An interaction occurs between two humans when they walk with converging trajectories. They need to adapt their motion in order to avoid and cross one another at respectful distance. This paper presents a model for solving interactions between virtual humans. The proposed model is elaborated from experimental interactions data. We first focus our study on the pair-interaction case. In a second stage, we extend our approach to the multiple interactions case. Our experimental data allow us to state the conditions for interactions to occur between walkers, as well as each one's role during interaction and the strategies walkers set to adapt their motion. The low number of parameters of the proposed model enables its automatic calibration from available experimental data. We validate our approach by comparing simulated trajectories with real ones. We also provide comparison with previous solutions. We finally discuss the ability of our model to be extended to complex situations.