STABILIZATION ANALYSIS OF A MULTIPLE LOOK-AHEAD MODEL WITH DRIVER REACTION DELAYS

2012 ◽  
Vol 23 (06) ◽  
pp. 1250048 ◽  
Author(s):  
JIANZHONG CHEN ◽  
ZHONGKE SHI ◽  
YANMEI HU
Keyword(s):  
Reaction Time ◽  
Time Delay ◽  
Kdv Equation ◽  
Mkdv Equation ◽  
Linear Stability Theory ◽  
Neutral Stability ◽  
Look Ahead ◽  
Unfavorable Effect ◽  
The Stability ◽  
Stability Line

A multiple look-ahead model is extended to take into account the reaction-time delay of drivers. The stability condition of this model is obtained by using the linear stability theory. Through nonlinear analysis, the Korteweg–de Vries (KdV) equation near the neutral stability line and the modified KdV (mKdV) equation near the critical point are derived. Both the analytical and simulation results demonstrate that the stabilization of traffic flow is weakened with increasing the reaction-time delay of drivers, and multiple look-ahead consideration could partially remedy this unfavorable effect.

Nonlinear Analysis of a New Extended Lattice Model With Consideration of Multi-Anticipation and Driver Reaction Delays

2014 ◽  
Vol 9 (3) ◽  
Author(s):  
Jianzhong Chen ◽  
Zhongke Shi ◽  
Lei Yu ◽  
Zhiyuan Peng
Keyword(s):  
Reaction Time ◽  
Time Delay ◽  
Nonlinear Analysis ◽  
Traffic Flow ◽  
Linear Stability ◽  
Lattice Model ◽  
Kdv Equation ◽  
Linear Stability Theory ◽  
Neutral Stability ◽  
De Vries

A new extended lattice model of traffic flow is presented by taking into account both multianticipative behavior and the reaction-time delay of drivers. The linear stability theory and the nonlinear analysis method are applied to the model. The linear stability condition is obtained. The Korteweg–de Vries (KdV) equation near the neutral stability line and the modified Korteweg–de Vries (mKdV) equation near the critical point are derived. The numerical results show that the stability of traffic flow will be enhanced by multianticipative consideration and will be weakened with the increase of the reaction-time delay. The unfavorable effect induced by driver reaction delays can be partly compensated by considering multianticipative behavior.

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 Car-Following Model Considering Effects of Weather and Road Conditions

2014 ◽  
Vol 488-489 ◽  
pp. 1289-1294
Author(s):  
Lu Jing ◽  
Peng Jun Zheng
Keyword(s):  
Vries Equation ◽  
Kdv Equation ◽  
Mkdv Equation ◽  
Reductive Perturbation Method ◽  
Neutral Stability ◽  
Traffic Jam ◽  
Car Following ◽  
The Kdv Equation ◽  
Car Following Model ◽  
The Stability

In this paper, a modified car-following model is proposed, in which, the weather and road conditions are taken into account. The stability condition of the model is obtained by using the control theory method. We investigated the property of the model using linear and nonlinear analyses. The Kortewegde Vries equation near the neutral stability line and the modified Kortewegde Vries equation around the critical point are derived by applying the reductive perturbation method. The traffic jam could be thus described by the KdV soliton and the kinkanti-kink soliton for the KdV equation and mKdV equation, respectively. Numerical simulations are carried out to verify the model, and good results are obtained with the new model.

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.

A new lattice hydrodynamic model for bidirectional pedestrian flow with consideration of pedestrians’ honk effect

2020 ◽  
Vol 31 (02) ◽  
pp. 2050031 ◽  
Author(s):  
Cong Zhai ◽  
Weitiao Wu
Keyword(s):  
Stability Analysis ◽  
Hydrodynamic Model ◽  
Mkdv Equation ◽  
Neutral Stability ◽  
Neutral Stability Curve ◽  
Lattice Hydrodynamic Model ◽  
Pedestrian Flow ◽  
Stability Curve ◽  
The Stability ◽  
Honk Effect

Understanding the pedestrian behavior contributes to traffic simulation and facility design/redesign. In practice, the interactions between individual pedestrians can lead to virtual honk effect, such as urging surrounding pedestrians to walk faster in a crowded environment. To better reflect the reality, this paper proposes a new lattice hydrodynamic model for bidirectional pedestrian flow with consideration of pedestrians’ honk effect. To this end, the concept of critical density is introduced to define the occurrence of pedestrians’ honk event. In the linear stability analysis, the stability condition of the new bidirectional pedestrian flow model is given based on the perturbation method, and the neutral stability curve is also obtained. Based on this, it is found that the honk effect has a significant impact on the stability of pedestrian flow. In the nonlinear stability analysis, the modified Korteweg–de Vries (mKdV) equation of the model is obtained based on the reductive perturbation method. By solving the mKdV equation, the kink-antikink soliton wave is obtained to describe the propagation mechanism and rules of pedestrian congestion near the neutral stability curve. The simulation example shows that the pedestrians’ honk effect can mitigate the pedestrians crowding efficiently and improve the stability of the bidirectional pedestrian flow.

