Real-world traffic systems are inherently uncertain, influenced by factors such as driver behavior, environmental conditions, and infrastructure variability. To accurately capture these complexities, we focus on non-intrusive uncertainty quantification techniques within the framework of kinetic traffic flow models. In this talk, we employ a Monte Carlo approach both in the physical space, solving the kinetic equation, and in the stochastic space, to investigate the propagation of uncertainty. One of the main challenges of this approach is the high-dimensional nature of the problem, which leads to significant computational costs. To address this, we investigate control variate strategies, specifically multi-level and multi-fidelity Monte Carlo methods, which proved to be particularly effective. These techniques exploit a hierarchy of models, where high-fidelity simulations provide accurate but computationally demanding solutions, while low-fidelity approximations offer computational efficiency at the cost of reduced precision. Combining these models, we achieve a significant reduction in computational cost while maintaining high accuracy. Numerical simulations show that the multi-fidelity approach offers significant improvements over standard Monte Carlo methods, in both accuracy and efficiency.