Modeling Continuous Traffic Flow with the Average Velocity Effect of Multiple Vehicles Ahead on Gyroidal Roads

In future connected vehicle environment, the information of multiple vehicles ahead can be readily collected in real-time, such as the velocity or headway, which provides more opportunities for information exchange and cooperative control. Meanwhile, gyroidal roads are one of fundamental road patterns and prevalent in mountainous areas. To effectively control the system, it is therefore significant to explore the evolution mechanism of traffic flow on gyroidal roads under connected vehicle environment. In this paper, we present a new continuum model with the average velocity of multiple vehicles ahead on gyroidal roads. The stability criterion and KdV-Burger equation corresponding to the continuum model are deduced via the small perturbation method in the linear and nonlinear stability analysis, respectively. Solving the above KdV-Burger equation yields the density wave solution, which can be used to explore the formation and propagation property of traffic jams near the neutral stability curve. Results reveal that proposed continuum model can reproduce the complex phenomena, including shock waves, rarefaction wave and local clustering effects in real traffic scenarios. We also show that the number of considered vehicles ahead, the radius information, and the slope information of gyroidal roads can exert great influence on traffic jams; the effect of first and second terms are positive, while the last term is negative