Analysis of drivers' characteristics in car-following theory

2014 ◽  
Vol 28 (24) ◽  
pp. 1450191 ◽  
Author(s):  
Geng Zhang ◽  
Di-Hua Sun ◽  
Hui Liu ◽  
Min Zhao
Keyword(s):  
Numerical Simulation ◽  
Traffic Flow ◽  
Mkdv Equation ◽  
Reductive Perturbation Method ◽  
Linear Stability Theory ◽  
Traffic Density ◽  
Car Following ◽  
Car Following Model ◽  
The Stability ◽  
The Impact

In recent years, the influence of drivers' behaviors on traffic flow has attracted considerable attention according to Transportation Cyber Physical Systems. In this paper, an extended car-following model is presented by considering drivers' timid or aggressive characteristics. The impact of drivers' timid or aggressive characteristics on the stability of traffic flow has been analyzed through linear stability theory and nonlinear reductive perturbation method. Numerical simulation shows that the propagating behavior of traffic density waves near the critical point can be described by the kink–antikink soliton of the mKdV equation. The good agreement between the numerical simulation and the analytical results shows that drivers' characteristics play an important role in traffic jamming transition.

A novel lattice traffic flow model on a curved road

2015 ◽  
Vol 26 (11) ◽  
pp. 1550121 ◽  
Author(s):  
Jin-Liang Cao ◽  
Zhon-Ke Shi
Keyword(s):  
Friction Coefficient ◽  
Traffic Flow ◽  
Flow Model ◽  
Mkdv Equation ◽  
Linear Stability Theory ◽  
Stable Region ◽  
Traffic Flow Model ◽  
De Vries ◽  
Curved Road ◽  
The Stability

Due to the existence of curved roads in real traffic situation, a novel lattice traffic flow model on a curved road is proposed by taking the effect of friction coefficient and radius into account. The stability condition is obtained by using linear stability theory. The result shows that the traffic flow becomes stable with the decrease of friction coefficient and radius of the curved road. Using nonlinear analysis method, the Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equation are derived to describe soliton waves and the kink–antikink waves in the meta-stable region and unstable region, respectively. Numerical simulations are carried out and the results are consistent with the theoretical results.

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.

scholarly journals On the stability of waves in classically neutral flows

2020 ◽  
Vol 85 (2) ◽  
pp. 309-340
Author(s):  
Colin Huber ◽  
Meaghan Hoitt ◽  
Nathaniel S Barlow ◽  
Nicole Hill ◽  
Kimberlee Keithley ◽  
...  
Keyword(s):  
Stability Boundary ◽  
Fractional Power ◽  
Single Mode ◽  
Fourier Integral ◽  
Linear Stability Theory ◽  
System Response ◽  
Neutral Stability ◽  
Complex Frequency ◽  
The Stability ◽  
Dispersive Flows

Abstract This paper reports a breakdown in linear stability theory under conditions of neutral stability that is deduced by an examination of exponential modes of the form $h\approx{{e}^{i(kx-\omega t)}}$, where $h$ is a response to a disturbance, $k$ is a real wavenumber and $\omega (k)$ is a wavelength-dependent complex frequency. In a previous paper, King et al. (2016, Stability of algebraically unstable dispersive flows. Phys. Rev. Fluids, 1, 073604) demonstrates that when Im$[\omega (k)]=0$ for all $k$, it is possible for a system response to grow or damp algebraically as $h\approx{{t}^{s}}$ where $s$ is a fractional power. The growth is deduced through an asymptotic analysis of the Fourier integral that inherently invokes the superposition of an infinite number of modes. In this paper, the more typical case associated with the transition from stability to instability is examined in which Im$[\omega (k)]=0$ for a single mode (i.e. for one value of $k$) at neutral stability. Two partial differential equation systems are examined, one that has been constructed to elucidate key features of the stability threshold, and a second that models the well-studied problem of rectilinear Newtonian flow down an inclined plane. In both cases, algebraic growth/decay is deduced at the neutral stability boundary, and the propagation features of the responses are examined.

scholarly journals The Car Following Model with Relative Speed in Front on the Three-Lane Road

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Zichu Gao ◽  
Ning Zhang ◽  
Livia Mannini ◽  
Ernesto Cipriani
Keyword(s):  
Traffic Flow ◽  
Traffic Safety ◽  
Traffic Management ◽  
Real Life ◽  
Mkdv Equation ◽  
Linear Stability Theory ◽  
Neutral Stability ◽  
Nonlinear Stability Analysis ◽  
Car Following ◽  
Car Following Model

An improved car following model on one road with three lanes is presented in this paper, which considers the relative velocity in front on the main lane and the left and the right adjacent lanes. The stability criterion and neutral stability curve are obtained by linear stability theory. The nonlinear stability analysis is investigated further to get the solution of the modified Korteweg-de Vries (mKdV) equation and get the three areas of stability, metastability, and unstability. The new LRVD model (left and right lane velocity difference model) with bigger stable area can stabilize middle lane traffic flow better, which is proved by the linear theory, nonlinear theory, and the simulation. The LRVD model shows if drivers on the middle lane pay more attention to more cars in front on the two side lanes on the three-lane road, the middle lane traffic flow is certain to be more stable in real life. On the complex three-lane road, if intelligent traffic management system based on the huge traffic data for drivers is applied in real life, it is very helpful to ensure traffic safety, which is also the trend of transportation development in future.

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