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A new continuum model with consideration of driver’s forecast effect is obtained to study the density wave problem and the stop-and-go phenomena. The stability condition of the new model is derived by using linear analysis. The triangular shock wave, one type of density wave, which is determined by Burgers equation in the stable region, is discussed in great detail with reductive perturbation method. The local cluster appears when we perform the numerical simulations for the new model. It also proves that the driver’s forecast effect has the positive effect of reducing the local cluster.

Traffic jams, the typical signature of the complex behavior of vehicular traffic, have been studied by various traffic models [

Bando et al. [

The pioneer work of continuum traffic flow models is the LWR model [

However, the consistency between microscopic and macroscopic models has been proved [

There are many studies to reveal nonlinear phenomena of vehicular traffic, such as stop-and-go, phase transition, self-organized, and the nonlinear waves. Kurtze and Hong [

In fact, the future traffic situation can be forecasted by the intelligent transportation system (ITS) based on the current traffic status, so the driver may be guided by the forecast information to adjust his/her current acceleration. However, few models consider the drivers forecast effect. Recently, a new car-following model with the driver’s forecast effect is proposed by Tang et al. [

In this paper, a new macroversion is obtained based on the anisotropic continuum model proposed by Tang et al. [

The new car-following model with the consideration of the driver’s forecast effect can be written as follows [

To derive the stability condition, the Burgers equation, and its shock solution of the macroversion of (

The linear stability theory will be applied to derive the linear stability condition of model (

The linear stability condition of (

To investigate the system behavior in the stable region, we consider the long wavelength modes on coarse-grained scales. The reductive perturbation method as in [

If

Temporal evolution of traffic flow before 40 minutes for different

To check the theoretical results, we carry out numerical simulations for model (

(a) if

(b) if

To study the local cluster effect of (

Figures

Temporal evolution of traffic flow before 40 minutes for different

Figure

Figure

Comparing every subfigure of Figures

The above numerical results are not so perfect. The propagation speeds of the perturbation waves we get from our figures are about 40–60 km/h against the traffic direction, which are not very consistent with the ones from the real data. References [

In this paper, a new macroversion is proposed with the consideration of the driver’s forecast effect proposed. The stability condition of the model is derived by using linear analysis. The triangular shock wave which is determined by Burgers equation in the stable region is discussed with reductive perturbation method. The stop-and-go phenomena appear when we carry out the numerical simulation for the model. The driver’s forecast effect which has the positive effect of reducing the local cluster is proved.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work is supported by National Natural Science Foundation of China (Grants nos. 11102155 and 11102165), Natural Science Foundation of Shaanxi Province (2013JQ7014 and 2012JM1001), the new direction of the Young Scholar of Northwestern Polytechnical University, and Foundation for Fundamental Research of Northwestern Polytechnical University (JC20110265).