The goal of this paper is to provide insight about the effect of acceleration saturation in the car-following model. In this contribution, we consider a heterogeneous, mixed-traffic scenario which contains both human-driven and autonomous vehicles subjected to time delays. Corresponding stability charts are provided from which one can tune the control parameters of the automated vehicles to achieve smooth traffic flow. By taking into account the acceleration saturation, it modifies the global behaviour of the system and reduces the range of the optimal technological parameters. On a demonstrative example, we highlight the complex dynamical phenomenon induced by the saturation and we attempt to connect these nonlinear investigations to the engineering practice and point out their relevance.