A macroscopic traffic flow model considering the velocity difference between adjacent vehicles on uphill and downhill slopes

2020 ◽  
Vol 34 (21) ◽  
pp. 2050217
Author(s):  
Peng Zhang ◽  
Yu Xue ◽  
Yi-Cai Zhang ◽  
Xue Wang ◽  
Bing-Lin Cen
Keyword(s):  
Traffic Flow ◽  
Kdv Equation ◽  
Density Wave ◽  
Traffic Model ◽  
Neutral Stability ◽  
Density Waves ◽  
Unstable Region ◽  
Velocity Difference ◽  
Macroscopic Traffic Model ◽  
The Stability

In this paper, we deduced a macroscopic traffic model on the uphill and downhill slopes by employing the transformation relation from microscopic variables to macroscopic ones based on a microscopic car-following model considering the velocity difference between adjacent vehicles. The angle [Formula: see text] of the uphill and downhill and the gravitational force have a great impact upon the stability of traffic flow. The linear stability analysis for macroscopic traffic model yielded the stability condition. The Korteweg–de Vries (KdV) equation is derived by nonlinear analysis and the corresponding solution to the density wave near the neutral stability line is obtained. By using the upwind finite difference scheme for simulation, the spatiotemporal evolution patterns of traffic flow on the uphill and downhill are attained. The unstable region is shrunken with slope of the gradient increasing and backward-traveling density waves gradually decrease and even disappear on uphill. Conversely, the unstable region on downhill is extended and density waves propagate quickly backward to the whole road with slope of the gradient increasing.

DENSITY WAVE IN A NEW ANISOTROPIC CONTINUUM MODEL FOR TRAFFIC FLOW

2009 ◽  
Vol 20 (11) ◽  
pp. 1849-1859 ◽  
Author(s):  
LEI YU ◽  
ZHONG-KE SHI
Keyword(s):  
Traffic Flow ◽  
Continuum Model ◽  
Local Density ◽  
Kdv Equation ◽  
Density Wave ◽  
Flow Speed ◽  
Nonlinear Phenomena ◽  
Neutral Stability ◽  
Local Cluster ◽  
The Stability

In this paper, we apply a new anisotropic continuum model proposed by Gupta and Katiyar (GK model, for short) [J. Phys. A: Math. Gen.38, 4069 (2005)] to study the density wave of traffic flow. The GK model guarantees the characteristic speeds are always less than or equal to the macroscopic flow speed and overcomes the wrong way travel problem which exists in many high-order continuum models. The stability condition of the GK model is obtained. Applying nonlinear analysis to the GK model, we can obtain the soliton, one type of local density wave, which is induced by the density fluctuation in traffic flow. The soliton wave, which is determined near the neutral stability line by the Korteweg-de Vries (KdV) equation, is discussed in great detail. The numerical results show that local cluster effects which are consistent with the diverse nonlinear phenomena observed in realistic traffic flow can be induced from the GK model.

KdV–Berger solution and local cluster effect of two-sided lateral gap continuum traffic flow model

2019 ◽  
Vol 33 (15) ◽  
pp. 1950153 ◽  
Author(s):  
Hari Krishna Gaddam ◽  
Asha Kumari Meena ◽  
K. Ramachandra Rao
Keyword(s):  
Traffic Flow ◽  
Density Wave ◽  
Traveling Wave Solutions ◽  
Neutral Stability ◽  
Local Cluster ◽  
Traffic Jams ◽  
Proposed Model ◽  
The Stability ◽  
Lateral Gaps ◽  
Stability Line

This study proposes a new nonlane-based continuum model derived from a two-sided lateral gap-following theory using the relation between microscopic and macroscopic variables. The model considers the effect of lateral gaps of the leading vehicles available on both sides of the following vehicle in multilane scenario. Linear stability analysis is performed to establish the neutral stability condition for the stable traffic flow. Nonlinear analysis is carried out at neutral stability line to derive the KdV–Berger equation, which describes density wave propagation. For that, one of the traveling wave solutions is also obtained. Numerical simulation results show that the two-sided lateral gap in the model improves the stability of the traffic flow by suppressing the traffic jams even at high-density conditions. The results implies that the proposed model is successful in replicating the properties of actual traffic jams in nonlane-based traffic environment.

