the consideration of the honk effect. The stability condition is obtained by the linear stability analysis. The modified Korteweg–de Vries (KdV) equation is derived to describe the phase transition of traffic flow through nonlinear analysis. The space is divided into three regions: the stable region, the metastable region and the unstable region, respectively. And numerical simulation is carried out to validate the analytic results. The results implied that the honk effect could stabilize traffic flow and suppress the traffic jam in lattice model of traffic flow.

Analysis of Phase Transition in Traffic Flow based on a New Model of Driving Decision

Different driving decisions will cause different processes of phase transition in traffic flow. To reveal the inner mechanism, this paper built a new cellular automaton (CA) model, based on the driving decision (DD). In the DD model, a driver's decision is divided into three stages: decision-making, action, and result. The acceleration is taken as a decision variable and three core factors, i.e. distance between adjacent vehicles, their own velocity, and the preceding vehicle's velocity, are considered. Simulation results show that the DD model can simulate the synchronized flow effectively and describe the phase transition in traffic flow well. Further analyses illustrate that various density will cause the phase transition and the random probability will impact the process. Compared with the traditional NaSch model, the DD model considered the preceding vehicle's velocity, the deceleration limitation, and a safe distance, so it can depict closer to the driver preferences on pursuing safety, stability and fuel-saving and has strong theoretical innovation for future studies.

Non-lane-based lattice hydrodynamic model of traffic flow considering the lateral effects of the lane width

A new non-lane-based lattice model is proposed by incorporating the lateral separation effects of the lane width in traffic flow. The stability condition of the extended model is obtained by using the linear stability theory. The modified KdV equation near the critical point is derived to describe the phase transition of traffic flow and to estimate the evolution of traffic congestion through nonlinear analysis. Numerical simulation also shows that the incorporation of the lane width effects in lattice model can stabilize traffic flow and suppress the traffic jam, which implies that the lateral separation effects have important impacts in lattice models.

Non-lane-based full velocity difference car following model

In order to describe car following behavior in real world, this paper presents a non-lane-based car following model by incorporating the effects of the lane width in traffic. The stability condition of the model is obtained by using the linear stability theory. And numerical simulation is carried out to validate the analytic results. The property of the model is investigated, and it is found that the proposed model can describe the phase transition of traffic flow and estimate the evolution of traffic congestion. The results implied that incorporating the lane width effects in car following model not only stabilize traffic flow and suppress the traffic jam, but also lower critical headway and increase capacity. Thus, the lateral separation effects greatly enhance the realism of car following models.