Narrow Results

This research proposes a modified Crank–Nicolson finite difference scheme with local fractional derivatives to approximate the solutions of local fractional LWR traffic flow model. The stability and consistency of the scheme are examined. Further, convergence of the scheme is assured by using Lax’s equivalence theorem. Some exemplary instances are discussed along with their simulations to validate the proposed method. The obtained numerical solutions show the dynamical evolution of traffic density with respect to time and space. The results derived using the proposed numerical scheme establish that they are quite effective in obtaining the numerical solution to the fractal vehicular traffic flow problem.

Recently, we have proposed a Euler–Lagrange transformation for cellular automata (CA) by developing new transformation formulas. Applying this method to the Burgers CA (BCA), we have succeeded in obtaining the Lagrange representation of the BCA. In this paper, we apply this method to multi-value generalized Burgers CA (GBCA) which include the Fukui–Ishibashi model and the quick-start model associated with traffic flow. As a result, we have succeeded in clarifying the Euler–Lagrange correspondence of these models. It turns out moreover that the GBCA can naturally be considered as a simple model of a multi-lane traffic flow.

Intersections without signal control widely exist in urban road networks. This paper studied the traffic flow in a noncontrolled intersection within an iterated game framework. We assume drivers have learning ability and can repetitively adjust their strategies (to give way or to rush through) in the intersection according to memories. A cellular automata model is applied to investigate the characteristics of the traffic flow. Numerical experiments indicate two main findings. First, the traffic flow experiences a "volcano-shaped" fundamental diagram with three different phases. Second, most drivers choose to give way in the intersection, but the aggressive drivers cannot be completely eliminated, which is coincident with field observations. Analysis are also given out to explain the observed phenomena. These findings allow deeper insight of the real-world bottleneck traffic flow.

A modified cellular automata traffic model is proposed to simulate four-lane traffic flow, in which drivers are classified into aggressive drivers and cautious drivers and the anticipative velocity of the adjacent vehicles is considered. Analysis from the vehicles’ evolution pattern indicates that vehicles driven by the aggressive drivers are more powerful in behaviors of lane-changing and car-following. The model is refined by using the small cell of one meter long in order to simulate the traffic flow meticulously and realistically. The results indicate that the lane-changing maneuver exhibits different property as the density varies, and it does have a significant impact on the characteristics of the surrounding traffic flow due to their interfering effects on the following vehicles. Furthermore, the phenomenon of high-speed car-following is exhibited, and the results coincide with the empirical data very well. It is shown that the proposed model is reasonable and can partially reflect the real traffic.

Traffic flow models are important tools for traffic management applications such as traffic incident detection and traffic control. In this paper, we propose a novel numerical approximation method for second-order macroscopic traffic flow models. The method is based on the semi-discrete central-upwind numerical flux and high-order reconstructions for spatial discretizations. We then apply the designed high-resolution schemes to three representative types of second-order traffic flow models and perform a variety of numerical experiments to validate the proposed methods. The simulation results illustrate the effectiveness, simplicity and universality of the central-upwind scheme as numerical approximation method for macroscopic traffic flow models.

In this paper, a modified microscopic traffic flow model accounting for the optimal velocity has been proposed. Different with previous models, drivers’ response ability and the maximum of accelerations are considered in the term of the optimal velocity. The effect of parameters in the term of the optimal velocity on bifurcations in the rotary traffic is studied here. Besides, the evolvement of bifurcations in the system is calculated by performing numerical simulation experiments. Moreover, the linear stability analysis of the proposed model is presented.

In this work, a heterogeneous traffic flow model coupled with the periodic boundary condition is proposed. Based on the previous models, a heterogeneous system composed of more than one kind of vehicles is considered. By bifurcation analysis, bifurcation patterns of the heterogeneous system are discussed in three situations in detail and illustrated by diagrams of bifurcation patterns. Besides, the stability analysis of the heterogeneous system is performed to test its anti-interference ability. The relationship between the number of vehicles and the stability is obtained. Furthermore, the attractor analysis is applied to investigate the nature of the heterogeneous system near its steady-state neighborhood. Phase diagrams of the process of the heterogeneous system from initial state to equilibrium state are intuitively presented.

In this paper, the nonlinear analysis of a viscous continuum traffic flow model is studied. The stability condition of the viscous continuum model is given by using the linear analysis method. The Korteweg–de Vries (KdV) equation is derived to describe the traffic jams. The effect of the viscous term is investigated by numerical simulations. The results show that the existence of the viscous term induces oscillation of traffic flow and the amplitude of the oscillation increases with increasing the coefficient of the viscous term. It is also found that the local clusters are compressed by increasing the coefficient of the viscous term.

To describe the dynamics of traffic flow in the urban link accurately, the waves which generate at intersections are adopted as the influencing factors of traffic flow. Based on the urban traffic waves, a wave-oriented variable cell transmission model (WVCTM) is proposed to illustrate the urban traffic flow. In this model, the average density and length are the state variables. The cells are divided by traffic waves. The upstream cell is the influence area of the waves at the upstream intersection, the downstream cell is the influence area of the waves at the downstream intersection, and the rest is the mediate cell. Consistent with the fundamental diagram and the cell division, the traffic states of urban links are divided into six modes. The variation of modes is explained by hybrid automata. Finally, an experiment is designed to verify the feasibility of WVCTM. The data in the experiment come from the actual scene. Compared with the cell transmission model (CTM) and variable-length CTM (VCTM), WVCTM possesses the valuable performance to predict the traffic states. Likewise, it is rational that WVCTM can correctly illustrate the urban traffic flow.

In this study, we developed a microcosmic mobile emissions model based on an intelligent agent model of vehicles. The intelligent agent was first introduced into a micro-traffic flow system. Individual differences in driver behavior were considered, and the theory of probability was applied to reflect the distribution of drivers' stochastic characteristic dispositions. Each vehicle expressed its intelligence through its own character by perceiving the leading vehicle. From an operational perspective, differences in drivers' dispositions were reflected by a weighted coefficient. Finally, a hybrid microcosmic mobile emissions model was proposed. Its coefficients were determined using traffic data and experiments. Because it addresses more aspects of the car-following process, this model is theoretically superior to previous models, as verified by a numerical simulation. The proposed model was applied to a case study of the emissions from ten vehicles in an urban setting. The model effectively estimated mobile emissions rates. The results indicate that the model can reflect individual differences among drivers and demonstrate that reckless drivers generate more emissions.

The well-known Lighthill–Whitham–Richards kinematic traffic flow model for unidirectional flow on a single-lane highway is extended to include both abruptly changing road surface conditions and drivers' reaction time and anticipation length. The result is a strongly degenerate convection–diffusion equation, where the diffusion term, accounting for the drivers' behavior, is effective only where the local car density exceeds a critical value, and the convective flux function depends discontinuously on the location. It is shown that the validity of the proposed traffic model is supported by a recent mathematical well-posedness (existence and uniqueness) theory for quasilinear degenerate parabolic convection–diffusion equations with discontinuous coefficients.^20,22 This theory includes a convergence proof for a monotone finite-difference scheme, which is used herein to simulate the traffic flow model for a variety of situations.