A continuum model considering the uncertain velocity of preceding vehicles on gradient highways

Gradient roads are not uncommon in mountainous areas and freeways. The driving field of vision will be limited under such a complex road environment, which hinders the drivers from accurately perceiving the speed of the preceding vehicle. Accurate modeling of traffic flow in such an environment is therefore paramount to make accurate predictions and to effectively control the system. To this end, we present a modified continuum model accounting for the uncertain velocity of preceding vehicles on gradient highways. We derive the stability criterion and the KdV–Burgers equation of the proposed model via linear and nonlinear stability analysis. The density wave solution obtained by solving the above KdV–Burgers equation can explain the propagation mechanism of traffic jams near the stability curve. Numerical examples reveal that the slope information and uncertainty term exert great influence on traffic jams and energy consumption. Specifically, the effect of the slope information is positive, whereas the effect of the uncertainty term is negative.