۱- Introduction

۲- The new model

۳- Linear stability analysis

۴- Nonlinear stability analysis

۵- Simulations

۶- Conclusions

References

Abstract

Advanced communications technology enables us to obtain the Headway Variation Tendency (HVT) of the next moment in a car following scenario. To maximize the benefits of the new technology, we developed a new traffic flow model that takes into consideration the effect of HVT. First, linear analysis method is used to derive the linear stability condition, that determines whether the HVT can improve traffic system stability. Then, using the reductive perturbation method, a modified KdV (mKdV) equation is obtained and the kink–antikink solutions are derived. The phase diagram of driver sensitivity against equilibrium headway is also plotted by using the neutral stability line, derived from linear analysis and the coexisting line, derived from nonlinear analysis. This diagram demonstrates that HVT does have the ability to improve the stability of traffic stream. Finally, the effect of HVT is validated through numerical simulations, where it is evident that the information of HVT can smooth the traffic stream and prevent the formation of traffic congestion.

Introduction

The growing traffic jam causes excessive fuel consumption as well as emissions to the urban environment. Such adverse impacts pose a severe threat to the traffic system performance. Various traffic flow models have been developed, to explore the mechanism of traffic jam formation [1–۴۰]. Generally, traffic flow models are divided into macroscopic models based on fluid mechanics, mesoscopic models based on gas dynamics theory and microscopic models based on self-driven particles. The macroscopic models include continuum [1–۵] and lattice hydrodynamic models [6–۱۳]. The mesoscopic models [14], as a bridge between microscopic and macroscopic models, can capture the probabilistic nature of interactions between vehicles and describe the macroscopic characteristics of the traffic system. The microscopic models investigate the movement of the individual vehicle, and mainly include cellular automata [15–۱۹], car-following models [20–۲۸] and application of microscopic models in various scenarios [29–۳۴].