An extended lattice model for two-lane traffic flow with consideration of the slope effect

2015 ◽  
Vol 29 (05) ◽  
pp. 1550017 ◽  
Author(s):  
Jianzhong Chen ◽  
Zhiyuan Peng ◽  
Yuan Fang
Keyword(s):  
Traffic Flow ◽  
Lattice Model ◽  
Kdv Equation ◽  
Slope Angle ◽  
Mkdv Equation ◽  
Neutral Stability ◽  
Maximal Velocity ◽  
De Vries ◽  
Stability Method ◽  
The Stability

An extended two-lane lattice model of traffic flow with consideration of the slope effect is proposed. The slope effect is reflected in both the maximal velocity and the relative current. The stability condition of the model is derived by applying the linear stability method. By using the nonlinear analysis method, we obtain the Korteweg–de Vries (KdV) equation near the neutral stability line and the modified Korteweg–de Vries (mKdV) equation near the critical point. The analytical and numerical results demonstrate that the stability of traffic flow is enhanced on the uphill but is weakened on the downhill when the slope angle increases.

A NOVEL LATTICE TRAFFIC FLOW MODEL AND ITS SOLITARY DENSITY WAVES

2012 ◽  
Vol 23 (03) ◽  
pp. 1250025 ◽  
Author(s):  
WEN-XING ZHU ◽  
LI-DONG ZHANG
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Kdv Equation ◽  
Density Wave ◽  
Critical Density ◽  
Average Density ◽  
Linear Stability Theory ◽  
Stable Region ◽  
Neutral Stability ◽  
Traffic Flow Model

A novel lattice traffic flow model with a slope effect is proposed. Neutral stability condition is obtained by the use of the linear stability theory. The standard KdV equation is derived in the meta-stable region and soliton solution is obtained near the neutral stability line. The solitary waves are reproduced through the numerical simulations. Results show that the solitary density wave appears in upward form when the average density is less than critical density, otherwise it exhibits downward form.

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

2011 ◽  
Vol 22 (09) ◽  
pp. 967-976 ◽  
Author(s):  
GUANGHAN PENG ◽  
XINHUA CAI ◽  
CHANGQING LIU ◽  
BINFANG CAO
Keyword(s):  
Phase Transition ◽  
Traffic Flow ◽  
Lattice Model ◽  
Kdv Equation ◽  
Stable Region ◽  
Unstable Region ◽  
Traffic Jam ◽  
Flow Through ◽  
The Stability ◽  
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.

A two-lane lattice model considering taillight effect and man–machine hybrid driving

2020 ◽  
Vol 34 (32) ◽  
pp. 2050365
Author(s):  
Siyuan Chen ◽  
Changxi Ma ◽  
Jinchou Gong
Keyword(s):  
Traffic Flow ◽  
Lattice Model ◽  
Critical Density ◽  
Mkdv Equation ◽  
Flow Stability ◽  
Stability Conditions ◽  
Neutral Stability ◽  
Nonlinear Stability Analysis ◽  
Traffic Flow Stability ◽  
The Stability

At present, drivers can rely on road communication technology to obtain the current traffic status information, and the development of intelligent transportation makes self-driving possible. In this paper, considering the mixed traffic flow with self-driving vehicles and the taillight effect, a new macro-two-lane lattice model is established. Combined with the concept of critical density, the judgment conditions for vehicles to take braking measures are given. Based on the linear analysis, the stability conditions of the new model are obtained, and the mKdV equation describing the evolution mechanism of density waves is derived through the nonlinear stability analysis. Finally, with the help of numerical simulation, the phase diagram and kink–anti-kink waveform of neutral stability conditions are obtained, and the effects of different parameters of the model on traffic flow stability are analyzed. The results show that the braking probability, the proportion of self-driving vehicles and the critical density have significant effects on the traffic flow stability. Considering taillight effect and increasing the mixing ratio of self-driving vehicles can effectively enhance the stability of traffic flow, but a larger critical density will destroy the stability of traffic flow.

