We address the conflict resolution problem in air traffic management. It is widely acknowledged that air traffic controllers’ (ATCs) workload is related to the density of flights. ATCs’ main task is to ensure the safety of flights throughout their trips and consists of ensuring the respect of separation standards. Recently, the concept of subliminal control has emerged as a promising conflict resolution technique that could be used to reduce the impact of conflicts on ATCs’ workload. In this research, we present deterministic conflict resolution models adapted to subliminal speed control. The proposed models are formulated as nonlinear optimization problems that seek to minimize indicators related to ATCs’ workload (total conflict duration, total number of conflicts) using only minor speed adjustments. We introduce a linear approximation of the aircraft separation equations to implement the obtained mixed integer programs on a continental size air traffic network. Specifically, we develop a simulation framework aiming at reproducing realistic navigation conditions and evaluate the robustness of our conflict resolution models using a generic uncertainty model. We show that the impact of conflicts on ATCs’ workload can be significantly reduced using only limited resources, i.e., a narrow speed modulation range, even in the presence of perturbations. Further, we demonstrate that a significant share of the potential conflicts can be resolved without inducing important delays to flights. Finally, we report that our model does not require extensive computational resources as most instances can be solved to global optimality in a few seconds