In the 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 the fundamental road patterns 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 a 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 are deduced via linear and nonlinear stability analysis, respectively. Solving the above KdV-Burger equation yields the density wave solution, which explores the formation and propagation property of traffic jams near the neutral stability curve. Simulation examples verify that the model can reproduce complex phenomena, such as shock waves and rarefaction waves. The analysis of the local cluster effect shows that the number of vehicles ahead and the radius information, and the slope information of gyroidal roads can exert a great influence on traffic jams. The effect of the first and second terms are positive, while the last term is negative.
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