scholarly journals A Macroscopic Traffic Model based on Driver Reaction and Traffic Stimuli

2019 ◽  
Vol 9 (14) ◽  
pp. 2848 ◽  
Author(s):  
Zawar H. Khan ◽  
Waheed Imran ◽  
Sajid Azeem ◽  
Khurram S. Khattak ◽  
T. Aaron Gulliver ◽  
...  
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Traffic Model ◽  
Traffic Flow Model ◽  
Velocity Constant ◽  
Model Based ◽  
Proposed Model ◽  
Macroscopic Traffic Flow ◽  
Macroscopic Traffic Model ◽  
Traffic Behavior

A new macroscopic traffic flow model is proposed, which considers driver presumption based on driver reaction and traffic stimuli. The Payne–Whitham (PW) model characterizes the traffic flow based on a velocity constant C 0 which results in unrealistic density and velocity behavior. Conversely, the proposed model characterizes traffic behavior with velocities based on the distance headway. The performance of the proposed and PW models is evaluated over a 300 m circular road for an inactive bottleneck. The results obtained show that the traffic behavior with the proposed model is more realistic.

Theoretical analysis of a hybrid traffic model accounting for safe velocity

2017 ◽  
Vol 31 (11) ◽  
pp. 1750104 ◽  
Author(s):  
Yu-Qing Wang ◽  
Chao-Fan Zhou ◽  
Bo-Wen Yan ◽  
De-Chen Zhang ◽  
Ji-Xin Wang ◽  
...  
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Local Equilibrium ◽  
Density Wave ◽  
Traffic Model ◽  
Safe Driving ◽  
Traffic Flow Model ◽  
Velocity Wave ◽  
Vehicle Velocity ◽  
Global Equilibrium

A hybrid traffic-flow model [Wang–Zhou–Yan (WZY) model] is brought out in this paper. In WZY model, the global equilibrium velocity is replaced by the local equilibrium one, which emphasizes that the modification of vehicle velocity is based on the view of safe-driving rather than the global deployment. In the view of safe-driving, the effect of drivers’ estimation is taken into account. Moreover, the linear stability of the traffic model has been performed. Furthermore, in order to test the robustness of the system, the evolvement of the density wave and the velocity wave of the traffic flow has been numerically calculated.

scholarly journals A Modified Car-following Model Considering Traffic Density and Acceleration of Leading Vehicle

2020 ◽  
Vol 10 (4) ◽  
pp. 1268
Author(s):  
Xudong Cao ◽  
Jianjun Wang ◽  
Chenchen Chen
Keyword(s):  
Traffic Flow ◽  
Linear Stability Theory ◽  
Traffic Density ◽  
Neutral Stability ◽  
Difference Model ◽  
Velocity Difference ◽  
Car Following ◽  
Car Following Model ◽  
The Difference ◽  
Improved Model

Although the difference between the velocity of two successive vehicles is considered in the full velocity difference model (FVDM), more status information from preceding vehicles affecting the behavior of car-following has not been effectively utilized. For improving the performance of the FVDM, an extended modified car-following model taking into account traffic density and the acceleration of a leading vehicle (DAVD, density and acceleration velocity difference model) is presented under the condition of vehicle-to-vehicle (V2V) communications. Stability in the developed model is derived through applying linear stability theory. The curves of neutral stability for the improved model indicate that when the driver pays more attention to the traffic status in front, the traffic flow stability region is larger. Numerical simulation illustrates that traffic flow disturbance could be suppressed by gaining more information on preceding vehicles.

Sign in / Sign up

Export Citation Format

Share Document